Cortex.Wire.AdmissionArtifact.ValidatorCoreCheck

On this page
  1. Overview
  2. Decidable Validity Leaves
  3. Boundary Checks
  4. Primitive Row Checks
  5. Validator-Ready Core
  6. Primitive Prefix Checks
  7. Generated-Form Row Checks
  8. Phantom Adapter Row Checks
  9. Select Row Checks
  10. Component Frontier Cross-Reference Checks
  11. Phantom Bridge Cross-Reference Checks
Imports
import Cortex.Wire.AdmissionArtifact.Check import Cortex.Wire.AdmissionArtifact.PrimitiveTraceCheck import Cortex.Wire.AdmissionArtifact.Sound

Overview

Executable core checks for decoded Wire admission artifacts.

This module is the Lean-owned executable validator for decoded artifact rows. The historical ValidatorReadyCore name remains as the checker-record layer, but it now covers every field of ValidatorReady: schema and summary invariants, component-domain and frontier cross-references, local generated/select/phantom row validity, component-row uniqueness, primitive row validity, and executable primitive stack replay.

Each checker has a theorem of the form check = true → predicate, so this file tests whether replacing mirrored Haskell validator clauses with Lean-owned executable checks scales locally.

namespace Cortex.Wirenamespace AdmissionArtifactopen Cortex.Wire.ElaborationIR

Decidable Validity Leaves

namespace AdmissionPortLabelinstance validDecidable (label : AdmissionPortLabel) : Decidable label.Valid := label:AdmissionPortLabel⊢ Decidable label.Valid cases label with ⊢ Decidable noLabel.Valid All goals completed! 🐙 portLabel:FieldLabel⊢ Decidable (label portLabel).Valid portLabel:FieldLabel⊢ Decidable (match label portLabel with | noLabel => True | label portLabel => portLabel.Valid) All goals completed! 🐙end AdmissionPortLabelnamespace AdmissionBoundaryPortinstance validDecidable (boundary : AdmissionBoundaryPort) : Decidable boundary.Valid := boundary:AdmissionBoundaryPort⊢ Decidable boundary.Valid cases boundary with node:NodeIdport:FieldLabelcontract:ContractIdlabel:AdmissionPortLabelexclusiveGroup:Option (NodeId × ℕ)⊢ Decidable { node := node, port := port, contract := contract, label := label, exclusiveGroup := exclusiveGroup }.Valid cases label with node:NodeIdport:FieldLabelcontract:ContractIdexclusiveGroup:Option (NodeId × ℕ)⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := exclusiveGroup }.Valid cases exclusiveGroup with node:NodeIdport:FieldLabelcontract:ContractId⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.Valid node:NodeIdport:FieldLabelcontract:ContractId⊢ Decidable ({ node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.node.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.port.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.contract.Valid ∧ (match { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.label with | AdmissionPortLabel.noLabel => True | AdmissionPortLabel.label portLabel => portLabel.Valid) ∧ match { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.exclusiveGroup with | none => True | some (owner, _index) => owner = { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := none }.node ∧ owner.Valid) All goals completed! 🐙 node:NodeIdport:FieldLabelcontract:ContractIdgroup:NodeId × ℕ⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some group }.Valid node:NodeIdport:FieldLabelcontract:ContractIdfst✝:NodeIdsnd✝:ℕ⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.Valid node:NodeIdport:FieldLabelcontract:ContractIdfst✝:NodeIdsnd✝:ℕ⊢ Decidable ({ node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.node.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.port.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.contract.Valid ∧ (match { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.label with | AdmissionPortLabel.noLabel => True | AdmissionPortLabel.label portLabel => portLabel.Valid) ∧ match { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.exclusiveGroup with | none => True | some (owner, _index) => owner = { node := node, port := port, contract := contract, label := AdmissionPortLabel.noLabel, exclusiveGroup := some (fst✝, snd✝) }.node ∧ owner.Valid) All goals completed! 🐙 node:NodeIdport:FieldLabelcontract:ContractIdexclusiveGroup:Option (NodeId × ℕ)label:FieldLabel⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := exclusiveGroup }.Valid cases exclusiveGroup with node:NodeIdport:FieldLabelcontract:ContractIdlabel:FieldLabel⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.Valid node:NodeIdport:FieldLabelcontract:ContractIdlabel:FieldLabel⊢ Decidable ({ node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.node.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.port.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.contract.Valid ∧ (match { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.label with | AdmissionPortLabel.noLabel => True | AdmissionPortLabel.label portLabel => portLabel.Valid) ∧ match { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.exclusiveGroup with | none => True | some (owner, _index) => owner = { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := none }.node ∧ owner.Valid) All goals completed! 🐙 node:NodeIdport:FieldLabelcontract:ContractIdlabel:FieldLabelgroup:NodeId × ℕ⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some group }.Valid node:NodeIdport:FieldLabelcontract:ContractIdlabel:FieldLabelfst✝:NodeIdsnd✝:ℕ⊢ Decidable { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.Valid node:NodeIdport:FieldLabelcontract:ContractIdlabel:FieldLabelfst✝:NodeIdsnd✝:ℕ⊢ Decidable ({ node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.node.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.port.Valid ∧ { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.contract.Valid ∧ (match { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.label with | AdmissionPortLabel.noLabel => True | AdmissionPortLabel.label portLabel => portLabel.Valid) ∧ match { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.exclusiveGroup with | none => True | some (owner, _index) => owner = { node := node, port := port, contract := contract, label := AdmissionPortLabel.label label, exclusiveGroup := some (fst✝, snd✝) }.node ∧ owner.Valid) All goals completed! 🐙end AdmissionBoundaryPortnamespace AdmissionConnectioninstance validDecidable (connection : AdmissionConnection) : Decidable connection.Valid := connection:AdmissionConnection⊢ Decidable connection.Valid connection:AdmissionConnection⊢ Decidable (connection.fromPort.Valid ∧ connection.toPort.Valid ∧ connection.fromPort.label = connection.toPort.label ∧ connection.fromPort.contract = connection.toPort.contract) All goals completed! 🐙end AdmissionConnectionnamespace AdmissionEndpointRefinstance validDecidable (endpoint : AdmissionEndpointRef) : Decidable endpoint.Valid := endpoint:AdmissionEndpointRef⊢ Decidable endpoint.Valid cases endpoint with node:NodeIdport:Option FieldLabel⊢ Decidable { node := node, port := port }.Valid cases port with node:NodeId⊢ Decidable { node := node, port := none }.Valid node:NodeId⊢ Decidable ({ node := node, port := none }.node.Valid ∧ match { node := node, port := none }.port with | none => True | some port => port.Valid) All goals completed! 🐙 node:NodeIdport:FieldLabel⊢ Decidable { node := node, port := some port }.Valid node:NodeIdport:FieldLabel⊢ Decidable ({ node := node, port := some port }.node.Valid ∧ match { node := node, port := some port }.port with | none => True | some port => port.Valid) All goals completed! 🐙end AdmissionEndpointRefnamespace AdmissionRawConnectioninstance validDecidable (connection : AdmissionRawConnection) : Decidable connection.Valid := connection:AdmissionRawConnection⊢ Decidable connection.Valid connection:AdmissionRawConnection⊢ Decidable (connection.fromEndpoint.Valid ∧ connection.toEndpoint.Valid) All goals completed! 🐙end AdmissionRawConnection

Boundary Checks

namespace AdmissionArtifactCheck

Every boundary port in a decoded list is structurally valid.

def boundaryPortsValidCheck (ports : List AdmissionBoundaryPort) : Bool := Check.allDecide ports AdmissionBoundaryPort.Valid

Successful boundary-port validity checking proves the relational list predicate.

theorem boundaryPortsValidCheck_sound {ports : List AdmissionBoundaryPort} (hCheck : boundaryPortsValidCheck ports = true) : BoundaryPortsValid ports := Check.allDecide_sound hCheck

Every boundary contraction in a decoded list is structurally valid.

def connectionsValidCheck (connections : List AdmissionConnection) : Bool := Check.allDecide connections AdmissionConnection.Valid

Successful connection-row validity checking proves the relational list predicate.

theorem connectionsValidCheck_sound {connections : List AdmissionConnection} (hCheck : connectionsValidCheck connections = true) : ConnectionsValid connections := Check.allDecide_sound hCheckend AdmissionArtifactCheck

Primitive Row Checks

namespace PrimitiveGraphStep

Primitive node frontiers are owned by the node row that serializes them.

def nodeFrontiersOwnedCheck (nodeId : NodeId) (entries exits : List AdmissionBoundaryPort) : Bool := Check.allDecide entries (fun entry => entry.node = nodeId) && Check.allDecide exits (fun exit => exit.node = nodeId)

Successful ownership checking proves NodeFrontiersOwned.

theorem nodeFrontiersOwnedCheck_sound {nodeId : NodeId} {entries exits : List AdmissionBoundaryPort} (hCheck : nodeFrontiersOwnedCheck nodeId entries exits = true) : NodeFrontiersOwned nodeId entries exits := nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:nodeFrontiersOwnedCheck nodeId entries exits = true⊢ NodeFrontiersOwned nodeId entries exits nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:((Check.allDecide entries fun entry => entry.node = nodeId) && Check.allDecide exits fun exit => exit.node = nodeId) = true⊢ NodeFrontiersOwned nodeId entries exits nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(Check.allDecide entries fun entry => entry.node = nodeId) = true ∧ (Check.allDecide exits fun exit => exit.node = nodeId) = true⊢ NodeFrontiersOwned nodeId entries exits All goals completed! 🐙

Primitive node frontier keys are duplicate-free per direction.

def nodeFrontiersLinearCheck (entries exits : List AdmissionBoundaryPort) : Bool := Check.nodupMapCheck entries AdmissionBoundaryPort.key && Check.nodupMapCheck exits AdmissionBoundaryPort.key

Successful frontier-linearity checking proves NodeFrontiersLinear.

theorem nodeFrontiersLinearCheck_sound {entries exits : List AdmissionBoundaryPort} (hCheck : nodeFrontiersLinearCheck entries exits = true) : NodeFrontiersLinear entries exits := entries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:nodeFrontiersLinearCheck entries exits = true⊢ NodeFrontiersLinear entries exits entries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(Check.nodupMapCheck entries AdmissionBoundaryPort.key && Check.nodupMapCheck exits AdmissionBoundaryPort.key) = true⊢ NodeFrontiersLinear entries exits entries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:Check.nodupMapCheck entries AdmissionBoundaryPort.key = true ∧ Check.nodupMapCheck exits AdmissionBoundaryPort.key = true⊢ NodeFrontiersLinear entries exits All goals completed! 🐙

Executable checker for primitive node-row validity.

def nodeValidCheck (nodeId : NodeId) (entries exits : List AdmissionBoundaryPort) : Bool := decide nodeId.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck entries && AdmissionArtifactCheck.boundaryPortsValidCheck exits && nodeFrontiersOwnedCheck nodeId entries exits && nodeFrontiersLinearCheck entries exits

Successful primitive node-row checking proves NodeValid.

theorem nodeValidCheck_sound {nodeId : NodeId} {entries exits : List AdmissionBoundaryPort} (hCheck : nodeValidCheck nodeId entries exits = true) : NodeValid nodeId entries exits := nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:nodeValidCheck nodeId entries exits = true⊢ NodeValid nodeId entries exits nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(decide nodeId.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck entries && AdmissionArtifactCheck.boundaryPortsValidCheck exits && nodeFrontiersOwnedCheck nodeId entries exits && nodeFrontiersLinearCheck entries exits) = true⊢ NodeValid nodeId entries exits nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(((decide nodeId.Valid = true ∧ AdmissionArtifactCheck.boundaryPortsValidCheck entries = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck exits = true) ∧ nodeFrontiersOwnedCheck nodeId entries exits = true) ∧ nodeFrontiersLinearCheck entries exits = true⊢ NodeValid nodeId entries exits nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthLinear:nodeFrontiersLinearCheck entries exits = truehOwned:nodeFrontiersOwnedCheck nodeId entries exits = truehExits:AdmissionArtifactCheck.boundaryPortsValidCheck exits = truehNode:decide nodeId.Valid = truehEntries:AdmissionArtifactCheck.boundaryPortsValidCheck entries = true⊢ NodeValid nodeId entries exits All goals completed! 🐙

Primitive overlay side ledgers are duplicate-free before merge.

def overlayLedgersUniqueCheck (leftNodeIds rightNodeIds : List NodeId) (leftBindings rightBindings : List BindingName) : Bool := Check.nodupCheck leftNodeIds && Check.nodupCheck rightNodeIds && Check.nodupCheck leftBindings && Check.nodupCheck rightBindings

Successful overlay-uniqueness checking proves OverlayLedgersUnique.

theorem overlayLedgersUniqueCheck_sound {leftNodeIds rightNodeIds : List NodeId} {leftBindings rightBindings : List BindingName} (hCheck : overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings = true) : OverlayLedgersUnique leftNodeIds rightNodeIds leftBindings rightBindings := leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings = true⊢ OverlayLedgersUnique leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.nodupCheck leftNodeIds && Check.nodupCheck rightNodeIds && Check.nodupCheck leftBindings && Check.nodupCheck rightBindings) = true⊢ OverlayLedgersUnique leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:((Check.nodupCheck leftNodeIds = true ∧ Check.nodupCheck rightNodeIds = true) ∧ Check.nodupCheck leftBindings = true) ∧ Check.nodupCheck rightBindings = true⊢ OverlayLedgersUnique leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehRightBindings:Check.nodupCheck rightBindings = truehLeftBindings:Check.nodupCheck leftBindings = truehLeftNodes:Check.nodupCheck leftNodeIds = truehRightNodes:Check.nodupCheck rightNodeIds = true⊢ OverlayLedgersUnique leftNodeIds rightNodeIds leftBindings rightBindings All goals completed! 🐙

Primitive overlay side ledgers are disjoint before merge.

def overlayLedgersDisjointCheck (leftNodeIds rightNodeIds : List NodeId) (leftBindings rightBindings : List BindingName) : Bool := Check.allDecide leftNodeIds (fun node => node ∉ rightNodeIds) && Check.allDecide leftBindings (fun binding => binding ∉ rightBindings)

Successful overlay-disjointness checking proves OverlayLedgersDisjoint.

theorem overlayLedgersDisjointCheck_sound {leftNodeIds rightNodeIds : List NodeId} {leftBindings rightBindings : List BindingName} (hCheck : overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings = true) : OverlayLedgersDisjoint leftNodeIds rightNodeIds leftBindings rightBindings := leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings = true⊢ OverlayLedgersDisjoint leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:((Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) && Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ OverlayLedgersDisjoint leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ OverlayLedgersDisjoint leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ ∀ node ∈ leftNodeIds, node ∈ rightNodeIds → FalseleftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ ∀ binding ∈ leftBindings, binding ∈ rightBindings → False leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ ∀ node ∈ leftNodeIds, node ∈ rightNodeIds → False intro node leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = truenode:NodeIdhLeft:node ∈ leftNodeIds⊢ node ∈ rightNodeIds → False leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = truenode:NodeIdhLeft:node ∈ leftNodeIdshRight:node ∈ rightNodeIds⊢ False All goals completed! 🐙 leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = true⊢ ∀ binding ∈ leftBindings, binding ∈ rightBindings → False intro binding leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = truebinding:BindingNamehLeft:binding ∈ leftBindings⊢ binding ∈ rightBindings → False leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds fun node => node ∉ rightNodeIds) = true ∧ (Check.allDecide leftBindings fun binding => binding ∉ rightBindings) = truebinding:BindingNamehLeft:binding ∈ leftBindingshRight:binding ∈ rightBindings⊢ False All goals completed! 🐙

Executable checker for primitive overlay-row validity.

def overlayValidCheck (leftNodeIds rightNodeIds : List NodeId) (leftBindings rightBindings : List BindingName) : Bool := Check.allDecide leftNodeIds NodeId.Valid && Check.allDecide rightNodeIds NodeId.Valid && Check.allDecide leftBindings BindingName.Valid && Check.allDecide rightBindings BindingName.Valid && overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings && overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings

Successful primitive overlay-row checking proves OverlayValid.

theorem overlayValidCheck_sound {leftNodeIds rightNodeIds : List NodeId} {leftBindings rightBindings : List BindingName} (hCheck : overlayValidCheck leftNodeIds rightNodeIds leftBindings rightBindings = true) : OverlayValid leftNodeIds rightNodeIds leftBindings rightBindings := leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:overlayValidCheck leftNodeIds rightNodeIds leftBindings rightBindings = true⊢ OverlayValid leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide leftNodeIds NodeId.Valid && Check.allDecide rightNodeIds NodeId.Valid && Check.allDecide leftBindings BindingName.Valid && Check.allDecide rightBindings BindingName.Valid && overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings && overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings) = true⊢ OverlayValid leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:((((Check.allDecide leftNodeIds NodeId.Valid = true ∧ Check.allDecide rightNodeIds NodeId.Valid = true) ∧ Check.allDecide leftBindings BindingName.Valid = true) ∧ Check.allDecide rightBindings BindingName.Valid = true) ∧ overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings = true) ∧ overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings = true⊢ OverlayValid leftNodeIds rightNodeIds leftBindings rightBindings leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehDisjoint:overlayLedgersDisjointCheck leftNodeIds rightNodeIds leftBindings rightBindings = truehUnique:overlayLedgersUniqueCheck leftNodeIds rightNodeIds leftBindings rightBindings = truehRightBindings:Check.allDecide rightBindings BindingName.Valid = truehLeftBindings:Check.allDecide leftBindings BindingName.Valid = truehLeftNodes:Check.allDecide leftNodeIds NodeId.Valid = truehRightNodes:Check.allDecide rightNodeIds NodeId.Valid = true⊢ OverlayValid leftNodeIds rightNodeIds leftBindings rightBindings All goals completed! 🐙

Matched primitive connect pairs do not reuse outputs or inputs.

def connectPairsLinearCheck (matchedPairs : List AdmissionConnection) : Bool := Check.nodupMapCheck matchedPairs AdmissionConnection.fromKey && Check.nodupMapCheck matchedPairs AdmissionConnection.toKey

Successful connect-pair linearity checking proves ConnectPairsLinear.

theorem connectPairsLinearCheck_sound {matchedPairs : List AdmissionConnection} (hCheck : connectPairsLinearCheck matchedPairs = true) : ConnectPairsLinear matchedPairs := matchedPairs:List AdmissionConnectionhCheck:connectPairsLinearCheck matchedPairs = true⊢ ConnectPairsLinear matchedPairs matchedPairs:List AdmissionConnectionhCheck:(Check.nodupMapCheck matchedPairs AdmissionConnection.fromKey && Check.nodupMapCheck matchedPairs AdmissionConnection.toKey) = true⊢ ConnectPairsLinear matchedPairs matchedPairs:List AdmissionConnectionhCheck:Check.nodupMapCheck matchedPairs AdmissionConnection.fromKey = true ∧ Check.nodupMapCheck matchedPairs AdmissionConnection.toKey = true⊢ ConnectPairsLinear matchedPairs All goals completed! 🐙

Serialized primitive connect frontiers are duplicate-free per side.

def connectFrontiersLinearCheck (leftExits rightEntries : List AdmissionBoundaryPort) : Bool := Check.nodupMapCheck leftExits AdmissionBoundaryPort.key && Check.nodupMapCheck rightEntries AdmissionBoundaryPort.key

Successful connect-frontier linearity checking proves ConnectFrontiersLinear.

theorem connectFrontiersLinearCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} (hCheck : connectFrontiersLinearCheck leftExits rightEntries = true) : ConnectFrontiersLinear leftExits rightEntries := leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPorthCheck:connectFrontiersLinearCheck leftExits rightEntries = true⊢ ConnectFrontiersLinear leftExits rightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPorthCheck:(Check.nodupMapCheck leftExits AdmissionBoundaryPort.key && Check.nodupMapCheck rightEntries AdmissionBoundaryPort.key) = true⊢ ConnectFrontiersLinear leftExits rightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPorthCheck:Check.nodupMapCheck leftExits AdmissionBoundaryPort.key = true ∧ Check.nodupMapCheck rightEntries AdmissionBoundaryPort.key = true⊢ ConnectFrontiersLinear leftExits rightEntries All goals completed! 🐙

Matched and residual connect rows partition the serialized frontiers.

def connectFrontierPartitionCheck (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort) : Bool := Check.permCheck ((matchedPairs.map AdmissionConnection.fromKey) ++ (unmatchedLeftExits.map AdmissionBoundaryPort.key)) (leftExits.map AdmissionBoundaryPort.key) && Check.permCheck ((matchedPairs.map AdmissionConnection.toKey) ++ (unmatchedRightEntries.map AdmissionBoundaryPort.key)) (rightEntries.map AdmissionBoundaryPort.key)

Successful partition checking proves ConnectFrontierPartition.

theorem connectFrontierPartitionCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} {matchedPairs : List AdmissionConnection} {unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort} (hCheck : connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true) : ConnectFrontierPartition leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries := leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true⊢ ConnectFrontierPartition leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(Check.permCheck (List.map AdmissionConnection.fromKey matchedPairs ++ List.map AdmissionBoundaryPort.key unmatchedLeftExits) (List.map AdmissionBoundaryPort.key leftExits) && Check.permCheck (List.map AdmissionConnection.toKey matchedPairs ++ List.map AdmissionBoundaryPort.key unmatchedRightEntries) (List.map AdmissionBoundaryPort.key rightEntries)) = true⊢ ConnectFrontierPartition leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:Check.permCheck (List.map AdmissionConnection.fromKey matchedPairs ++ List.map AdmissionBoundaryPort.key unmatchedLeftExits) (List.map AdmissionBoundaryPort.key leftExits) = true ∧ Check.permCheck (List.map AdmissionConnection.toKey matchedPairs ++ List.map AdmissionBoundaryPort.key unmatchedRightEntries) (List.map AdmissionBoundaryPort.key rightEntries) = true⊢ ConnectFrontierPartition leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries All goals completed! 🐙

Matched pairs are drawn from the frontiers serialized in the same connect row.

def connectPairsDrawnFromFrontiersCheck (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) : Bool := Check.allDecide matchedPairs fun pair => pair.fromPort ∈ leftExits ∧ pair.toPort ∈ rightEntries

Successful pair-frontier checking proves the matched-pair inclusion fact.

theorem connectPairsDrawnFromFrontiersCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} {matchedPairs : List AdmissionConnection} (hCheck : connectPairsDrawnFromFrontiersCheck leftExits rightEntries matchedPairs = true) : ∀ pair, pair ∈ matchedPairs → pair.fromPort ∈ leftExits ∧ pair.toPort ∈ rightEntries := Check.allDecide_sound hCheck

Residual left exits are drawn from the serialized left frontier.

def unmatchedLeftDrawnFromFrontierCheck (leftExits unmatchedLeftExits : List AdmissionBoundaryPort) : Bool := Check.allDecide unmatchedLeftExits fun boundary => boundary ∈ leftExits

Successful residual-left checking proves the inclusion fact.

theorem unmatchedLeftDrawnFromFrontierCheck_sound {leftExits unmatchedLeftExits : List AdmissionBoundaryPort} (hCheck : unmatchedLeftDrawnFromFrontierCheck leftExits unmatchedLeftExits = true) : ∀ boundary, boundary ∈ unmatchedLeftExits → boundary ∈ leftExits := Check.allDecide_sound hCheck

Residual right entries are drawn from the serialized right frontier.

def unmatchedRightDrawnFromFrontierCheck (rightEntries unmatchedRightEntries : List AdmissionBoundaryPort) : Bool := Check.allDecide unmatchedRightEntries fun boundary => boundary ∈ rightEntries

Successful residual-right checking proves the inclusion fact.

theorem unmatchedRightDrawnFromFrontierCheck_sound {rightEntries unmatchedRightEntries : List AdmissionBoundaryPort} (hCheck : unmatchedRightDrawnFromFrontierCheck rightEntries unmatchedRightEntries = true) : ∀ boundary, boundary ∈ unmatchedRightEntries → boundary ∈ rightEntries := Check.allDecide_sound hCheck

Search a matched-pair ledger for a concrete compatible frontier pair.

def exactMatchedPairCheck (matchedPairs : List AdmissionConnection) (leftExit rightEntry : AdmissionBoundaryPort) : Bool := Check.anyDecide matchedPairs fun pair => pair.fromPort = leftExit ∧ pair.toPort = rightEntry

Successful exact-pair search returns the matching connection row.

theorem exactMatchedPairCheck_sound {matchedPairs : List AdmissionConnection} {leftExit rightEntry : AdmissionBoundaryPort} (hCheck : exactMatchedPairCheck matchedPairs leftExit rightEntry = true) : ∃ pair, pair ∈ matchedPairs ∧ pair.fromPort = leftExit ∧ pair.toPort = rightEntry := matchedPairs:List AdmissionConnectionleftExit:AdmissionBoundaryPortrightEntry:AdmissionBoundaryPorthCheck:exactMatchedPairCheck matchedPairs leftExit rightEntry = true⊢ ∃ pair ∈ matchedPairs, pair.fromPort = leftExit ∧ pair.toPort = rightEntry matchedPairs:List AdmissionConnectionleftExit:AdmissionBoundaryPortrightEntry:AdmissionBoundaryPorthCheck:(Check.anyDecide matchedPairs fun pair => pair.fromPort = leftExit ∧ pair.toPort = rightEntry) = true⊢ ∃ pair ∈ matchedPairs, pair.fromPort = leftExit ∧ pair.toPort = rightEntry matchedPairs:List AdmissionConnectionleftExit:AdmissionBoundaryPortrightEntry:AdmissionBoundaryPorthCheck:(Check.anyDecide matchedPairs fun pair => pair.fromPort = leftExit ∧ pair.toPort = rightEntry) = truepair:AdmissionConnectionhPair:pair ∈ matchedPairshExact:pair.fromPort = leftExit ∧ pair.toPort = rightEntry⊢ ∃ pair ∈ matchedPairs, pair.fromPort = leftExit ∧ pair.toPort = rightEntry All goals completed! 🐙

Every compatible frontier pair is recorded in the matched-pair ledger.

def connectMatchesAllCompatibleCheck (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) : Bool := Check.allPairsWhenCheck leftExits rightEntries AdmissionBoundaryPort.CompatibleWith (exactMatchedPairCheck matchedPairs)

Successful compatibility matching proves ConnectMatchesAllCompatible.

theorem connectMatchesAllCompatibleCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} {matchedPairs : List AdmissionConnection} (hCheck : connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs = true) : ConnectMatchesAllCompatible leftExits rightEntries matchedPairs := leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionhCheck:connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs = true⊢ ConnectMatchesAllCompatible leftExits rightEntries matchedPairs leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionhCheck:Check.allPairsWhenCheck leftExits rightEntries AdmissionBoundaryPort.CompatibleWith (exactMatchedPairCheck matchedPairs) = true⊢ ConnectMatchesAllCompatible leftExits rightEntries matchedPairs All goals completed! 🐙

Boundary rows inside a primitive connect row are structurally valid.

def connectRowsValidCheck (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort) : Bool := AdmissionArtifactCheck.boundaryPortsValidCheck leftExits && AdmissionArtifactCheck.boundaryPortsValidCheck rightEntries && AdmissionArtifactCheck.connectionsValidCheck matchedPairs && AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedLeftExits && AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedRightEntries

Successful connect-row boundary checking proves ConnectRowsValid.

theorem connectRowsValidCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} {matchedPairs : List AdmissionConnection} {unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort} (hCheck : connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true) : ConnectRowsValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries := leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true⊢ ConnectRowsValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(AdmissionArtifactCheck.boundaryPortsValidCheck leftExits && AdmissionArtifactCheck.boundaryPortsValidCheck rightEntries && AdmissionArtifactCheck.connectionsValidCheck matchedPairs && AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedLeftExits && AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedRightEntries) = true⊢ ConnectRowsValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(((AdmissionArtifactCheck.boundaryPortsValidCheck leftExits = true ∧ AdmissionArtifactCheck.boundaryPortsValidCheck rightEntries = true) ∧ AdmissionArtifactCheck.connectionsValidCheck matchedPairs = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedLeftExits = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedRightEntries = true⊢ ConnectRowsValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthUnmatchedRight:AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedRightEntries = truehUnmatchedLeft:AdmissionArtifactCheck.boundaryPortsValidCheck unmatchedLeftExits = truehPairs:AdmissionArtifactCheck.connectionsValidCheck matchedPairs = truehLeftExits:AdmissionArtifactCheck.boundaryPortsValidCheck leftExits = truehRightEntries:AdmissionArtifactCheck.boundaryPortsValidCheck rightEntries = true⊢ ConnectRowsValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries All goals completed! 🐙

Executable checker for primitive connect-row validity.

def connectValidCheck (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort) : Bool := connectPairsDrawnFromFrontiersCheck leftExits rightEntries matchedPairs && unmatchedLeftDrawnFromFrontierCheck leftExits unmatchedLeftExits && unmatchedRightDrawnFromFrontierCheck rightEntries unmatchedRightEntries && connectPairsLinearCheck matchedPairs && connectFrontiersLinearCheck leftExits rightEntries && connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs && connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries && connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries

Successful primitive connect-row checking proves ConnectValid.

theorem connectValidCheck_sound {leftExits rightEntries : List AdmissionBoundaryPort} {matchedPairs : List AdmissionConnection} {unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort} (hCheck : connectValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true) : ConnectValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries := leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:connectValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true⊢ ConnectValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(connectPairsDrawnFromFrontiersCheck leftExits rightEntries matchedPairs && unmatchedLeftDrawnFromFrontierCheck leftExits unmatchedLeftExits && unmatchedRightDrawnFromFrontierCheck rightEntries unmatchedRightEntries && connectPairsLinearCheck matchedPairs && connectFrontiersLinearCheck leftExits rightEntries && connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs && connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries && connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) = true⊢ ConnectValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:((((((connectPairsDrawnFromFrontiersCheck leftExits rightEntries matchedPairs = true ∧ unmatchedLeftDrawnFromFrontierCheck leftExits unmatchedLeftExits = true) ∧ unmatchedRightDrawnFromFrontierCheck rightEntries unmatchedRightEntries = true) ∧ connectPairsLinearCheck matchedPairs = true) ∧ connectFrontiersLinearCheck leftExits rightEntries = true) ∧ connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs = true) ∧ connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true) ∧ connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = true⊢ ConnectValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthRowsValid:connectRowsValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = truehPartition:connectFrontierPartitionCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = truehMatchesAll:connectMatchesAllCompatibleCheck leftExits rightEntries matchedPairs = truehFrontiersLinear:connectFrontiersLinearCheck leftExits rightEntries = truehPairsLinear:connectPairsLinearCheck matchedPairs = truehUnmatchedRight:unmatchedRightDrawnFromFrontierCheck rightEntries unmatchedRightEntries = truehPairsDrawn:connectPairsDrawnFromFrontiersCheck leftExits rightEntries matchedPairs = truehUnmatchedLeft:unmatchedLeftDrawnFromFrontierCheck leftExits unmatchedLeftExits = true⊢ ConnectValid leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries All goals completed! 🐙

Executable checker for primitive graph-step row validity.

def validCheck : PrimitiveGraphStep → Bool | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node nodeId entries exits => nodeValidCheck nodeId entries exits | PrimitiveGraphStep.bindingRef binding => decide binding.Valid | PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings => overlayValidCheck leftNodeIds rightNodeIds leftBindings rightBindings | PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries => connectValidCheck leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries

Successful primitive graph-step checking proves row-local Valid.

theorem validCheck_sound {primitiveStep : PrimitiveGraphStep} (hCheck : primitiveStep.validCheck = true) : primitiveStep.Valid := primitiveStep:PrimitiveGraphStephCheck:primitiveStep.validCheck = true⊢ primitiveStep.Valid cases primitiveStep with hCheck:empty.validCheck = true⊢ empty.Valid All goals completed! 🐙 nodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(node nodeId entries exits).validCheck = true⊢ (node nodeId entries exits).Valid All goals completed! 🐙 binding:BindingNamehCheck:(bindingRef binding).validCheck = true⊢ (bindingRef binding).Valid binding:BindingNamehCheck:(bindingRef binding).validCheck = true⊢ binding.Valid All goals completed! 🐙 leftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(overlay leftNodeIds rightNodeIds leftBindings rightBindings).validCheck = true⊢ (overlay leftNodeIds rightNodeIds leftBindings rightBindings).Valid All goals completed! 🐙 leftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries).validCheck = true⊢ (connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries).Valid All goals completed! 🐙end PrimitiveGraphStep

Validator-Ready Core

namespace WireAdmissionArtifact

Executable checker for top-level summary-key uniqueness.

def summaryKeysUniqueCheck (artifact : WireAdmissionArtifact) : Bool := Check.nodupCheck artifact.nodes && Check.nodupCheck artifact.bindingRefs && Check.nodupMapCheck artifact.entries AdmissionBoundaryPort.key && Check.nodupMapCheck artifact.exits AdmissionBoundaryPort.key && Check.nodupCheck artifact.connections

Successful summary-key checking proves SummaryKeysUnique.

theorem summaryKeysUniqueCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryKeysUniqueCheck = true) : artifact.SummaryKeysUnique := artifact:WireAdmissionArtifacthCheck:artifact.summaryKeysUniqueCheck = true⊢ artifact.SummaryKeysUnique artifact:WireAdmissionArtifacthCheck:(Check.nodupCheck artifact.nodes && Check.nodupCheck artifact.bindingRefs && Check.nodupMapCheck artifact.entries AdmissionBoundaryPort.key && Check.nodupMapCheck artifact.exits AdmissionBoundaryPort.key && Check.nodupCheck artifact.connections) = true⊢ artifact.SummaryKeysUnique artifact:WireAdmissionArtifacthCheck:(((Check.nodupCheck artifact.nodes = true ∧ Check.nodupCheck artifact.bindingRefs = true) ∧ Check.nodupMapCheck artifact.entries AdmissionBoundaryPort.key = true) ∧ Check.nodupMapCheck artifact.exits AdmissionBoundaryPort.key = true) ∧ Check.nodupCheck artifact.connections = true⊢ artifact.SummaryKeysUnique artifact:WireAdmissionArtifacthConnections:Check.nodupCheck artifact.connections = truehExits:Check.nodupMapCheck artifact.exits AdmissionBoundaryPort.key = truehEntries:Check.nodupMapCheck artifact.entries AdmissionBoundaryPort.key = truehNodes:Check.nodupCheck artifact.nodes = truehBindings:Check.nodupCheck artifact.bindingRefs = true⊢ artifact.SummaryKeysUnique All goals completed! 🐙

Executable checker for top-level summary row validity.

def summaryRowsValidCheck (artifact : WireAdmissionArtifact) : Bool := Check.allDecide artifact.nodes NodeId.Valid && Check.allDecide artifact.bindingRefs BindingName.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.entries && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.exits && Check.allDecide artifact.connections AdmissionRawConnection.Valid

Successful summary-row checking proves SummaryRowsValid.

theorem summaryRowsValidCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryRowsValidCheck = true) : artifact.SummaryRowsValid := artifact:WireAdmissionArtifacthCheck:artifact.summaryRowsValidCheck = true⊢ artifact.SummaryRowsValid artifact:WireAdmissionArtifacthCheck:(Check.allDecide artifact.nodes NodeId.Valid && Check.allDecide artifact.bindingRefs BindingName.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.entries && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.exits && Check.allDecide artifact.connections AdmissionRawConnection.Valid) = true⊢ artifact.SummaryRowsValid artifact:WireAdmissionArtifacthCheck:(((Check.allDecide artifact.nodes NodeId.Valid = true ∧ Check.allDecide artifact.bindingRefs BindingName.Valid = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck artifact.entries = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck artifact.exits = true) ∧ Check.allDecide artifact.connections AdmissionRawConnection.Valid = true⊢ artifact.SummaryRowsValid artifact:WireAdmissionArtifacthConnections:Check.allDecide artifact.connections AdmissionRawConnection.Valid = truehExits:AdmissionArtifactCheck.boundaryPortsValidCheck artifact.exits = truehEntries:AdmissionArtifactCheck.boundaryPortsValidCheck artifact.entries = truehNodes:Check.allDecide artifact.nodes NodeId.Valid = truehBindings:Check.allDecide artifact.bindingRefs BindingName.Valid = true⊢ artifact.SummaryRowsValid All goals completed! 🐙

Executable checker for boundary rows being closed over a node summary.

def boundaryPortClosedCheck (nodes : List NodeId) (port : AdmissionBoundaryPort) : Bool := Check.memCheck port.node nodes && match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes

Successful boundary-row closure checking proves AdmissionBoundaryPort.ClosedOver.

theorem boundaryPortClosedCheck_sound {nodes : List NodeId} {port : AdmissionBoundaryPort} (hCheck : boundaryPortClosedCheck nodes port = true) : port.ClosedOver nodes := nodes:List NodeIdport:AdmissionBoundaryPorthCheck:boundaryPortClosedCheck nodes port = true⊢ AdmissionBoundaryPort.ClosedOver nodes port nodes:List NodeIdport:AdmissionBoundaryPorthCheck:(Check.memCheck port.node nodes && match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ AdmissionBoundaryPort.ClosedOver nodes port nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ AdmissionBoundaryPort.ClosedOver nodes port nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ port.node ∈ nodesnodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ match port.exclusiveGroup with | none => True | some (owner, _index) => owner ∈ nodes nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ port.node ∈ nodes All goals completed! 🐙 nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = true⊢ match port.exclusiveGroup with | none => True | some (owner, _index) => owner ∈ nodes cases hGroup : port.exclusiveGroup with nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = truehGroup:port.exclusiveGroup = none⊢ match none with | none => True | some (owner, _index) => owner ∈ nodes All goals completed! 🐙 nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = truegroup:NodeId × ℕhGroup:port.exclusiveGroup = some group⊢ match some group with | none => True | some (owner, _index) => owner ∈ nodes cases group with nodes:List NodeIdport:AdmissionBoundaryPorthCheck:Check.memCheck port.node nodes = true ∧ (match port.exclusiveGroup with | none => true | some (owner, _index) => Check.memCheck owner nodes) = trueowner:NodeIdindex:ℕhGroup:port.exclusiveGroup = some (owner, index)⊢ match some (owner, index) with | none => True | some (owner, _index) => owner ∈ nodes have hOwnerCheck : Check.memCheck owner nodes = true := nodes:List NodeIdport:AdmissionBoundaryPorthCheck:boundaryPortClosedCheck nodes port = true⊢ AdmissionBoundaryPort.ClosedOver nodes port All goals completed! 🐙 All goals completed! 🐙

Executable checker for boundary lists being closed over a node summary.

def boundaryPortsClosedCheck (nodes : List NodeId) (ports : List AdmissionBoundaryPort) : Bool := Check.allBool ports (boundaryPortClosedCheck nodes)

Successful boundary-closure checking proves BoundaryPortsClosed.

theorem boundaryPortsClosedCheck_sound {nodes : List NodeId} {ports : List AdmissionBoundaryPort} (hCheck : boundaryPortsClosedCheck nodes ports = true) : BoundaryPortsClosed nodes ports := Check.allBool_sound hCheck (fun _port _ hPortCheck => boundaryPortClosedCheck_sound hPortCheck)

Executable checker for raw connection endpoints being closed over a node summary.

def rawConnectionsClosedCheck (nodes : List NodeId) (connections : List AdmissionRawConnection) : Bool := Check.allDecide connections fun connection => connection.fromEndpoint.node ∈ nodes ∧ connection.toEndpoint.node ∈ nodes

Successful raw-connection closure checking proves endpoint-node closure.

theorem rawConnectionsClosedCheck_sound {nodes : List NodeId} {connections : List AdmissionRawConnection} (hCheck : rawConnectionsClosedCheck nodes connections = true) : ∀ connection, connection ∈ connections → connection.fromEndpoint.node ∈ nodes ∧ connection.toEndpoint.node ∈ nodes := Check.allDecide_sound hCheck

Executable checker for a boundary contraction being closed over a node summary.

def connectionClosedCheck (nodes : List NodeId) (connection : AdmissionConnection) : Bool := boundaryPortClosedCheck nodes connection.fromPort && boundaryPortClosedCheck nodes connection.toPort

Successful connection-closure checking proves both endpoints are closed.

theorem connectionClosedCheck_sound {nodes : List NodeId} {connection : AdmissionConnection} (hCheck : connectionClosedCheck nodes connection = true) : connection.fromPort.ClosedOver nodes ∧ connection.toPort.ClosedOver nodes := nodes:List NodeIdconnection:AdmissionConnectionhCheck:connectionClosedCheck nodes connection = true⊢ AdmissionBoundaryPort.ClosedOver nodes connection.fromPort ∧ AdmissionBoundaryPort.ClosedOver nodes connection.toPort nodes:List NodeIdconnection:AdmissionConnectionhCheck:(boundaryPortClosedCheck nodes connection.fromPort && boundaryPortClosedCheck nodes connection.toPort) = true⊢ AdmissionBoundaryPort.ClosedOver nodes connection.fromPort ∧ AdmissionBoundaryPort.ClosedOver nodes connection.toPort nodes:List NodeIdconnection:AdmissionConnectionhCheck:boundaryPortClosedCheck nodes connection.fromPort = true ∧ boundaryPortClosedCheck nodes connection.toPort = true⊢ AdmissionBoundaryPort.ClosedOver nodes connection.fromPort ∧ AdmissionBoundaryPort.ClosedOver nodes connection.toPort All goals completed! 🐙

Executable checker for boundary contraction lists being closed over a node summary.

def connectionsClosedCheck (nodes : List NodeId) (connections : List AdmissionConnection) : Bool := Check.allBool connections (connectionClosedCheck nodes)

Successful connection-list closure checking proves ConnectionsClosed.

theorem connectionsClosedCheck_sound {nodes : List NodeId} {connections : List AdmissionConnection} (hCheck : connectionsClosedCheck nodes connections = true) : ConnectionsClosed nodes connections := Check.allBool_sound hCheck (fun _connection _ hConnection => connectionClosedCheck_sound hConnection)

Executable checker for top-level summary closure over serialized nodes.

def summaryDomainClosedCheck (artifact : WireAdmissionArtifact) : Bool := boundaryPortsClosedCheck artifact.nodes artifact.entries && boundaryPortsClosedCheck artifact.nodes artifact.exits && rawConnectionsClosedCheck artifact.nodes artifact.connections

Successful summary-domain checking proves SummaryDomainClosed.

theorem summaryDomainClosedCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryDomainClosedCheck = true) : artifact.SummaryDomainClosed := artifact:WireAdmissionArtifacthCheck:artifact.summaryDomainClosedCheck = true⊢ artifact.SummaryDomainClosed artifact:WireAdmissionArtifacthCheck:(boundaryPortsClosedCheck artifact.nodes artifact.entries && boundaryPortsClosedCheck artifact.nodes artifact.exits && rawConnectionsClosedCheck artifact.nodes artifact.connections) = true⊢ artifact.SummaryDomainClosed artifact:WireAdmissionArtifacthCheck:(boundaryPortsClosedCheck artifact.nodes artifact.entries = true ∧ boundaryPortsClosedCheck artifact.nodes artifact.exits = true) ∧ rawConnectionsClosedCheck artifact.nodes artifact.connections = true⊢ artifact.SummaryDomainClosed artifact:WireAdmissionArtifacthConnections:rawConnectionsClosedCheck artifact.nodes artifact.connections = truehEntries:boundaryPortsClosedCheck artifact.nodes artifact.entries = truehExits:boundaryPortsClosedCheck artifact.nodes artifact.exits = true⊢ artifact.SummaryDomainClosed All goals completed! 🐙

Executable checker for primitive trace rows being closed over artifact summaries.

def primitiveStepDomainClosedCheck (nodes : List NodeId) (bindingRefs : List BindingName) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node nodeId entries exits => Check.memCheck nodeId nodes && boundaryPortsClosedCheck nodes entries && boundaryPortsClosedCheck nodes exits | PrimitiveGraphStep.bindingRef binding => Check.memCheck binding bindingRefs | PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings => Check.allDecide leftNodeIds (fun node => node ∈ nodes) && Check.allDecide rightNodeIds (fun node => node ∈ nodes) && Check.allDecide leftBindings (fun binding => binding ∈ bindingRefs) && Check.allDecide rightBindings (fun binding => binding ∈ bindingRefs) | PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries => boundaryPortsClosedCheck nodes leftExits && boundaryPortsClosedCheck nodes rightEntries && connectionsClosedCheck nodes matchedPairs && boundaryPortsClosedCheck nodes unmatchedLeftExits && boundaryPortsClosedCheck nodes unmatchedRightEntries

Successful primitive-domain checking proves PrimitiveGraphStep.DomainClosed.

theorem primitiveStepDomainClosedCheck_sound {nodes : List NodeId} {bindingRefs : List BindingName} {primitiveStep : PrimitiveGraphStep} (hCheck : primitiveStepDomainClosedCheck nodes bindingRefs primitiveStep = true) : PrimitiveGraphStep.DomainClosed nodes bindingRefs primitiveStep := nodes:List NodeIdbindingRefs:List BindingNameprimitiveStep:PrimitiveGraphStephCheck:primitiveStepDomainClosedCheck nodes bindingRefs primitiveStep = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs primitiveStep cases primitiveStep with nodes:List NodeIdbindingRefs:List BindingNamehCheck:primitiveStepDomainClosedCheck nodes bindingRefs PrimitiveGraphStep.empty = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs PrimitiveGraphStep.empty All goals completed! 🐙 nodes:List NodeIdbindingRefs:List BindingNamenodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:primitiveStepDomainClosedCheck nodes bindingRefs (PrimitiveGraphStep.node nodeId entries exits) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.node nodeId entries exits) nodes:List NodeIdbindingRefs:List BindingNamenodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(match PrimitiveGraphStep.node nodeId entries exits with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node nodeId entries exits => Check.memCheck nodeId nodes && boundaryPortsClosedCheck nodes entries && boundaryPortsClosedCheck nodes exits | PrimitiveGraphStep.bindingRef binding => Check.memCheck binding bindingRefs | PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings => (((Check.allDecide leftNodeIds fun node => node ∈ nodes) && Check.allDecide rightNodeIds fun node => node ∈ nodes) && Check.allDecide leftBindings fun binding => binding ∈ bindingRefs) && Check.allDecide rightBindings fun binding => binding ∈ bindingRefs | PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries => boundaryPortsClosedCheck nodes leftExits && boundaryPortsClosedCheck nodes rightEntries && connectionsClosedCheck nodes matchedPairs && boundaryPortsClosedCheck nodes unmatchedLeftExits && boundaryPortsClosedCheck nodes unmatchedRightEntries) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.node nodeId entries exits) nodes:List NodeIdbindingRefs:List BindingNamenodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(Check.memCheck nodeId nodes = true ∧ boundaryPortsClosedCheck nodes entries = true) ∧ boundaryPortsClosedCheck nodes exits = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.node nodeId entries exits) nodes:List NodeIdbindingRefs:List BindingNamenodeId:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthExits:boundaryPortsClosedCheck nodes exits = truehNode:Check.memCheck nodeId nodes = truehEntries:boundaryPortsClosedCheck nodes entries = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.node nodeId entries exits) All goals completed! 🐙 nodes:List NodeIdbindingRefs:List BindingNamebinding:BindingNamehCheck:primitiveStepDomainClosedCheck nodes bindingRefs (PrimitiveGraphStep.bindingRef binding) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.bindingRef binding) All goals completed! 🐙 nodes:List NodeIdbindingRefs:List BindingNameleftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:primitiveStepDomainClosedCheck nodes bindingRefs (PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings) nodes:List NodeIdbindingRefs:List BindingNameleftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(match PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node nodeId entries exits => Check.memCheck nodeId nodes && boundaryPortsClosedCheck nodes entries && boundaryPortsClosedCheck nodes exits | PrimitiveGraphStep.bindingRef binding => Check.memCheck binding bindingRefs | PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings => (((Check.allDecide leftNodeIds fun node => node ∈ nodes) && Check.allDecide rightNodeIds fun node => node ∈ nodes) && Check.allDecide leftBindings fun binding => binding ∈ bindingRefs) && Check.allDecide rightBindings fun binding => binding ∈ bindingRefs | PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries => boundaryPortsClosedCheck nodes leftExits && boundaryPortsClosedCheck nodes rightEntries && connectionsClosedCheck nodes matchedPairs && boundaryPortsClosedCheck nodes unmatchedLeftExits && boundaryPortsClosedCheck nodes unmatchedRightEntries) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings) nodes:List NodeIdbindingRefs:List BindingNameleftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(((Check.allDecide leftNodeIds fun node => node ∈ nodes) = true ∧ (Check.allDecide rightNodeIds fun node => node ∈ nodes) = true) ∧ (Check.allDecide leftBindings fun binding => binding ∈ bindingRefs) = true) ∧ (Check.allDecide rightBindings fun binding => binding ∈ bindingRefs) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings) nodes:List NodeIdbindingRefs:List BindingNameleftNodeIds:List NodeIdrightNodeIds:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehRightBindings:(Check.allDecide rightBindings fun binding => binding ∈ bindingRefs) = truehLeftBindings:(Check.allDecide leftBindings fun binding => binding ∈ bindingRefs) = truehLeftNodes:(Check.allDecide leftNodeIds fun node => node ∈ nodes) = truehRightNodes:(Check.allDecide rightNodeIds fun node => node ∈ nodes) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings) All goals completed! 🐙 nodes:List NodeIdbindingRefs:List BindingNameleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:primitiveStepDomainClosedCheck nodes bindingRefs (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) nodes:List NodeIdbindingRefs:List BindingNameleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(match PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node nodeId entries exits => Check.memCheck nodeId nodes && boundaryPortsClosedCheck nodes entries && boundaryPortsClosedCheck nodes exits | PrimitiveGraphStep.bindingRef binding => Check.memCheck binding bindingRefs | PrimitiveGraphStep.overlay leftNodeIds rightNodeIds leftBindings rightBindings => (((Check.allDecide leftNodeIds fun node => node ∈ nodes) && Check.allDecide rightNodeIds fun node => node ∈ nodes) && Check.allDecide leftBindings fun binding => binding ∈ bindingRefs) && Check.allDecide rightBindings fun binding => binding ∈ bindingRefs | PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries => boundaryPortsClosedCheck nodes leftExits && boundaryPortsClosedCheck nodes rightEntries && connectionsClosedCheck nodes matchedPairs && boundaryPortsClosedCheck nodes unmatchedLeftExits && boundaryPortsClosedCheck nodes unmatchedRightEntries) = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) nodes:List NodeIdbindingRefs:List BindingNameleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:(((boundaryPortsClosedCheck nodes leftExits = true ∧ boundaryPortsClosedCheck nodes rightEntries = true) ∧ connectionsClosedCheck nodes matchedPairs = true) ∧ boundaryPortsClosedCheck nodes unmatchedLeftExits = true) ∧ boundaryPortsClosedCheck nodes unmatchedRightEntries = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) nodes:List NodeIdbindingRefs:List BindingNameleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthUnmatchedRight:boundaryPortsClosedCheck nodes unmatchedRightEntries = truehUnmatchedLeft:boundaryPortsClosedCheck nodes unmatchedLeftExits = truehMatchedPairs:connectionsClosedCheck nodes matchedPairs = truehLeftExits:boundaryPortsClosedCheck nodes leftExits = truehRightEntries:boundaryPortsClosedCheck nodes rightEntries = true⊢ PrimitiveGraphStep.DomainClosed nodes bindingRefs (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) All goals completed! 🐙

Executable checker that summary identities match primitive identity rows.

def summaryIdentitiesMatchPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.permCheck artifact.nodes (PrimitiveGraphStep.nodeRowsList artifact.primitiveSteps) && Check.permCheck artifact.bindingRefs (PrimitiveGraphStep.bindingRowsList artifact.primitiveSteps)

Successful identity matching proves SummaryIdentitiesMatchPrimitive.

theorem summaryIdentitiesMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryIdentitiesMatchPrimitiveCheck = true) : artifact.SummaryIdentitiesMatchPrimitive := artifact:WireAdmissionArtifacthCheck:artifact.summaryIdentitiesMatchPrimitiveCheck = true⊢ artifact.SummaryIdentitiesMatchPrimitive artifact:WireAdmissionArtifacthCheck:(Check.permCheck artifact.nodes (PrimitiveGraphStep.nodeRowsList artifact.primitiveSteps) && Check.permCheck artifact.bindingRefs (PrimitiveGraphStep.bindingRowsList artifact.primitiveSteps)) = true⊢ artifact.SummaryIdentitiesMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.permCheck artifact.nodes (PrimitiveGraphStep.nodeRowsList artifact.primitiveSteps) = true ∧ Check.permCheck artifact.bindingRefs (PrimitiveGraphStep.bindingRowsList artifact.primitiveSteps) = true⊢ artifact.SummaryIdentitiesMatchPrimitive All goals completed! 🐙

Executable checker that summary frontiers are backed by primitive residual frontiers.

def summaryFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := (Check.allDecide artifact.entries fun entry => entry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ entry.key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) && (Check.allDecide artifact.exits fun exit => exit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ exit.key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps)

Successful frontier-backing checking proves SummaryFrontiersBackedByPrimitive.

theorem summaryFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryFrontiersBackedByPrimitiveCheck = true) : artifact.SummaryFrontiersBackedByPrimitive := artifact:WireAdmissionArtifacthCheck:artifact.summaryFrontiersBackedByPrimitiveCheck = true⊢ artifact.SummaryFrontiersBackedByPrimitive artifact:WireAdmissionArtifacthCheck:((Check.allDecide artifact.entries fun entry => entry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ entry.key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) && Check.allDecide artifact.exits fun exit => exit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ exit.key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true⊢ artifact.SummaryFrontiersBackedByPrimitive artifact:WireAdmissionArtifacthCheck:(Check.allDecide artifact.entries fun entry => entry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ entry.key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide artifact.exits fun exit => exit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ exit.key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true⊢ artifact.SummaryFrontiersBackedByPrimitive All goals completed! 🐙

Primitive entry keys that remain source-visible after primitive connection replay.

def residualPrimitiveEntryKeys (artifact : WireAdmissionArtifact) : List (NodeId × FieldLabel × ContractId) := (PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps).filter fun key => decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps)

Boolean check that one exit row witnesses a select-internal key.

def selectInternalExitRowKeyCheck (selectAdmission : SelectAdmissionArtifact) (key : NodeId × FieldLabel × ContractId) (exit : AdmissionBoundaryPort) : Bool := decide (exit.key = key) && match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)

Successful row-level select-internal checking returns the matched exit and variant facts.

theorem selectInternalExitRowKeyCheck_sound {selectAdmission : SelectAdmissionArtifact} {key : NodeId × FieldLabel × ContractId} {exit : AdmissionBoundaryPort} (hCheck : selectInternalExitRowKeyCheck selectAdmission key exit = true) : exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant, variant ∈ selectAdmission.variants ∧ variant.port.CompatibleWith exit := selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:selectInternalExitRowKeyCheck selectAdmission key exit = true⊢ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:(decide (exit.key = key) && match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true⊢ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true⊢ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = key⊢ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit cases hGroup : exit.exclusiveGroup with selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyhGroup:exit.exclusiveGroup = none⊢ exit.key = key ∧ (∃ index, none = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keygroup:NodeId × ℕhGroup:exit.exclusiveGroup = some group⊢ exit.key = key ∧ (∃ index, some group = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit cases group with selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)⊢ exit.key = key ∧ (∃ index_1, some (owner, index) = some (selectAdmission.conditionNode, index_1)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit have hTail : (decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any (fun variant => decide (variant.port.CompatibleWith exit))) = true := selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:selectInternalExitRowKeyCheck selectAdmission key exit = true⊢ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hTail:decide (owner = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true⊢ exit.key = key ∧ (∃ index_1, some (owner, index) = some (selectAdmission.conditionNode, index_1)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hTail:decide (owner = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehOwner:owner = selectAdmission.conditionNode⊢ exit.key = key ∧ (∃ index_1, some (owner, index) = some (selectAdmission.conditionNode, index_1)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hTail:decide (owner = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehOwner:owner = selectAdmission.conditionNodevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatibleBool:decide (variant.port.CompatibleWith exit) = true⊢ exit.key = key ∧ (∃ index_1, some (owner, index) = some (selectAdmission.conditionNode, index_1)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hTail:decide (owner = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehOwner:owner = selectAdmission.conditionNodevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatibleBool:decide (variant.port.CompatibleWith exit) = truehCompatible:variant.port.CompatibleWith exit⊢ exit.key = key ∧ (∃ index_1, some (owner, index) = some (selectAdmission.conditionNode, index_1)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit exact ⟨ hKey , ⟨index, selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthCheck:decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehKey:exit.key = keyowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hTail:decide (owner = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = truehOwner:owner = selectAdmission.conditionNodevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatibleBool:decide (variant.port.CompatibleWith exit) = truehCompatible:variant.port.CompatibleWith exit⊢ some (owner, index) = some (selectAdmission.conditionNode, index) All goals completed! 🐙⟩ , variant , hVariant , hCompatible ⟩

Row-level select-internal key witnesses are accepted by the boolean checker.

theorem selectInternalExitRowKeyCheck_complete {selectAdmission : SelectAdmissionArtifact} {key : NodeId × FieldLabel × ContractId} {exit : AdmissionBoundaryPort} (hKey : exit.key = key) (hGroup : ∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) (hVariant : ∃ variant, variant ∈ selectAdmission.variants ∧ variant.port.CompatibleWith exit) : selectInternalExitRowKeyCheck selectAdmission key exit = true := selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ selectInternalExitRowKeyCheck selectAdmission key exit = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyhVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exitindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)⊢ selectInternalExitRowKeyCheck selectAdmission key exit = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ selectInternalExitRowKeyCheck selectAdmission key exit = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (decide (exit.key = key) && match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (exit.key = key) = true ∧ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (exit.key = key) = trueselectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (exit.key = key) = true All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (match some (selectAdmission.conditionNode, index) with | none => false | some (owner, _index) => decide (owner = selectAdmission.conditionNode) && selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = true ∧ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = trueselectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = true All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdexit:AdmissionBoundaryPorthKey:exit.key = keyindex:ℕhGroupEq:exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (selectAdmission.variants.any fun variant => decide (variant.port.CompatibleWith exit)) = true All goals completed! 🐙

Boolean check that a primitive node row witnesses a select-internal key.

def selectInternalNodeKeyCheck (selectAdmission : SelectAdmissionArtifact) (key : NodeId × FieldLabel × ContractId) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false

Successful primitive-node key checking returns the primitive row and exit witness.

theorem selectInternalNodeKeyCheck_sound {selectAdmission : SelectAdmissionArtifact} {key : NodeId × FieldLabel × ContractId} {primitiveStep : PrimitiveGraphStep} (hCheck : selectInternalNodeKeyCheck selectAdmission key primitiveStep = true) : ∃ entries exits, primitiveStep = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit, exit ∈ exits ∧ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant, variant ∈ selectAdmission.variants ∧ variant.port.CompatibleWith exit := selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdprimitiveStep:PrimitiveGraphStephCheck:selectInternalNodeKeyCheck selectAdmission key primitiveStep = true⊢ ∃ entries exits, primitiveStep = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit cases primitiveStep with selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:selectInternalNodeKeyCheck selectAdmission key PrimitiveGraphStep.empty = true⊢ ∃ entries exits, PrimitiveGraphStep.empty = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdbinding:BindingNamehCheck:selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.bindingRef binding) = true⊢ ∃ entries exits, PrimitiveGraphStep.bindingRef binding = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings) = true⊢ ∃ entries exits, PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthCheck:selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries) = true⊢ ∃ entries exits, PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.node node entries exits) = true⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:(match PrimitiveGraphStep.node node entries exits with | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:decide (node = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = true⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:decide (node = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = truehNode:node = selectAdmission.conditionNode⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:decide (node = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = truehNode:node = selectAdmission.conditionNodeexit:AdmissionBoundaryPorthExit:exit ∈ exitshExitCheck:selectInternalExitRowKeyCheck selectAdmission key exit = true⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:decide (node = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = truehNode:node = selectAdmission.conditionNodeexit:AdmissionBoundaryPorthExit:exit ∈ exitshExitCheck:selectInternalExitRowKeyCheck selectAdmission key exit = truehKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ ∃ entries_1 exits_1, PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries_1 exits_1 ∧ ∃ exit ∈ exits_1, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit exact ⟨ entries , exits , selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdnode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthCheck:decide (node = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = truehNode:node = selectAdmission.conditionNodeexit:AdmissionBoundaryPorthExit:exit ∈ exitshExitCheck:selectInternalExitRowKeyCheck selectAdmission key exit = truehKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ PrimitiveGraphStep.node node entries exits = PrimitiveGraphStep.node selectAdmission.conditionNode entries exits All goals completed! 🐙 , exit , hExit , hKey , hGroup , hVariant ⟩

Primitive-node key witnesses are accepted by the boolean checker.

theorem selectInternalNodeKeyCheck_complete {selectAdmission : SelectAdmissionArtifact} {key : NodeId × FieldLabel × ContractId} {entries exits : List AdmissionBoundaryPort} (hExit : ∃ exit, exit ∈ exits ∧ exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant, variant ∈ selectAdmission.variants ∧ variant.port.CompatibleWith exit) : selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.node selectAdmission.conditionNode entries exits) = true := selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthExit:∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.node selectAdmission.conditionNode entries exits) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.node selectAdmission.conditionNode entries exits) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ (match PrimitiveGraphStep.node selectAdmission.conditionNode entries exits with | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = true ∧ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = trueselectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = true selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ decide (selectAdmission.conditionNode = selectAdmission.conditionNode) = true All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactkey:NodeId × FieldLabel × ContractIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExitMem:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)hVariant:∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit⊢ (exits.any fun exit => selectInternalExitRowKeyCheck selectAdmission key exit) = true All goals completed! 🐙

Boolean form of key-level select-internal exit detection.

def selectInternalExitKeyCheck (artifact : WireAdmissionArtifact) (key : NodeId × FieldLabel × ContractId) : Bool := artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep

The key-level select-internal checker is exact for SelectInternalExitKey.

theorem selectInternalExitKeyCheck_eq_true_iff {artifact : WireAdmissionArtifact} {key : NodeId × FieldLabel × ContractId} : artifact.selectInternalExitKeyCheck key = true ↔ artifact.SelectInternalExitKey key := artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ artifact.selectInternalExitKeyCheck key = true ↔ artifact.SelectInternalExitKey key artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true ↔ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true → ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exitartifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ (∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit) → (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true → ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:(artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true⊢ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:(artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectshPrimitiveCheck:(artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true⊢ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:(artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectshPrimitiveCheck:(artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueprimitiveStep:PrimitiveGraphStephPrimitive:primitiveStep ∈ artifact.primitiveStepshNodeCheck:selectInternalNodeKeyCheck selectAdmission key primitiveStep = true⊢ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:(artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectshPrimitiveCheck:(artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueprimitiveStep:PrimitiveGraphStephPrimitive:primitiveStep ∈ artifact.primitiveStepshNodeCheck:selectInternalNodeKeyCheck selectAdmission key primitiveStep = trueentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthStep:primitiveStep = PrimitiveGraphStep.node selectAdmission.conditionNode entries exitsexit:AdmissionBoundaryPorthExit:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdhCheck:(artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectshPrimitiveCheck:(artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = trueentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPortexit:AdmissionBoundaryPorthExit:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exithPrimitive:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepshNodeCheck:selectInternalNodeKeyCheck selectAdmission key (PrimitiveGraphStep.node selectAdmission.conditionNode entries exits) = true⊢ ∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit All goals completed! 🐙 artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractId⊢ (∃ selectAdmission ∈ artifact.selects, ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∃ exit ∈ exits, exit.key = key ∧ (∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)) ∧ ∃ variant ∈ selectAdmission.variants, variant.port.CompatibleWith exit) → (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true artifact:WireAdmissionArtifactkey:NodeId × FieldLabel × ContractIdselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitive:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsexit:AdmissionBoundaryPorthExit:exit ∈ exitshKey:exit.key = keyhGroup:∃ index, exit.exclusiveGroup = some (selectAdmission.conditionNode, index)variant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshCompatible:variant.port.CompatibleWith exit⊢ (artifact.selects.any fun selectAdmission => artifact.primitiveSteps.any fun primitiveStep => selectInternalNodeKeyCheck selectAdmission key primitiveStep) = true All goals completed! 🐙

Primitive exit keys that remain source-visible after replay and select erasure.

def residualPrimitiveExitKeys (artifact : WireAdmissionArtifact) : List (NodeId × FieldLabel × ContractId) := (PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps).filter fun key => decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !(artifact.selectInternalExitKeyCheck key)

Executable checker that summary frontiers exactly match residual primitive frontiers.

def summaryFrontiersMatchPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.sameMembersCheck (artifact.entries.map AdmissionBoundaryPort.key) artifact.residualPrimitiveEntryKeys && Check.sameMembersCheck (artifact.exits.map AdmissionBoundaryPort.key) artifact.residualPrimitiveExitKeys

Successful frontier-exactness checking proves SummaryFrontiersMatchPrimitive.

theorem summaryFrontiersMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.summaryFrontiersMatchPrimitiveCheck = true) : artifact.SummaryFrontiersMatchPrimitive := artifact:WireAdmissionArtifacthCheck:artifact.summaryFrontiersMatchPrimitiveCheck = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:(Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys && Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys) = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeys⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeys⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeys⊢ ∀ (key : NodeId × FieldLabel × ContractId), key ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveStepsartifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeys⊢ ∀ (key : NodeId × FieldLabel × ContractId), key ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeys⊢ ∀ (key : NodeId × FieldLabel × ContractId), key ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.entries → key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveStepsartifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps → key ∈ List.map AdmissionBoundaryPort.key artifact.entries artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.entries → key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.entries⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.entrieshResidual:key ∈ artifact.residualPrimitiveEntryKeys⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.entrieshResidual:key ∈ List.filter (fun key => decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps)) (PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps)⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.entrieshResidual:key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) = true⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps → key ∈ List.map AdmissionBoundaryPort.key artifact.entries artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.entries have hResidual : key ∈ artifact.residualPrimitiveEntryKeys := artifact:WireAdmissionArtifacthCheck:artifact.summaryFrontiersMatchPrimitiveCheck = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps⊢ key ∈ List.filter (fun key => decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps)) (PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps⊢ key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) = true exact ⟨hPrimitive.left, artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps⊢ decide (key ∉ PrimitiveGraphStep.consumedEntryKeysList artifact.primitiveSteps) = true All goals completed! 🐙⟩ All goals completed! 🐙 artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeys⊢ ∀ (key : NodeId × FieldLabel × ContractId), key ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.exits → key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey keyartifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key → key ∈ List.map AdmissionBoundaryPort.key artifact.exits artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.exits → key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exits⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ artifact.residualPrimitiveExitKeys⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ List.filter (fun key => decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !artifact.selectInternalExitKeyCheck key) (PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps)⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ (decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !artifact.selectInternalExitKeyCheck key) = true⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!artifact.selectInternalExitKeyCheck key) = true⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!artifact.selectInternalExitKeyCheck key) = truehNotConsumed:key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key have hNotInternal : ¬ artifact.SelectInternalExitKey key := artifact:WireAdmissionArtifacthCheck:artifact.summaryFrontiersMatchPrimitiveCheck = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!artifact.selectInternalExitKeyCheck key) = truehNotConsumed:key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveStepshInternal:artifact.SelectInternalExitKey key⊢ False artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!artifact.selectInternalExitKeyCheck key) = truehNotConsumed:key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveStepshInternal:artifact.SelectInternalExitKey keyhInternalCheck:artifact.selectInternalExitKeyCheck key = true⊢ False artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhSummary:key ∈ List.map AdmissionBoundaryPort.key artifact.exitshResidual:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!true) = truehNotConsumed:key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveStepshInternal:artifact.SelectInternalExitKey keyhInternalCheck:artifact.selectInternalExitKeyCheck key = true⊢ False All goals completed! 🐙 All goals completed! 🐙 artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractId⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key → key ∈ List.map AdmissionBoundaryPort.key artifact.exits artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ key ∈ List.map AdmissionBoundaryPort.key artifact.exits have hResidual : key ∈ artifact.residualPrimitiveExitKeys := artifact:WireAdmissionArtifacthCheck:artifact.summaryFrontiersMatchPrimitiveCheck = true⊢ artifact.SummaryFrontiersMatchPrimitive artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ key ∈ List.filter (fun key => decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !artifact.selectInternalExitKeyCheck key) (PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ (decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !artifact.selectInternalExitKeyCheck key) = true artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ (decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) && !artifact.selectInternalExitKeyCheck key) = true artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true ∧ (!artifact.selectInternalExitKeyCheck key) = true artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = trueartifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ (!artifact.selectInternalExitKeyCheck key) = true artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ decide (key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps) = true All goals completed! 🐙 artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey key⊢ (!artifact.selectInternalExitKeyCheck key) = true cases hInternalCheck : artifact.selectInternalExitKeyCheck key with artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey keyhInternalCheck:artifact.selectInternalExitKeyCheck key = false⊢ (!false) = true All goals completed! 🐙 artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey keyhInternalCheck:artifact.selectInternalExitKeyCheck key = true⊢ (!true) = true artifact:WireAdmissionArtifacthCheck:Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.entries) artifact.residualPrimitiveEntryKeys = true ∧ Check.sameMembersCheck (List.map AdmissionBoundaryPort.key artifact.exits) artifact.residualPrimitiveExitKeys = truehEntriesMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.entries ↔ item ∈ artifact.residualPrimitiveEntryKeyshExitsMembers:∀ (item : NodeId × FieldLabel × ContractId), item ∈ List.map AdmissionBoundaryPort.key artifact.exits ↔ item ∈ artifact.residualPrimitiveExitKeyskey:NodeId × FieldLabel × ContractIdhPrimitive:key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ key ∉ PrimitiveGraphStep.consumedExitKeysList artifact.primitiveSteps ∧ ¬artifact.SelectInternalExitKey keyhInternalCheck:artifact.selectInternalExitKeyCheck key = truehInternal:artifact.SelectInternalExitKey key⊢ (!true) = true All goals completed! 🐙 All goals completed! 🐙

Executable checker that top-level raw connections match primitive connect projections.

def rawConnectionsMatchPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.permCheck artifact.connections (PrimitiveGraphStep.rawConnectionsList artifact.primitiveSteps)

Successful raw-connection matching proves RawConnectionsMatchPrimitive.

theorem rawConnectionsMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.rawConnectionsMatchPrimitiveCheck = true) : artifact.RawConnectionsMatchPrimitive := Check.permCheck_sound hCheck

Primitive Prefix Checks

Replay-order scan for primitive predicates whose truth depends on the trace prefix.

def primitivePrefixScanCheck (rowCheck : List PrimitiveGraphStep → PrimitiveGraphStep → Bool) (priorSteps : List PrimitiveGraphStep) : List PrimitiveGraphStep → Bool | [] => true | primitiveStep :: primitiveSteps => rowCheck priorSteps primitiveStep && primitivePrefixScanCheck rowCheck (priorSteps ++ [primitiveStep]) primitiveSteps

A successful prefix scan proves the row predicate at every trace position.

theorem primitivePrefixScanCheck_at_step_sound {rowCheck : List PrimitiveGraphStep → PrimitiveGraphStep → Bool} {rowPredicate : List PrimitiveGraphStep → PrimitiveGraphStep → Prop} (rowSound : ∀ priorSteps primitiveStep, rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStep) {priorSteps primitiveSteps : List PrimitiveGraphStep} (hCheck : primitivePrefixScanCheck rowCheck priorSteps primitiveSteps = true) : ∀ tracePrefix suffix primitiveStep, primitiveSteps = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep := rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStepprimitiveSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps primitiveSteps = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), primitiveSteps = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep induction primitiveSteps generalizing priorSteps with rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), [] = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep intro tracePrefix rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStep⊢ ∀ (primitiveStep : PrimitiveGraphStep), [] = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStep⊢ [] = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephEq:[] = tracePrefix ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ tracePrefix) primitiveStep cases tracePrefix with rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephEq:[] = [] ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ []) primitiveStep All goals completed! 🐙 rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps [] = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceHead:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephEq:[] = traceHead :: traceTail ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ traceHead :: traceTail) primitiveStep All goals completed! 🐙 rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps (head :: tail) = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), head :: tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:(rowCheck priorSteps head && primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail) = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), head :: tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), head :: tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep intro tracePrefix rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStep⊢ ∀ (primitiveStep : PrimitiveGraphStep), head :: tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStep⊢ head :: tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephEq:head :: tail = tracePrefix ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ tracePrefix) primitiveStep cases tracePrefix with rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephEq:head :: tail = [] ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ []) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephEq:head = primitiveStep ∧ tail = suffix⊢ rowPredicate (priorSteps ++ []) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephHead:head = primitiveStep_hTail:tail = suffix⊢ rowPredicate (priorSteps ++ []) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStep_hTail:tail = suffix⊢ rowPredicate (priorSteps ++ []) head All goals completed! 🐙 rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceHead:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephEq:head :: tail = traceHead :: traceTail ++ [primitiveStep] ++ suffix⊢ rowPredicate (priorSteps ++ traceHead :: traceTail) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceHead:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephEq:head = traceHead ∧ tail = traceTail ++ primitiveStep :: suffix⊢ rowPredicate (priorSteps ++ traceHead :: traceTail) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceHead:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephHead:head = traceHeadhTail:tail = traceTail ++ primitiveStep :: suffix⊢ rowPredicate (priorSteps ++ traceHead :: traceTail) primitiveStep rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephTail:tail = traceTail ++ primitiveStep :: suffix⊢ rowPredicate (priorSteps ++ head :: traceTail) primitiveStep have hTailEq : tail = traceTail ++ [primitiveStep] ++ suffix := rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveSteppriorSteps:List PrimitiveGraphStepprimitiveSteps:List PrimitiveGraphStephCheck:primitivePrefixScanCheck rowCheck priorSteps primitiveSteps = true⊢ ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), primitiveSteps = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveStep All goals completed! 🐙 rowCheck:List PrimitiveGraphStep → PrimitiveGraphStep → BoolrowPredicate:List PrimitiveGraphStep → PrimitiveGraphStep → ProprowSound:∀ (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), rowCheck priorSteps primitiveStep = true → rowPredicate priorSteps primitiveStephead:PrimitiveGraphSteptail:List PrimitiveGraphStepih:∀ {priorSteps : List PrimitiveGraphStep}, primitivePrefixScanCheck rowCheck priorSteps tail = true → ∀ (tracePrefix suffix : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep), tail = tracePrefix ++ [primitiveStep] ++ suffix → rowPredicate (priorSteps ++ tracePrefix) primitiveSteppriorSteps:List PrimitiveGraphStephCheck:rowCheck priorSteps head = true ∧ primitivePrefixScanCheck rowCheck (priorSteps ++ [head]) tail = truesuffix:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphSteptraceTail:List PrimitiveGraphStephTail:tail = traceTail ++ primitiveStep :: suffixhTailEq:tail = traceTail ++ [primitiveStep] ++ suffixhTailPredicate:rowPredicate (priorSteps ++ [head] ++ traceTail) primitiveStep⊢ rowPredicate (priorSteps ++ head :: traceTail) primitiveStep All goals completed! 🐙

Row predicate for overlay ledgers being backed by primitive identity rows in prior steps.

def primitiveOverlayLedgersPrefixAvailableAt (priorSteps : List PrimitiveGraphStep) : PrimitiveGraphStep → Prop | PrimitiveGraphStep.empty => True | PrimitiveGraphStep.node _node _entries _exits => True | PrimitiveGraphStep.bindingRef _binding => True | PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings => (∀ node, node ∈ leftNodes ++ rightNodes → node ∈ PrimitiveGraphStep.nodeRowsList priorSteps) ∧ (∀ binding, binding ∈ leftBindings ++ rightBindings → binding ∈ PrimitiveGraphStep.bindingRowsList priorSteps) | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => True

Row checker for overlay ledgers being backed by primitive identity rows in prior steps.

def primitiveOverlayLedgersPrefixStepCheck (priorSteps : List PrimitiveGraphStep) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings => let nodeRows := PrimitiveGraphStep.nodeRowsList priorSteps let bindingRows := PrimitiveGraphStep.bindingRowsList priorSteps Check.allDecide (leftNodes ++ rightNodes) (fun node => node ∈ nodeRows) && Check.allDecide (leftBindings ++ rightBindings) (fun binding => binding ∈ bindingRows) | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => true

Successful row checking proves overlay ledger prefix availability at that row.

theorem primitiveOverlayLedgersPrefixStepCheck_sound (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep) (hCheck : primitiveOverlayLedgersPrefixStepCheck priorSteps primitiveStep = true) : primitiveOverlayLedgersPrefixAvailableAt priorSteps primitiveStep := priorSteps:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps primitiveStep = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps primitiveStep cases primitiveStep with priorSteps:List PrimitiveGraphStephCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps PrimitiveGraphStep.empty = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps PrimitiveGraphStep.empty All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_node:NodeId_entries:List AdmissionBoundaryPort_exits:List AdmissionBoundaryPorthCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps (PrimitiveGraphStep.node _node _entries _exits) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.node _node _entries _exits) All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_binding:BindingNamehCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps (PrimitiveGraphStep.bindingRef _binding) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.bindingRef _binding) All goals completed! 🐙 priorSteps:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings) priorSteps:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(match PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings => have nodeRows := PrimitiveGraphStep.nodeRowsList priorSteps; have bindingRows := PrimitiveGraphStep.bindingRowsList priorSteps; (Check.allDecide (leftNodes ++ rightNodes) fun node => node ∈ nodeRows) && Check.allDecide (leftBindings ++ rightBindings) fun binding => binding ∈ bindingRows | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => true) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings) priorSteps:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehCheck:(Check.allDecide (leftNodes ++ rightNodes) fun node => node ∈ PrimitiveGraphStep.nodeRowsList priorSteps) = true ∧ (Check.allDecide (leftBindings ++ rightBindings) fun binding => binding ∈ PrimitiveGraphStep.bindingRowsList priorSteps) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings) All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:primitiveOverlayLedgersPrefixStepCheck priorSteps (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ primitiveOverlayLedgersPrefixAvailableAt priorSteps (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) All goals completed! 🐙

Executable checker for primitive overlay ledger replay-order availability.

def primitiveOverlayLedgersPrefixAvailableCheck (artifact : WireAdmissionArtifact) : Bool := primitivePrefixScanCheck primitiveOverlayLedgersPrefixStepCheck [] artifact.primitiveSteps

Successful overlay-prefix checking proves PrimitiveOverlayLedgersPrefixAvailable.

theorem primitiveOverlayLedgersPrefixAvailableCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) : artifact.PrimitiveOverlayLedgersPrefixAvailable := artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = true⊢ artifact.PrimitiveOverlayLedgersPrefixAvailable intro tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStep⊢ ∀ (leftNodes rightNodes : List NodeId) (leftBindings rightBindings : List BindingName), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix → (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeId⊢ ∀ (rightNodes : List NodeId) (leftBindings rightBindings : List BindingName), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix → (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeId⊢ ∀ (leftBindings rightBindings : List BindingName), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix → (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingName⊢ ∀ (rightBindings : List BindingName), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix → (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingName⊢ artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix → (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehTrace:artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffix⊢ (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftNodes:List NodeIdrightNodes:List NodeIdleftBindings:List BindingNamerightBindings:List BindingNamehTrace:artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings] ++ suffixhAt:primitiveOverlayLedgersPrefixAvailableAt ([] ++ tracePrefix) (PrimitiveGraphStep.overlay leftNodes rightNodes leftBindings rightBindings)⊢ (∀ node ∈ leftNodes ++ rightNodes, node ∈ PrimitiveGraphStep.nodeRowsList tracePrefix) ∧ ∀ binding ∈ leftBindings ++ rightBindings, binding ∈ PrimitiveGraphStep.bindingRowsList tracePrefix All goals completed! 🐙

Row predicate for connect frontiers being backed by primitive node rows.

def primitiveConnectFrontiersBackedByNodesAt (artifact : WireAdmissionArtifact) : PrimitiveGraphStep → Prop | PrimitiveGraphStep.empty => True | PrimitiveGraphStep.node _node _entries _exits => True | PrimitiveGraphStep.bindingRef _binding => True | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => True | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => (∀ leftExit, leftExit ∈ leftExits → leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ (∀ rightEntry, rightEntry ∈ rightEntries → rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps)

Row checker for connect frontiers being backed by primitive node rows.

def primitiveConnectFrontiersBackedByNodesStepCheck (artifact : WireAdmissionArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => let nodeExitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps let nodeEntryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps Check.allDecide leftExits (fun leftExit => leftExit.key ∈ nodeExitKeys) && Check.allDecide rightEntries (fun rightEntry => rightEntry.key ∈ nodeEntryKeys)

Successful row checking proves connect frontier backing at that row.

theorem primitiveConnectFrontiersBackedByNodesStepCheck_sound {artifact : WireAdmissionArtifact} {primitiveStep : PrimitiveGraphStep} (hCheck : primitiveConnectFrontiersBackedByNodesStepCheck artifact primitiveStep = true) : primitiveConnectFrontiersBackedByNodesAt artifact primitiveStep := artifact:WireAdmissionArtifactprimitiveStep:PrimitiveGraphStephCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck primitiveStep = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt primitiveStep cases primitiveStep with artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck PrimitiveGraphStep.empty = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt PrimitiveGraphStep.empty All goals completed! 🐙 artifact:WireAdmissionArtifact_node:NodeId_entries:List AdmissionBoundaryPort_exits:List AdmissionBoundaryPorthCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck (PrimitiveGraphStep.node _node _entries _exits) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.node _node _entries _exits) All goals completed! 🐙 artifact:WireAdmissionArtifact_binding:BindingNamehCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck (PrimitiveGraphStep.bindingRef _binding) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.bindingRef _binding) All goals completed! 🐙 artifact:WireAdmissionArtifact_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) All goals completed! 🐙 artifact:WireAdmissionArtifact_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:artifact.primitiveConnectFrontiersBackedByNodesStepCheck (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) artifact:WireAdmissionArtifact_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:(match PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => have nodeExitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; have nodeEntryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; (Check.allDecide leftExits fun leftExit => leftExit.key ∈ nodeExitKeys) && Check.allDecide rightEntries fun rightEntry => rightEntry.key ∈ nodeEntryKeys) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) artifact:WireAdmissionArtifact_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:(Check.allDecide _leftExits fun leftExit => leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide _rightEntries fun rightEntry => rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) = true⊢ artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) All goals completed! 🐙

Executable checker for primitive connect frontier node-row backing.

def primitiveConnectFrontiersBackedByNodesCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.primitiveSteps (primitiveConnectFrontiersBackedByNodesStepCheck artifact)

Successful connect-backing checking proves PrimitiveConnectFrontiersBackedByNodes.

theorem primitiveConnectFrontiersBackedByNodesCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.primitiveConnectFrontiersBackedByNodesCheck = true) : artifact.PrimitiveConnectFrontiersBackedByNodes := artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = true⊢ artifact.PrimitiveConnectFrontiersBackedByNodes intro leftExits artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPort⊢ ∀ (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveSteps → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnection⊢ ∀ (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveSteps → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPort⊢ ∀ (unmatchedRightEntries : List AdmissionBoundaryPort), PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveSteps → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPort⊢ PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveSteps → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthStep:PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveSteps⊢ (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersBackedByNodesCheck = trueleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthStep:PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries ∈ artifact.primitiveStepshAt:artifact.primitiveConnectFrontiersBackedByNodesAt (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries)⊢ (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps All goals completed! 🐙

Row predicate for connect frontiers being available and unconsumed in prior steps.

def primitiveConnectFrontiersPrefixAvailableAt (priorSteps : List PrimitiveGraphStep) : PrimitiveGraphStep → Prop | PrimitiveGraphStep.empty => True | PrimitiveGraphStep.node _node _entries _exits => True | PrimitiveGraphStep.bindingRef _binding => True | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => True | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => (∀ leftExit, leftExit ∈ leftExits → leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList priorSteps ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList priorSteps) ∧ (∀ rightEntry, rightEntry ∈ rightEntries → rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList priorSteps ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList priorSteps)

Row checker for connect frontiers being available and unconsumed in prior steps.

def primitiveConnectFrontiersPrefixStepCheck (priorSteps : List PrimitiveGraphStep) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => let availableExits := PrimitiveGraphStep.nodeExitKeysList priorSteps let consumedExits := PrimitiveGraphStep.consumedExitKeysList priorSteps let availableEntries := PrimitiveGraphStep.nodeEntryKeysList priorSteps let consumedEntries := PrimitiveGraphStep.consumedEntryKeysList priorSteps Check.allDecide leftExits (fun leftExit => leftExit.key ∈ availableExits ∧ leftExit.key ∉ consumedExits) && Check.allDecide rightEntries (fun rightEntry => rightEntry.key ∈ availableEntries ∧ rightEntry.key ∉ consumedEntries)

Successful row checking proves connect frontier prefix availability at that row.

theorem primitiveConnectFrontiersPrefixStepCheck_sound (priorSteps : List PrimitiveGraphStep) (primitiveStep : PrimitiveGraphStep) (hCheck : primitiveConnectFrontiersPrefixStepCheck priorSteps primitiveStep = true) : primitiveConnectFrontiersPrefixAvailableAt priorSteps primitiveStep := priorSteps:List PrimitiveGraphStepprimitiveStep:PrimitiveGraphStephCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps primitiveStep = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps primitiveStep cases primitiveStep with priorSteps:List PrimitiveGraphStephCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps PrimitiveGraphStep.empty = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps PrimitiveGraphStep.empty All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_node:NodeId_entries:List AdmissionBoundaryPort_exits:List AdmissionBoundaryPorthCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps (PrimitiveGraphStep.node _node _entries _exits) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.node _node _entries _exits) All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_binding:BindingNamehCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps (PrimitiveGraphStep.bindingRef _binding) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.bindingRef _binding) All goals completed! 🐙 priorSteps:List PrimitiveGraphStep_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) All goals completed! 🐙 priorSteps:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:primitiveConnectFrontiersPrefixStepCheck priorSteps (PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) priorSteps:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:(match PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries with | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.node _node _entries _exits => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => have availableExits := PrimitiveGraphStep.nodeExitKeysList priorSteps; have consumedExits := PrimitiveGraphStep.consumedExitKeysList priorSteps; have availableEntries := PrimitiveGraphStep.nodeEntryKeysList priorSteps; have consumedEntries := PrimitiveGraphStep.consumedEntryKeysList priorSteps; (Check.allDecide leftExits fun leftExit => leftExit.key ∈ availableExits ∧ leftExit.key ∉ consumedExits) && Check.allDecide rightEntries fun rightEntry => rightEntry.key ∈ availableEntries ∧ rightEntry.key ∉ consumedEntries) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) priorSteps:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthCheck:(Check.allDecide leftExits fun leftExit => leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList priorSteps ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList priorSteps) = true ∧ (Check.allDecide rightEntries fun rightEntry => rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList priorSteps ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList priorSteps) = true⊢ primitiveConnectFrontiersPrefixAvailableAt priorSteps (PrimitiveGraphStep.connect leftExits rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) All goals completed! 🐙

Executable checker for primitive connect frontier replay-order availability.

def primitiveConnectFrontiersPrefixAvailableCheck (artifact : WireAdmissionArtifact) : Bool := primitivePrefixScanCheck primitiveConnectFrontiersPrefixStepCheck [] artifact.primitiveSteps

Successful connect-prefix checking proves PrimitiveConnectFrontiersPrefixAvailable.

theorem primitiveConnectFrontiersPrefixAvailableCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) : artifact.PrimitiveConnectFrontiersPrefixAvailable := artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = true⊢ artifact.PrimitiveConnectFrontiersPrefixAvailable intro tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStep⊢ ∀ (leftExits rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPort⊢ ∀ (rightEntries : List AdmissionBoundaryPort) (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPort⊢ ∀ (matchedPairs : List AdmissionConnection) (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnection⊢ ∀ (unmatchedLeftExits unmatchedRightEntries : List AdmissionBoundaryPort), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPort⊢ ∀ (unmatchedRightEntries : List AdmissionBoundaryPort), artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPort⊢ artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix → (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthTrace:artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffix⊢ (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix artifact:WireAdmissionArtifacthCheck:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truetracePrefix:List PrimitiveGraphStepsuffix:List PrimitiveGraphStepleftExits:List AdmissionBoundaryPortrightEntries:List AdmissionBoundaryPortmatchedPairs:List AdmissionConnectionunmatchedLeftExits:List AdmissionBoundaryPortunmatchedRightEntries:List AdmissionBoundaryPorthTrace:artifact.primitiveSteps = tracePrefix ++ [PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries] ++ suffixhAt:primitiveConnectFrontiersPrefixAvailableAt ([] ++ tracePrefix) (PrimitiveGraphStep.connect leftExits rightEntries matchedPairs unmatchedLeftExits unmatchedRightEntries)⊢ (∀ leftExit ∈ leftExits, leftExit.key ∈ PrimitiveGraphStep.nodeExitKeysList tracePrefix ∧ leftExit.key ∉ PrimitiveGraphStep.consumedExitKeysList tracePrefix) ∧ ∀ rightEntry ∈ rightEntries, rightEntry.key ∈ PrimitiveGraphStep.nodeEntryKeysList tracePrefix ∧ rightEntry.key ∉ PrimitiveGraphStep.consumedEntryKeysList tracePrefix All goals completed! 🐙

Generated-Form Row Checks

mutual

Executable checker for serialized static values in generated-form source rows.

def staticValueValidCheck : AdmissionStaticValue → Bool | AdmissionStaticValue.string _value => true | AdmissionStaticValue.bool _value => true | AdmissionStaticValue.nat _value => true | AdmissionStaticValue.list values => staticValueValuesValidCheck values | AdmissionStaticValue.record fields => Check.nodupMapCheck fields Prod.fst && staticValueFieldsValidCheck fields

Executable checker for serialized static-value lists.

def staticValueValuesValidCheck : List AdmissionStaticValue → Bool | [] => true | value :: values => staticValueValidCheck value && staticValueValuesValidCheck values

Executable checker for serialized static record fields.

def staticValueFieldsValidCheck : List (FieldLabel × AdmissionStaticValue) → Bool | [] => true | field :: fields => decide field.fst.Valid && staticValueValidCheck field.snd && staticValueFieldsValidCheck fields endmutual

Successful static-value checking proves AdmissionStaticValue.Valid.

theorem staticValueValidCheck_sound {value : AdmissionStaticValue} (hCheck : staticValueValidCheck value = true) : value.Valid := value:AdmissionStaticValuehCheck:staticValueValidCheck value = true⊢ value.Valid cases value with value:StringhCheck:staticValueValidCheck (AdmissionStaticValue.string value) = true⊢ (AdmissionStaticValue.string value).Valid All goals completed! 🐙 value:BoolhCheck:staticValueValidCheck (AdmissionStaticValue.bool value) = true⊢ (AdmissionStaticValue.bool value).Valid All goals completed! 🐙 value:ℕhCheck:staticValueValidCheck (AdmissionStaticValue.nat value) = true⊢ (AdmissionStaticValue.nat value).Valid All goals completed! 🐙 values:List AdmissionStaticValuehCheck:staticValueValidCheck (AdmissionStaticValue.list values) = true⊢ (AdmissionStaticValue.list values).Valid All goals completed! 🐙 fields:List (FieldLabel × AdmissionStaticValue)hCheck:staticValueValidCheck (AdmissionStaticValue.record fields) = true⊢ (AdmissionStaticValue.record fields).Valid fields:List (FieldLabel × AdmissionStaticValue)hCheck:(Check.nodupMapCheck fields Prod.fst && staticValueFieldsValidCheck fields) = true⊢ (AdmissionStaticValue.record fields).Valid fields:List (FieldLabel × AdmissionStaticValue)hCheck:Check.nodupMapCheck fields Prod.fst = true ∧ staticValueFieldsValidCheck fields = true⊢ (AdmissionStaticValue.record fields).Valid All goals completed! 🐙

Successful static-value-list checking proves AdmissionStaticValue.ValuesValid.

theorem staticValueValuesValidCheck_sound {values : List AdmissionStaticValue} (hCheck : staticValueValuesValidCheck values = true) : AdmissionStaticValue.ValuesValid values := values:List AdmissionStaticValuehCheck:staticValueValuesValidCheck values = true⊢ AdmissionStaticValue.ValuesValid values cases values with hCheck:staticValueValuesValidCheck [] = true⊢ AdmissionStaticValue.ValuesValid [] All goals completed! 🐙 value:AdmissionStaticValuevalues:List AdmissionStaticValuehCheck:staticValueValuesValidCheck (value :: values) = true⊢ AdmissionStaticValue.ValuesValid (value :: values) value:AdmissionStaticValuevalues:List AdmissionStaticValuehCheck:(staticValueValidCheck value && staticValueValuesValidCheck values) = true⊢ AdmissionStaticValue.ValuesValid (value :: values) value:AdmissionStaticValuevalues:List AdmissionStaticValuehCheck:staticValueValidCheck value = true ∧ staticValueValuesValidCheck values = true⊢ AdmissionStaticValue.ValuesValid (value :: values) All goals completed! 🐙

Successful static-field checking proves AdmissionStaticValue.FieldsValid.

theorem staticValueFieldsValidCheck_sound {fields : List (FieldLabel × AdmissionStaticValue)} (hCheck : staticValueFieldsValidCheck fields = true) : AdmissionStaticValue.FieldsValid fields := fields:List (FieldLabel × AdmissionStaticValue)hCheck:staticValueFieldsValidCheck fields = true⊢ AdmissionStaticValue.FieldsValid fields cases fields with hCheck:staticValueFieldsValidCheck [] = true⊢ AdmissionStaticValue.FieldsValid [] All goals completed! 🐙 field:FieldLabel × AdmissionStaticValuefields:List (FieldLabel × AdmissionStaticValue)hCheck:staticValueFieldsValidCheck (field :: fields) = true⊢ AdmissionStaticValue.FieldsValid (field :: fields) cases field with fields:List (FieldLabel × AdmissionStaticValue)label:FieldLabelvalue:AdmissionStaticValuehCheck:staticValueFieldsValidCheck ((label, value) :: fields) = true⊢ AdmissionStaticValue.FieldsValid ((label, value) :: fields) fields:List (FieldLabel × AdmissionStaticValue)label:FieldLabelvalue:AdmissionStaticValuehCheck:(decide (label, value).1.Valid && staticValueValidCheck (label, value).2 && staticValueFieldsValidCheck fields) = true⊢ AdmissionStaticValue.FieldsValid ((label, value) :: fields) fields:List (FieldLabel × AdmissionStaticValue)label:FieldLabelvalue:AdmissionStaticValuehCheck:(decide label.Valid = true ∧ staticValueValidCheck value = true) ∧ staticValueFieldsValidCheck fields = true⊢ AdmissionStaticValue.FieldsValid ((label, value) :: fields) fields:List (FieldLabel × AdmissionStaticValue)label:FieldLabelvalue:AdmissionStaticValuehFields:staticValueFieldsValidCheck fields = truehLabel:decide label.Valid = truehValue:staticValueValidCheck value = true⊢ AdmissionStaticValue.FieldsValid ((label, value) :: fields) All goals completed! 🐙 end

Executable checker for optional static payloads on generated source children.

def generatedChildSourceStaticValueValidCheck (child : GeneratedChildSourceArtifact) : Bool := match child.value with | none => true | some value => staticValueValidCheck value

Successful optional-payload checking proves source-child static payload validity.

theorem generatedChildSourceStaticValueValidCheck_sound {child : GeneratedChildSourceArtifact} (hCheck : generatedChildSourceStaticValueValidCheck child = true) : child.StaticValueValid := child:GeneratedChildSourceArtifacthCheck:generatedChildSourceStaticValueValidCheck child = true⊢ child.StaticValueValid cases hValue : child.value with child:GeneratedChildSourceArtifacthCheck:generatedChildSourceStaticValueValidCheck child = truehValue:child.value = none⊢ child.StaticValueValid All goals completed! 🐙 child:GeneratedChildSourceArtifacthCheck:generatedChildSourceStaticValueValidCheck child = truevalue:AdmissionStaticValuehValue:child.value = some value⊢ child.StaticValueValid have hValueCheck : staticValueValidCheck value = true := child:GeneratedChildSourceArtifacthCheck:generatedChildSourceStaticValueValidCheck child = true⊢ child.StaticValueValid All goals completed! 🐙 All goals completed! 🐙

Executable checker for source generated-child row validity.

def generatedChildSourceValidCheck (child : GeneratedChildSourceArtifact) : Bool := decide child.node.Valid && decide child.label.Valid && generatedChildSourceStaticValueValidCheck child

Successful source-child checking proves GeneratedChildSourceArtifact.Valid.

theorem generatedChildSourceValidCheck_sound {child : GeneratedChildSourceArtifact} (hCheck : generatedChildSourceValidCheck child = true) : child.Valid := child:GeneratedChildSourceArtifacthCheck:generatedChildSourceValidCheck child = true⊢ child.Valid child:GeneratedChildSourceArtifacthCheck:(decide child.node.Valid && decide child.label.Valid && generatedChildSourceStaticValueValidCheck child) = true⊢ child.Valid child:GeneratedChildSourceArtifacthCheck:(decide child.node.Valid = true ∧ decide child.label.Valid = true) ∧ generatedChildSourceStaticValueValidCheck child = true⊢ child.Valid child:GeneratedChildSourceArtifacthStatic:generatedChildSourceStaticValueValidCheck child = truehNode:decide child.node.Valid = truehLabel:decide child.label.Valid = true⊢ child.Valid All goals completed! 🐙

Executable checker that generated-child frontiers are owned by the child node.

def generatedChildFrontiersOwnedCheck (child : GeneratedChildArtifact) : Bool := Check.allDecide child.outputs (fun output => output.node = child.node) && Check.allDecide child.inputs (fun input => input.node = child.node)

Successful generated-child frontier ownership proves FrontiersOwnedByChild.

theorem generatedChildFrontiersOwnedCheck_sound {child : GeneratedChildArtifact} (hCheck : generatedChildFrontiersOwnedCheck child = true) : child.FrontiersOwnedByChild := child:GeneratedChildArtifacthCheck:generatedChildFrontiersOwnedCheck child = true⊢ child.FrontiersOwnedByChild child:GeneratedChildArtifacthCheck:((Check.allDecide child.outputs fun output => output.node = child.node) && Check.allDecide child.inputs fun input => input.node = child.node) = true⊢ child.FrontiersOwnedByChild child:GeneratedChildArtifacthCheck:(Check.allDecide child.outputs fun output => output.node = child.node) = true ∧ (Check.allDecide child.inputs fun input => input.node = child.node) = true⊢ child.FrontiersOwnedByChild All goals completed! 🐙

Executable checker that generated-child frontier keys are unique per direction.

def generatedChildFrontierKeysUniqueCheck (child : GeneratedChildArtifact) : Bool := Check.nodupMapCheck child.outputs AdmissionBoundaryPort.key && Check.nodupMapCheck child.inputs AdmissionBoundaryPort.key

Successful generated-child frontier uniqueness proves FrontierKeysUnique.

theorem generatedChildFrontierKeysUniqueCheck_sound {child : GeneratedChildArtifact} (hCheck : generatedChildFrontierKeysUniqueCheck child = true) : child.FrontierKeysUnique := child:GeneratedChildArtifacthCheck:generatedChildFrontierKeysUniqueCheck child = true⊢ child.FrontierKeysUnique child:GeneratedChildArtifacthCheck:(Check.nodupMapCheck child.outputs AdmissionBoundaryPort.key && Check.nodupMapCheck child.inputs AdmissionBoundaryPort.key) = true⊢ child.FrontierKeysUnique child:GeneratedChildArtifacthCheck:Check.nodupMapCheck child.outputs AdmissionBoundaryPort.key = true ∧ Check.nodupMapCheck child.inputs AdmissionBoundaryPort.key = true⊢ child.FrontierKeysUnique All goals completed! 🐙

Executable checker for used generated-child row validity.

def generatedChildValidCheck (child : GeneratedChildArtifact) : Bool := decide child.node.Valid && decide child.label.Valid && generatedChildFrontiersOwnedCheck child && generatedChildFrontierKeysUniqueCheck child && AdmissionArtifactCheck.boundaryPortsValidCheck child.outputs && AdmissionArtifactCheck.boundaryPortsValidCheck child.inputs

Successful used-child checking proves GeneratedChildArtifact.Valid.

theorem generatedChildValidCheck_sound {child : GeneratedChildArtifact} (hCheck : generatedChildValidCheck child = true) : child.Valid := child:GeneratedChildArtifacthCheck:generatedChildValidCheck child = true⊢ child.Valid child:GeneratedChildArtifacthCheck:(decide child.node.Valid && decide child.label.Valid && generatedChildFrontiersOwnedCheck child && generatedChildFrontierKeysUniqueCheck child && AdmissionArtifactCheck.boundaryPortsValidCheck child.outputs && AdmissionArtifactCheck.boundaryPortsValidCheck child.inputs) = true⊢ child.Valid child:GeneratedChildArtifacthCheck:((((decide child.node.Valid = true ∧ decide child.label.Valid = true) ∧ generatedChildFrontiersOwnedCheck child = true) ∧ generatedChildFrontierKeysUniqueCheck child = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck child.outputs = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck child.inputs = true⊢ child.Valid child:GeneratedChildArtifacthInputs:AdmissionArtifactCheck.boundaryPortsValidCheck child.inputs = truehOutputs:AdmissionArtifactCheck.boundaryPortsValidCheck child.outputs = truehUnique:generatedChildFrontierKeysUniqueCheck child = truehOwned:generatedChildFrontiersOwnedCheck child = truehNode:decide child.node.Valid = truehLabel:decide child.label.Valid = true⊢ child.Valid All goals completed! 🐙

Executable checker for used generated-child domain closure.

def generatedChildDomainClosedCheck (nodes : List NodeId) (child : GeneratedChildArtifact) : Bool := Check.memCheck child.node nodes && boundaryPortsClosedCheck nodes child.outputs && boundaryPortsClosedCheck nodes child.inputs

Successful used-child closure checking proves GeneratedChildArtifact.DomainClosed.

theorem generatedChildDomainClosedCheck_sound {nodes : List NodeId} {child : GeneratedChildArtifact} (hCheck : generatedChildDomainClosedCheck nodes child = true) : child.DomainClosed nodes := nodes:List NodeIdchild:GeneratedChildArtifacthCheck:generatedChildDomainClosedCheck nodes child = true⊢ GeneratedChildArtifact.DomainClosed nodes child nodes:List NodeIdchild:GeneratedChildArtifacthCheck:(Check.memCheck child.node nodes && boundaryPortsClosedCheck nodes child.outputs && boundaryPortsClosedCheck nodes child.inputs) = true⊢ GeneratedChildArtifact.DomainClosed nodes child nodes:List NodeIdchild:GeneratedChildArtifacthCheck:(Check.memCheck child.node nodes = true ∧ boundaryPortsClosedCheck nodes child.outputs = true) ∧ boundaryPortsClosedCheck nodes child.inputs = true⊢ GeneratedChildArtifact.DomainClosed nodes child nodes:List NodeIdchild:GeneratedChildArtifacthInputs:boundaryPortsClosedCheck nodes child.inputs = truehNode:Check.memCheck child.node nodes = truehOutputs:boundaryPortsClosedCheck nodes child.outputs = true⊢ GeneratedChildArtifact.DomainClosed nodes child All goals completed! 🐙

Executable checker that used generated children are backed by source rows.

def generatedUsedChildrenFromSourceCheck (artifact : GeneratedFormArtifact) : Bool := Check.allDecide artifact.usedChildren fun child => child.key ∈ artifact.sourceChildKeys

Successful source-backing checking proves UsedChildrenFromSource.

theorem generatedUsedChildrenFromSourceCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedUsedChildrenFromSourceCheck artifact = true) : artifact.UsedChildrenFromSource := Check.allDecide_sound hCheck

Executable checker that generated child names follow the binding/label policy.

def generatedChildrenOwnedByBindingCheck (artifact : GeneratedFormArtifact) : Bool := Check.allDecide artifact.sourceChildren (fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label) && Check.allDecide artifact.usedChildren (fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label)

Successful generated-name checking proves ChildrenOwnedByBinding.

theorem generatedChildrenOwnedByBindingCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedChildrenOwnedByBindingCheck artifact = true) : artifact.ChildrenOwnedByBinding := artifact:GeneratedFormArtifacthCheck:generatedChildrenOwnedByBindingCheck artifact = true⊢ artifact.ChildrenOwnedByBinding artifact:GeneratedFormArtifacthCheck:((Check.allDecide artifact.sourceChildren fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label) && Check.allDecide artifact.usedChildren fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label) = true⊢ artifact.ChildrenOwnedByBinding artifact:GeneratedFormArtifacthCheck:(Check.allDecide artifact.sourceChildren fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label) = true ∧ (Check.allDecide artifact.usedChildren fun child => child.node = GeneratedFormArtifact.childNodeFor artifact.binding child.label) = true⊢ artifact.ChildrenOwnedByBinding All goals completed! 🐙

Executable checker that source and used generated child keys are duplicate-free.

def generatedChildKeysUniqueCheck (artifact : GeneratedFormArtifact) : Bool := Check.nodupCheck artifact.sourceChildKeys && Check.nodupCheck artifact.usedChildKeys

Successful generated-key checking proves ChildKeysUnique.

theorem generatedChildKeysUniqueCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedChildKeysUniqueCheck artifact = true) : artifact.ChildKeysUnique := artifact:GeneratedFormArtifacthCheck:generatedChildKeysUniqueCheck artifact = true⊢ artifact.ChildKeysUnique artifact:GeneratedFormArtifacthCheck:(Check.nodupCheck artifact.sourceChildKeys && Check.nodupCheck artifact.usedChildKeys) = true⊢ artifact.ChildKeysUnique artifact:GeneratedFormArtifacthCheck:Check.nodupCheck artifact.sourceChildKeys = true ∧ Check.nodupCheck artifact.usedChildKeys = true⊢ artifact.ChildKeysUnique All goals completed! 🐙

Executable checker that every generated source payload is structurally valid.

def generatedSourceValuesValidCheck (artifact : GeneratedFormArtifact) : Bool := Check.allBool artifact.sourceChildren generatedChildSourceStaticValueValidCheck

Successful generated source-payload checking proves SourceValuesValid.

theorem generatedSourceValuesValidCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedSourceValuesValidCheck artifact = true) : artifact.SourceValuesValid := Check.allBool_sound hCheck (fun _child _ hChild => generatedChildSourceStaticValueValidCheck_sound hChild)

Executable checker that make source labels are canonical.

def makeSourceLabelsCanonicalCheck (artifact : GeneratedFormArtifact) : Bool := decide (artifact.sourceLabels = (List.range artifact.sourceChildren.length).map (fun index => ⟨toString index⟩))

Successful canonical-label checking proves MakeSourceLabelsCanonical.

theorem makeSourceLabelsCanonicalCheck_sound {artifact : GeneratedFormArtifact} (hCheck : makeSourceLabelsCanonicalCheck artifact = true) : artifact.MakeSourceLabelsCanonical := artifact:GeneratedFormArtifacthCheck:makeSourceLabelsCanonicalCheck artifact = true⊢ artifact.MakeSourceLabelsCanonical artifact:GeneratedFormArtifacthCheck:makeSourceLabelsCanonicalCheck artifact = true⊢ artifact.sourceLabels = List.map (fun index => { name := toString index }) (List.range artifact.sourceChildren.length) All goals completed! 🐙

Executable checker that a source child carries no static payload.

def generatedSourceValueEmptyCheck (child : GeneratedChildSourceArtifact) : Bool := match child.value with | none => true | some _value => false

Successful empty-payload checking proves the child payload is absent.

theorem generatedSourceValueEmptyCheck_sound {child : GeneratedChildSourceArtifact} (hCheck : generatedSourceValueEmptyCheck child = true) : child.value = none := child:GeneratedChildSourceArtifacthCheck:generatedSourceValueEmptyCheck child = true⊢ child.value = none cases hValue : child.value with child:GeneratedChildSourceArtifacthCheck:generatedSourceValueEmptyCheck child = truehValue:child.value = none⊢ none = none All goals completed! 🐙 child:GeneratedChildSourceArtifacthCheck:generatedSourceValueEmptyCheck child = truevalue:AdmissionStaticValuehValue:child.value = some value⊢ some value = none All goals completed! 🐙

Executable checker that all source children carry no static payload.

def makeSourceValuesEmptyCheck (artifact : GeneratedFormArtifact) : Bool := Check.allBool artifact.sourceChildren generatedSourceValueEmptyCheck

Successful empty-payload-list checking proves MakeSourceValuesEmpty.

theorem makeSourceValuesEmptyCheck_sound {artifact : GeneratedFormArtifact} (hCheck : makeSourceValuesEmptyCheck artifact = true) : artifact.MakeSourceValuesEmpty := Check.allBool_sound hCheck (fun _child _ hChild => generatedSourceValueEmptyCheck_sound hChild)

Executable checker that generated-form payload shape matches its source form.

def generatedKindShapeMatchesCheck (artifact : GeneratedFormArtifact) : Bool := match artifact.kind with | GeneratedFormKind.make => makeSourceLabelsCanonicalCheck artifact && makeSourceValuesEmptyCheck artifact | GeneratedFormKind.makeEach => true

Successful generated-kind-shape checking proves KindShapeMatches.

theorem generatedKindShapeMatchesCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedKindShapeMatchesCheck artifact = true) : artifact.KindShapeMatches := artifact:GeneratedFormArtifacthCheck:generatedKindShapeMatchesCheck artifact = true⊢ artifact.KindShapeMatches cases hKind : artifact.kind with artifact:GeneratedFormArtifacthCheck:generatedKindShapeMatchesCheck artifact = truehKind:artifact.kind = GeneratedFormKind.make⊢ artifact.KindShapeMatches artifact:GeneratedFormArtifacthCheck:(match artifact.kind with | GeneratedFormKind.make => makeSourceLabelsCanonicalCheck artifact && makeSourceValuesEmptyCheck artifact | GeneratedFormKind.makeEach => true) = truehKind:artifact.kind = GeneratedFormKind.make⊢ artifact.KindShapeMatches artifact:GeneratedFormArtifacthCheck:(match GeneratedFormKind.make with | GeneratedFormKind.make => makeSourceLabelsCanonicalCheck artifact && makeSourceValuesEmptyCheck artifact | GeneratedFormKind.makeEach => true) = truehKind:artifact.kind = GeneratedFormKind.make⊢ artifact.KindShapeMatches artifact:GeneratedFormArtifacthCheck:makeSourceLabelsCanonicalCheck artifact = true ∧ makeSourceValuesEmptyCheck artifact = truehKind:artifact.kind = GeneratedFormKind.make⊢ artifact.KindShapeMatches artifact:GeneratedFormArtifacthCheck:makeSourceLabelsCanonicalCheck artifact = true ∧ makeSourceValuesEmptyCheck artifact = truehKind:artifact.kind = GeneratedFormKind.make⊢ match artifact.kind with | GeneratedFormKind.make => artifact.MakeSourceLabelsCanonical ∧ artifact.MakeSourceValuesEmpty | GeneratedFormKind.makeEach => True artifact:GeneratedFormArtifacthCheck:makeSourceLabelsCanonicalCheck artifact = true ∧ makeSourceValuesEmptyCheck artifact = truehKind:artifact.kind = GeneratedFormKind.make⊢ match GeneratedFormKind.make with | GeneratedFormKind.make => artifact.MakeSourceLabelsCanonical ∧ artifact.MakeSourceValuesEmpty | GeneratedFormKind.makeEach => True All goals completed! 🐙 artifact:GeneratedFormArtifacthCheck:generatedKindShapeMatchesCheck artifact = truehKind:artifact.kind = GeneratedFormKind.makeEach⊢ artifact.KindShapeMatches artifact:GeneratedFormArtifacthCheck:generatedKindShapeMatchesCheck artifact = truehKind:artifact.kind = GeneratedFormKind.makeEach⊢ match artifact.kind with | GeneratedFormKind.make => artifact.MakeSourceLabelsCanonical ∧ artifact.MakeSourceValuesEmpty | GeneratedFormKind.makeEach => True artifact:GeneratedFormArtifacthCheck:generatedKindShapeMatchesCheck artifact = truehKind:artifact.kind = GeneratedFormKind.makeEach⊢ match GeneratedFormKind.makeEach with | GeneratedFormKind.make => artifact.MakeSourceLabelsCanonical ∧ artifact.MakeSourceValuesEmpty | GeneratedFormKind.makeEach => True All goals completed! 🐙

Executable checker for generated-form row-local facts.

def generatedFormRowsValidCheck (artifact : GeneratedFormArtifact) : Bool := decide artifact.kindName.Valid && decide artifact.binding.Valid && Check.allBool artifact.sourceChildren generatedChildSourceValidCheck && Check.allBool artifact.usedChildren generatedChildValidCheck

Successful generated-form row checking proves GeneratedFormArtifact.RowsValid.

theorem generatedFormRowsValidCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedFormRowsValidCheck artifact = true) : artifact.RowsValid := artifact:GeneratedFormArtifacthCheck:generatedFormRowsValidCheck artifact = true⊢ artifact.RowsValid artifact:GeneratedFormArtifacthCheck:(decide artifact.kindName.Valid && decide artifact.binding.Valid && Check.allBool artifact.sourceChildren generatedChildSourceValidCheck && Check.allBool artifact.usedChildren generatedChildValidCheck) = true⊢ artifact.RowsValid artifact:GeneratedFormArtifacthCheck:((decide artifact.kindName.Valid = true ∧ decide artifact.binding.Valid = true) ∧ Check.allBool artifact.sourceChildren generatedChildSourceValidCheck = true) ∧ Check.allBool artifact.usedChildren generatedChildValidCheck = true⊢ artifact.RowsValid artifact:GeneratedFormArtifacthUsedChildren:Check.allBool artifact.usedChildren generatedChildValidCheck = truehSourceChildren:Check.allBool artifact.sourceChildren generatedChildSourceValidCheck = truehKind:decide artifact.kindName.Valid = truehBinding:decide artifact.binding.Valid = true⊢ artifact.RowsValid All goals completed! 🐙

Executable checker for one generated-form artifact.

def generatedFormValidCheck (artifact : GeneratedFormArtifact) : Bool := generatedUsedChildrenFromSourceCheck artifact && generatedChildrenOwnedByBindingCheck artifact && generatedChildKeysUniqueCheck artifact && generatedSourceValuesValidCheck artifact && generatedKindShapeMatchesCheck artifact && generatedFormRowsValidCheck artifact

Successful generated-form checking proves GeneratedFormArtifact.Valid.

theorem generatedFormValidCheck_sound {artifact : GeneratedFormArtifact} (hCheck : generatedFormValidCheck artifact = true) : artifact.Valid := artifact:GeneratedFormArtifacthCheck:generatedFormValidCheck artifact = true⊢ artifact.Valid artifact:GeneratedFormArtifacthCheck:(generatedUsedChildrenFromSourceCheck artifact && generatedChildrenOwnedByBindingCheck artifact && generatedChildKeysUniqueCheck artifact && generatedSourceValuesValidCheck artifact && generatedKindShapeMatchesCheck artifact && generatedFormRowsValidCheck artifact) = true⊢ artifact.Valid artifact:GeneratedFormArtifacthCheck:((((generatedUsedChildrenFromSourceCheck artifact = true ∧ generatedChildrenOwnedByBindingCheck artifact = true) ∧ generatedChildKeysUniqueCheck artifact = true) ∧ generatedSourceValuesValidCheck artifact = true) ∧ generatedKindShapeMatchesCheck artifact = true) ∧ generatedFormRowsValidCheck artifact = true⊢ artifact.Valid artifact:GeneratedFormArtifacthRows:generatedFormRowsValidCheck artifact = truehShape:generatedKindShapeMatchesCheck artifact = truehValues:generatedSourceValuesValidCheck artifact = truehUnique:generatedChildKeysUniqueCheck artifact = truehSource:generatedUsedChildrenFromSourceCheck artifact = truehOwned:generatedChildrenOwnedByBindingCheck artifact = true⊢ artifact.Valid All goals completed! 🐙

Executable checker for generated-form domain closure over the top-level node summary.

def generatedFormDomainClosedCheck (nodes : List NodeId) (artifact : GeneratedFormArtifact) : Bool := Check.allBool artifact.usedChildren (generatedChildDomainClosedCheck nodes)

Successful generated-form closure checking proves GeneratedFormArtifact.DomainClosed.

theorem generatedFormDomainClosedCheck_sound {nodes : List NodeId} {artifact : GeneratedFormArtifact} (hCheck : generatedFormDomainClosedCheck nodes artifact = true) : artifact.DomainClosed nodes := Check.allBool_sound hCheck (fun _child _ hChild => generatedChildDomainClosedCheck_sound hChild)

Executable checker that a generated-form row is anchored by used children or an empty binding.

def generatedFormReferencedCheck (bindingRefs : List BindingName) (artifact : GeneratedFormArtifact) : Bool := match artifact.usedChildren with | _child :: _children => true | [] => match artifact.sourceChildren with | [] => Check.memCheck artifact.binding bindingRefs | _source :: _sources => false

Successful generated-form reference checking proves the row is replay-addressable.

theorem generatedFormReferencedCheck_sound {bindingRefs : List BindingName} {artifact : GeneratedFormArtifact} (hCheck : generatedFormReferencedCheck bindingRefs artifact = true) : artifact.usedChildren ≠ [] ∨ (artifact.sourceChildren = [] ∧ artifact.binding ∈ bindingRefs) := bindingRefs:List BindingNameartifact:GeneratedFormArtifacthCheck:generatedFormReferencedCheck bindingRefs artifact = true⊢ artifact.usedChildren ≠ [] ∨ artifact.sourceChildren = [] ∧ artifact.binding ∈ bindingRefs bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesourceChildren:List GeneratedChildSourceArtifactusedChildren:List GeneratedChildArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := usedChildren } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := usedChildren }.usedChildren ≠ [] ∨ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := usedChildren }.sourceChildren = [] ∧ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := usedChildren }.binding ∈ bindingRefs cases usedChildren with bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesourceChildren:List GeneratedChildSourceArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := [] } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := [] }.usedChildren ≠ [] ∨ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := [] }.sourceChildren = [] ∧ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := [] }.binding ∈ bindingRefs cases sourceChildren with bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamehCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := [], usedChildren := [] } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := [], usedChildren := [] }.usedChildren ≠ [] ∨ { kind := kind, kindName := kindName, binding := binding, sourceChildren := [], usedChildren := [] }.sourceChildren = [] ∧ { kind := kind, kindName := kindName, binding := binding, sourceChildren := [], usedChildren := [] }.binding ∈ bindingRefs have hBinding : Check.memCheck binding bindingRefs = true := bindingRefs:List BindingNameartifact:GeneratedFormArtifacthCheck:generatedFormReferencedCheck bindingRefs artifact = true⊢ artifact.usedChildren ≠ [] ∨ artifact.sourceChildren = [] ∧ artifact.binding ∈ bindingRefs All goals completed! 🐙 All goals completed! 🐙 bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesource:GeneratedChildSourceArtifactsources:List GeneratedChildSourceArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := source :: sources, usedChildren := [] } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := source :: sources, usedChildren := [] }.usedChildren ≠ [] ∨ { kind := kind, kindName := kindName, binding := binding, sourceChildren := source :: sources, usedChildren := [] }.sourceChildren = [] ∧ { kind := kind, kindName := kindName, binding := binding, sourceChildren := source :: sources, usedChildren := [] }.binding ∈ bindingRefs All goals completed! 🐙 bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesourceChildren:List GeneratedChildSourceArtifactchild:GeneratedChildArtifactchildren:List GeneratedChildArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children }.usedChildren ≠ [] ∨ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children }.sourceChildren = [] ∧ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children }.binding ∈ bindingRefs exact Or.inl (bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesourceChildren:List GeneratedChildSourceArtifactchild:GeneratedChildArtifactchildren:List GeneratedChildArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children } = true⊢ { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children }.usedChildren ≠ [] bindingRefs:List BindingNamekind:GeneratedFormKindkindName:KindNamebinding:BindingNamesourceChildren:List GeneratedChildSourceArtifactchild:GeneratedChildArtifactchildren:List GeneratedChildArtifacthCheck:generatedFormReferencedCheck bindingRefs { kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children } = truehEmpty:{ kind := kind, kindName := kindName, binding := binding, sourceChildren := sourceChildren, usedChildren := child :: children }.usedChildren = []⊢ False; All goals completed! 🐙)

Phantom Adapter Row Checks

Executable checker for duplicate-free record field labels in product-shape rows.

def productShapeFieldLabelsUniqueCheck (shape : ProductShapeArtifact) : Bool := match shape with | ProductShapeArtifact.record _contract fields => Check.nodupMapCheck fields Prod.fst | ProductShapeArtifact.indexed _element _count => true

Successful product field-label checking proves ProductShapeArtifact.FieldLabelsUnique.

theorem productShapeFieldLabelsUniqueCheck_sound {shape : ProductShapeArtifact} (hCheck : productShapeFieldLabelsUniqueCheck shape = true) : shape.FieldLabelsUnique := shape:ProductShapeArtifacthCheck:productShapeFieldLabelsUniqueCheck shape = true⊢ shape.FieldLabelsUnique cases shape with contract:ContractIdfields:List (FieldLabel × ContractId)hCheck:productShapeFieldLabelsUniqueCheck (ProductShapeArtifact.record contract fields) = true⊢ (ProductShapeArtifact.record contract fields).FieldLabelsUnique All goals completed! 🐙 element:ContractIdcount:ℕhCheck:productShapeFieldLabelsUniqueCheck (ProductShapeArtifact.indexed element count) = true⊢ (ProductShapeArtifact.indexed element count).FieldLabelsUnique All goals completed! 🐙

Executable checker for product-shape contract and field-row validity.

def productShapeRowsValidCheck (shape : ProductShapeArtifact) : Bool := match shape with | ProductShapeArtifact.record contract fields => decide contract.Valid && Check.allDecide fields (fun field => field.fst.Valid ∧ field.snd.Valid) | ProductShapeArtifact.indexed element _count => decide element.Valid

Successful product row checking proves ProductShapeArtifact.RowsValid.

theorem productShapeRowsValidCheck_sound {shape : ProductShapeArtifact} (hCheck : productShapeRowsValidCheck shape = true) : shape.RowsValid := shape:ProductShapeArtifacthCheck:productShapeRowsValidCheck shape = true⊢ shape.RowsValid cases shape with contract:ContractIdfields:List (FieldLabel × ContractId)hCheck:productShapeRowsValidCheck (ProductShapeArtifact.record contract fields) = true⊢ (ProductShapeArtifact.record contract fields).RowsValid contract:ContractIdfields:List (FieldLabel × ContractId)hCheck:(match ProductShapeArtifact.record contract fields with | ProductShapeArtifact.record contract fields => decide contract.Valid && Check.allDecide fields fun field => field.1.Valid ∧ field.2.Valid | ProductShapeArtifact.indexed element _count => decide element.Valid) = true⊢ (ProductShapeArtifact.record contract fields).RowsValid contract:ContractIdfields:List (FieldLabel × ContractId)hCheck:decide contract.Valid = true ∧ (Check.allDecide fields fun field => field.1.Valid ∧ field.2.Valid) = true⊢ (ProductShapeArtifact.record contract fields).RowsValid All goals completed! 🐙 element:ContractIdcount:ℕhCheck:productShapeRowsValidCheck (ProductShapeArtifact.indexed element count) = true⊢ (ProductShapeArtifact.indexed element count).RowsValid element:ContractIdcount:ℕhCheck:productShapeRowsValidCheck (ProductShapeArtifact.indexed element count) = true⊢ element.Valid All goals completed! 🐙

Executable checker that indexed product elements are not serialized nested products.

def productShapeIndexedElementNominalCheck (shape : ProductShapeArtifact) : Bool := match shape with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed element _count => decide (element.name.startsWith "[" = false)

Successful nested-product rejection proves ProductShapeArtifact.IndexedElementNominal.

theorem productShapeIndexedElementNominalCheck_sound {shape : ProductShapeArtifact} (hCheck : productShapeIndexedElementNominalCheck shape = true) : shape.IndexedElementNominal := shape:ProductShapeArtifacthCheck:productShapeIndexedElementNominalCheck shape = true⊢ shape.IndexedElementNominal cases shape with contract:ContractIdfields:List (FieldLabel × ContractId)hCheck:productShapeIndexedElementNominalCheck (ProductShapeArtifact.record contract fields) = true⊢ (ProductShapeArtifact.record contract fields).IndexedElementNominal All goals completed! 🐙 element:ContractIdcount:ℕhCheck:productShapeIndexedElementNominalCheck (ProductShapeArtifact.indexed element count) = true⊢ (ProductShapeArtifact.indexed element count).IndexedElementNominal element:ContractIdcount:ℕhCheck:productShapeIndexedElementNominalCheck (ProductShapeArtifact.indexed element count) = true⊢ element.name.startsWith "[" = false All goals completed! 🐙

Executable checker for serialized product-shape validity.

def productShapeValidCheck (shape : ProductShapeArtifact) : Bool := productShapeFieldLabelsUniqueCheck shape && productShapeRowsValidCheck shape && productShapeIndexedElementNominalCheck shape

Successful product-shape checking proves ProductShapeArtifact.Valid.

theorem productShapeValidCheck_sound {shape : ProductShapeArtifact} (hCheck : productShapeValidCheck shape = true) : shape.Valid := shape:ProductShapeArtifacthCheck:productShapeValidCheck shape = true⊢ shape.Valid shape:ProductShapeArtifacthCheck:(productShapeFieldLabelsUniqueCheck shape && productShapeRowsValidCheck shape && productShapeIndexedElementNominalCheck shape) = true⊢ shape.Valid shape:ProductShapeArtifacthCheck:(productShapeFieldLabelsUniqueCheck shape = true ∧ productShapeRowsValidCheck shape = true) ∧ productShapeIndexedElementNominalCheck shape = true⊢ shape.Valid shape:ProductShapeArtifacthNominal:productShapeIndexedElementNominalCheck shape = truehFields:productShapeFieldLabelsUniqueCheck shape = truehRows:productShapeRowsValidCheck shape = true⊢ shape.Valid All goals completed! 🐙

Executable checker that multi-side boundaries match the serialized product shape.

def productShapeBoundariesMatchCheck (shape : ProductShapeArtifact) (multi : List AdmissionBoundaryPort) : Bool := match shape with | ProductShapeArtifact.record _contract fields => Check.permCheck (multi.filterMap AdmissionBoundaryPort.recordField) fields | ProductShapeArtifact.indexed element _count => Check.allDecide multi (fun boundary => boundary.contract = element)

Successful multi-side boundary checking proves ProductShapeArtifact.BoundariesMatch.

theorem productShapeBoundariesMatchCheck_sound {shape : ProductShapeArtifact} {multi : List AdmissionBoundaryPort} (hCheck : productShapeBoundariesMatchCheck shape multi = true) : shape.BoundariesMatch multi := shape:ProductShapeArtifactmulti:List AdmissionBoundaryPorthCheck:productShapeBoundariesMatchCheck shape multi = true⊢ shape.BoundariesMatch multi cases shape with multi:List AdmissionBoundaryPortcontract:ContractIdfields:List (FieldLabel × ContractId)hCheck:productShapeBoundariesMatchCheck (ProductShapeArtifact.record contract fields) multi = true⊢ (ProductShapeArtifact.record contract fields).BoundariesMatch multi All goals completed! 🐙 multi:List AdmissionBoundaryPortelement:ContractIdcount:ℕhCheck:productShapeBoundariesMatchCheck (ProductShapeArtifact.indexed element count) multi = true⊢ (ProductShapeArtifact.indexed element count).BoundariesMatch multi All goals completed! 🐙

Executable checker that a phantom row's multi-side length matches its product arity.

def phantomProductArityMatchesCheck (artifact : PhantomAdapterArtifact) : Bool := decide (artifact.multi.length = artifact.productShape.arity)

Successful arity checking proves ProductArityMatches.

theorem phantomProductArityMatchesCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomProductArityMatchesCheck artifact = true) : artifact.ProductArityMatches := artifact:PhantomAdapterArtifacthCheck:phantomProductArityMatchesCheck artifact = true⊢ artifact.ProductArityMatches artifact:PhantomAdapterArtifacthCheck:phantomProductArityMatchesCheck artifact = true⊢ artifact.multi.length = artifact.productShape.arity All goals completed! 🐙

Executable checker that a phantom row's multi-side boundary matches its product shape.

def phantomProductShapeMatchesMultiCheck (artifact : PhantomAdapterArtifact) : Bool := productShapeBoundariesMatchCheck artifact.productShape artifact.multi

Successful multi-side shape checking proves ProductShapeMatchesMulti.

theorem phantomProductShapeMatchesMultiCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomProductShapeMatchesMultiCheck artifact = true) : artifact.ProductShapeMatchesMulti := productShapeBoundariesMatchCheck_sound hCheck

Executable checker that the singular endpoint uses the aggregate product contract.

def phantomProductContractMatchesSingularCheck (artifact : PhantomAdapterArtifact) : Bool := decide (artifact.singular.contract = artifact.productShape.contract)

Successful singular-contract checking proves ProductContractMatchesSingular.

theorem phantomProductContractMatchesSingularCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomProductContractMatchesSingularCheck artifact = true) : artifact.ProductContractMatchesSingular := artifact:PhantomAdapterArtifacthCheck:phantomProductContractMatchesSingularCheck artifact = true⊢ artifact.ProductContractMatchesSingular artifact:PhantomAdapterArtifacthCheck:phantomProductContractMatchesSingularCheck artifact = true⊢ artifact.singular.contract = artifact.productShape.contract All goals completed! 🐙

Executable checker that source-visible multi-side endpoints are duplicate-free.

def phantomMultiEndpointKeysUniqueCheck (artifact : PhantomAdapterArtifact) : Bool := Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.key

Successful multi-endpoint checking proves MultiEndpointKeysUnique.

theorem phantomMultiEndpointKeysUniqueCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomMultiEndpointKeysUniqueCheck artifact = true) : artifact.MultiEndpointKeysUnique := Check.nodupMapCheck_sound hCheck

Executable checker that bulk endpoints match the phantom adapter direction.

def phantomBulkEndpointsMatchCheck (artifact : PhantomAdapterArtifact) : Bool := match artifact.direction with | PhantomAdapterDirection.gather => Check.allDecide artifact.leftBulk (fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk (fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular) | PhantomAdapterDirection.scatter => Check.allDecide artifact.leftBulk (fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk (fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi)

Successful bulk-endpoint checking proves BulkEndpointsMatch.

theorem phantomBulkEndpointsMatchCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomBulkEndpointsMatchCheck artifact = true) : artifact.BulkEndpointsMatch := artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointsMatchCheck artifact = true⊢ artifact.BulkEndpointsMatch cases hDirection : artifact.direction with artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointsMatchCheck artifact = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(match artifact.direction with | PhantomAdapterDirection.gather => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ match artifact.direction with | PhantomAdapterDirection.gather => (∀ pair ∈ artifact.leftBulk, pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (∀ pair ∈ artifact.leftBulk, pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => (∀ pair ∈ artifact.leftBulk, pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (∀ pair ∈ artifact.leftBulk, pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi All goals completed! 🐙 artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointsMatchCheck artifact = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(match artifact.direction with | PhantomAdapterDirection.gather => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) && Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointsMatch artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ match artifact.direction with | PhantomAdapterDirection.gather => (∀ pair ∈ artifact.leftBulk, pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (∀ pair ∈ artifact.leftBulk, pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi artifact:PhantomAdapterArtifacthCheck:(Check.allDecide artifact.leftBulk fun pair => pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) = true ∧ (Check.allDecide artifact.rightBulk fun pair => pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => (∀ pair ∈ artifact.leftBulk, pair.fromPort ∈ artifact.multi ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort = artifact.singular | PhantomAdapterDirection.scatter => (∀ pair ∈ artifact.leftBulk, pair.fromPort = artifact.singular ∧ pair.toPort.node = artifact.node) ∧ ∀ pair ∈ artifact.rightBulk, pair.fromPort.node = artifact.node ∧ pair.toPort ∈ artifact.multi All goals completed! 🐙

Executable checker that bulk ledgers cover the source-visible endpoints exactly.

def phantomBulkEndpointPartitionCheck (artifact : PhantomAdapterArtifact) : Bool := match artifact.direction with | PhantomAdapterDirection.gather => Check.permCheck artifact.leftBulkSourceKeys (artifact.multi.map AdmissionBoundaryPort.key) && Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] | PhantomAdapterDirection.scatter => Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] && Check.permCheck artifact.rightBulkTargetKeys (artifact.multi.map AdmissionBoundaryPort.key)

Successful bulk-partition checking proves BulkEndpointPartition.

theorem phantomBulkEndpointPartitionCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomBulkEndpointPartitionCheck artifact = true) : artifact.BulkEndpointPartition := artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointPartitionCheck artifact = true⊢ artifact.BulkEndpointPartition cases hDirection : artifact.direction with artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointPartitionCheck artifact = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:(match artifact.direction with | PhantomAdapterDirection.gather => Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) && Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] | PhantomAdapterDirection.scatter => Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] && Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi)) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:(match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) && Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] | PhantomAdapterDirection.scatter => Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] && Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi)) = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) = true ∧ Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) = true ∧ Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ match artifact.direction with | PhantomAdapterDirection.gather => artifact.leftBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) ∧ artifact.rightBulkTargetKeys.Perm [artifact.singular.key] | PhantomAdapterDirection.scatter => artifact.leftBulkSourceKeys.Perm [artifact.singular.key] ∧ artifact.rightBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) = true ∧ Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] = truehDirection:artifact.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => artifact.leftBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) ∧ artifact.rightBulkTargetKeys.Perm [artifact.singular.key] | PhantomAdapterDirection.scatter => artifact.leftBulkSourceKeys.Perm [artifact.singular.key] ∧ artifact.rightBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) All goals completed! 🐙 artifact:PhantomAdapterArtifacthCheck:phantomBulkEndpointPartitionCheck artifact = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:(match artifact.direction with | PhantomAdapterDirection.gather => Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) && Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] | PhantomAdapterDirection.scatter => Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] && Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi)) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:(match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => Check.permCheck artifact.leftBulkSourceKeys (List.map AdmissionBoundaryPort.key artifact.multi) && Check.permCheck artifact.rightBulkTargetKeys [artifact.singular.key] | PhantomAdapterDirection.scatter => Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] && Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi)) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] = true ∧ Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ artifact.BulkEndpointPartition artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] = true ∧ Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ match artifact.direction with | PhantomAdapterDirection.gather => artifact.leftBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) ∧ artifact.rightBulkTargetKeys.Perm [artifact.singular.key] | PhantomAdapterDirection.scatter => artifact.leftBulkSourceKeys.Perm [artifact.singular.key] ∧ artifact.rightBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) artifact:PhantomAdapterArtifacthCheck:Check.permCheck artifact.leftBulkSourceKeys [artifact.singular.key] = true ∧ Check.permCheck artifact.rightBulkTargetKeys (List.map AdmissionBoundaryPort.key artifact.multi) = truehDirection:artifact.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => artifact.leftBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) ∧ artifact.rightBulkTargetKeys.Perm [artifact.singular.key] | PhantomAdapterDirection.scatter => artifact.leftBulkSourceKeys.Perm [artifact.singular.key] ∧ artifact.rightBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key artifact.multi) All goals completed! 🐙

Executable checker for indexed multi-side compatibility-key uniqueness.

def phantomIndexedMultiCompatibilityKeysUniqueCheck (artifact : PhantomAdapterArtifact) : Bool := match artifact.productShape with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed _element _count => Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.compatibilityShape

Successful indexed compatibility-key checking proves the indexed uniqueness obligation.

theorem phantomIndexedMultiCompatibilityKeysUniqueCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = true) : artifact.IndexedMultiCompatibilityKeysUnique := artifact:PhantomAdapterArtifacthCheck:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = true⊢ artifact.IndexedMultiCompatibilityKeysUnique cases hShape : artifact.productShape with artifact:PhantomAdapterArtifacthCheck:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = truecontract:ContractIdfields:List (FieldLabel × ContractId)hShape:artifact.productShape = ProductShapeArtifact.record contract fields⊢ artifact.IndexedMultiCompatibilityKeysUnique artifact:PhantomAdapterArtifacthCheck:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = truecontract:ContractIdfields:List (FieldLabel × ContractId)hShape:artifact.productShape = ProductShapeArtifact.record contract fields⊢ match artifact.productShape with | ProductShapeArtifact.record contract fields => True | ProductShapeArtifact.indexed elementContract count => (List.map AdmissionBoundaryPort.compatibilityShape artifact.multi).Nodup artifact:PhantomAdapterArtifacthCheck:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = truecontract:ContractIdfields:List (FieldLabel × ContractId)hShape:artifact.productShape = ProductShapeArtifact.record contract fields⊢ match ProductShapeArtifact.record contract fields with | ProductShapeArtifact.record contract fields => True | ProductShapeArtifact.indexed elementContract count => (List.map AdmissionBoundaryPort.compatibilityShape artifact.multi).Nodup All goals completed! 🐙 artifact:PhantomAdapterArtifacthCheck:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = trueelement:ContractIdcount:ℕhShape:artifact.productShape = ProductShapeArtifact.indexed element count⊢ artifact.IndexedMultiCompatibilityKeysUnique artifact:PhantomAdapterArtifacthCheck:(match artifact.productShape with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed _element _count => Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.compatibilityShape) = trueelement:ContractIdcount:ℕhShape:artifact.productShape = ProductShapeArtifact.indexed element count⊢ artifact.IndexedMultiCompatibilityKeysUnique artifact:PhantomAdapterArtifactelement:ContractIdcount:ℕhCheck:(match ProductShapeArtifact.indexed element count with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed _element _count => Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.compatibilityShape) = truehShape:artifact.productShape = ProductShapeArtifact.indexed element count⊢ artifact.IndexedMultiCompatibilityKeysUnique artifact:PhantomAdapterArtifactelement:ContractIdcount:ℕhCheck:(match ProductShapeArtifact.indexed element count with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed _element _count => Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.compatibilityShape) = truehShape:artifact.productShape = ProductShapeArtifact.indexed element count⊢ match artifact.productShape with | ProductShapeArtifact.record contract fields => True | ProductShapeArtifact.indexed elementContract count => (List.map AdmissionBoundaryPort.compatibilityShape artifact.multi).Nodup artifact:PhantomAdapterArtifactelement:ContractIdcount:ℕhCheck:(match ProductShapeArtifact.indexed element count with | ProductShapeArtifact.record _contract _fields => true | ProductShapeArtifact.indexed _element _count => Check.nodupMapCheck artifact.multi AdmissionBoundaryPort.compatibilityShape) = truehShape:artifact.productShape = ProductShapeArtifact.indexed element count⊢ match ProductShapeArtifact.indexed element count with | ProductShapeArtifact.record contract fields => True | ProductShapeArtifact.indexed elementContract count => (List.map AdmissionBoundaryPort.compatibilityShape artifact.multi).Nodup All goals completed! 🐙

Executable checker for phantom-adapter row-local facts.

def phantomAdapterRowsValidCheck (artifact : PhantomAdapterArtifact) : Bool := decide artifact.node.Valid && decide artifact.singular.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.multi && AdmissionArtifactCheck.connectionsValidCheck artifact.leftBulk && AdmissionArtifactCheck.connectionsValidCheck artifact.rightBulk

Successful phantom row-local checking proves PhantomAdapterArtifact.RowsValid.

theorem phantomAdapterRowsValidCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomAdapterRowsValidCheck artifact = true) : artifact.RowsValid := artifact:PhantomAdapterArtifacthCheck:phantomAdapterRowsValidCheck artifact = true⊢ artifact.RowsValid artifact:PhantomAdapterArtifacthCheck:(decide artifact.node.Valid && decide artifact.singular.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck artifact.multi && AdmissionArtifactCheck.connectionsValidCheck artifact.leftBulk && AdmissionArtifactCheck.connectionsValidCheck artifact.rightBulk) = true⊢ artifact.RowsValid artifact:PhantomAdapterArtifacthCheck:(((decide artifact.node.Valid = true ∧ decide artifact.singular.Valid = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck artifact.multi = true) ∧ AdmissionArtifactCheck.connectionsValidCheck artifact.leftBulk = true) ∧ AdmissionArtifactCheck.connectionsValidCheck artifact.rightBulk = true⊢ artifact.RowsValid artifact:PhantomAdapterArtifacthRightBulk:AdmissionArtifactCheck.connectionsValidCheck artifact.rightBulk = truehLeftBulk:AdmissionArtifactCheck.connectionsValidCheck artifact.leftBulk = truehMulti:AdmissionArtifactCheck.boundaryPortsValidCheck artifact.multi = truehNode:decide artifact.node.Valid = truehSingular:decide artifact.singular.Valid = true⊢ artifact.RowsValid All goals completed! 🐙

Executable checker for one phantom-adapter artifact.

def phantomAdapterValidCheck (artifact : PhantomAdapterArtifact) : Bool := productShapeValidCheck artifact.productShape && phantomProductArityMatchesCheck artifact && phantomProductShapeMatchesMultiCheck artifact && phantomProductContractMatchesSingularCheck artifact && phantomMultiEndpointKeysUniqueCheck artifact && phantomBulkEndpointsMatchCheck artifact && phantomBulkEndpointPartitionCheck artifact && phantomIndexedMultiCompatibilityKeysUniqueCheck artifact && phantomAdapterRowsValidCheck artifact

Successful phantom-adapter checking proves PhantomAdapterArtifact.Valid.

theorem phantomAdapterValidCheck_sound {artifact : PhantomAdapterArtifact} (hCheck : phantomAdapterValidCheck artifact = true) : artifact.Valid := artifact:PhantomAdapterArtifacthCheck:phantomAdapterValidCheck artifact = true⊢ artifact.Valid artifact:PhantomAdapterArtifacthCheck:(productShapeValidCheck artifact.productShape && phantomProductArityMatchesCheck artifact && phantomProductShapeMatchesMultiCheck artifact && phantomProductContractMatchesSingularCheck artifact && phantomMultiEndpointKeysUniqueCheck artifact && phantomBulkEndpointsMatchCheck artifact && phantomBulkEndpointPartitionCheck artifact && phantomIndexedMultiCompatibilityKeysUniqueCheck artifact && phantomAdapterRowsValidCheck artifact) = true⊢ artifact.Valid artifact:PhantomAdapterArtifacthCheck:(((((((productShapeValidCheck artifact.productShape = true ∧ phantomProductArityMatchesCheck artifact = true) ∧ phantomProductShapeMatchesMultiCheck artifact = true) ∧ phantomProductContractMatchesSingularCheck artifact = true) ∧ phantomMultiEndpointKeysUniqueCheck artifact = true) ∧ phantomBulkEndpointsMatchCheck artifact = true) ∧ phantomBulkEndpointPartitionCheck artifact = true) ∧ phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = true) ∧ phantomAdapterRowsValidCheck artifact = true⊢ artifact.Valid artifact:PhantomAdapterArtifacthRows:phantomAdapterRowsValidCheck artifact = truehIndexedUnique:phantomIndexedMultiCompatibilityKeysUniqueCheck artifact = truehBulkPartition:phantomBulkEndpointPartitionCheck artifact = truehBulkMatch:phantomBulkEndpointsMatchCheck artifact = truehMultiUnique:phantomMultiEndpointKeysUniqueCheck artifact = truehSingularContract:phantomProductContractMatchesSingularCheck artifact = truehMultiShape:phantomProductShapeMatchesMultiCheck artifact = truehShape:productShapeValidCheck artifact.productShape = truehArity:phantomProductArityMatchesCheck artifact = true⊢ artifact.Valid All goals completed! 🐙

Executable checker for phantom-adapter domain closure over the top-level node summary.

def phantomAdapterDomainClosedCheck (nodes : List NodeId) (artifact : PhantomAdapterArtifact) : Bool := Check.memCheck artifact.node nodes && boundaryPortClosedCheck nodes artifact.singular && boundaryPortsClosedCheck nodes artifact.multi && connectionsClosedCheck nodes artifact.leftBulk && connectionsClosedCheck nodes artifact.rightBulk

Successful phantom-adapter closure checking proves PhantomAdapterArtifact.DomainClosed.

theorem phantomAdapterDomainClosedCheck_sound {nodes : List NodeId} {artifact : PhantomAdapterArtifact} (hCheck : phantomAdapterDomainClosedCheck nodes artifact = true) : artifact.DomainClosed nodes := nodes:List NodeIdartifact:PhantomAdapterArtifacthCheck:phantomAdapterDomainClosedCheck nodes artifact = true⊢ PhantomAdapterArtifact.DomainClosed nodes artifact nodes:List NodeIdartifact:PhantomAdapterArtifacthCheck:(Check.memCheck artifact.node nodes && boundaryPortClosedCheck nodes artifact.singular && boundaryPortsClosedCheck nodes artifact.multi && connectionsClosedCheck nodes artifact.leftBulk && connectionsClosedCheck nodes artifact.rightBulk) = true⊢ PhantomAdapterArtifact.DomainClosed nodes artifact nodes:List NodeIdartifact:PhantomAdapterArtifacthCheck:(((Check.memCheck artifact.node nodes = true ∧ boundaryPortClosedCheck nodes artifact.singular = true) ∧ boundaryPortsClosedCheck nodes artifact.multi = true) ∧ connectionsClosedCheck nodes artifact.leftBulk = true) ∧ connectionsClosedCheck nodes artifact.rightBulk = true⊢ PhantomAdapterArtifact.DomainClosed nodes artifact nodes:List NodeIdartifact:PhantomAdapterArtifacthRightBulk:connectionsClosedCheck nodes artifact.rightBulk = truehLeftBulk:connectionsClosedCheck nodes artifact.leftBulk = truehMulti:boundaryPortsClosedCheck nodes artifact.multi = truehNode:Check.memCheck artifact.node nodes = truehSingular:boundaryPortClosedCheck nodes artifact.singular = true⊢ PhantomAdapterArtifact.DomainClosed nodes artifact All goals completed! 🐙

Select Row Checks

Executable checker for one select variant row.

def selectVariantValidCheck (variant : SelectVariantArtifact) : Bool := decide variant.key.Valid && decide variant.port.Valid && decide (variant.key = variant.port.selectKey)

Successful select-variant checking proves SelectVariantArtifact.Valid.

theorem selectVariantValidCheck_sound {variant : SelectVariantArtifact} (hCheck : selectVariantValidCheck variant = true) : variant.Valid := variant:SelectVariantArtifacthCheck:selectVariantValidCheck variant = true⊢ variant.Valid variant:SelectVariantArtifacthCheck:(decide variant.key.Valid && decide variant.port.Valid && decide (variant.key = variant.port.selectKey)) = true⊢ variant.Valid variant:SelectVariantArtifacthCheck:(decide variant.key.Valid = true ∧ decide variant.port.Valid = true) ∧ decide (variant.key = variant.port.selectKey) = true⊢ variant.Valid variant:SelectVariantArtifacthCanonical:decide (variant.key = variant.port.selectKey) = truehKey:decide variant.key.Valid = truehPort:decide variant.port.Valid = true⊢ variant.Valid exact { keyValid := of_decide_eq_true hKey , portValid := of_decide_eq_true hPort , keyCanonical := variant:SelectVariantArtifacthCanonical:decide (variant.key = variant.port.selectKey) = truehKey:decide variant.key.Valid = truehPort:decide variant.port.Valid = true⊢ variant.KeyCanonical variant:SelectVariantArtifacthCanonical:decide (variant.key = variant.port.selectKey) = truehKey:decide variant.key.Valid = truehPort:decide variant.port.Valid = true⊢ variant.key = variant.port.selectKey All goals completed! 🐙 }

Executable checker for one select arm row.

def selectArmValidCheck (arm : SelectArmAdmissionArtifact) : Bool := decide arm.sourceKey.Valid && decide arm.canonicalKey.Valid && boundaryPortsClosedCheck arm.bodyNodes arm.bodyEntries && boundaryPortsClosedCheck arm.bodyNodes arm.bodyExits && Check.nodupCheck arm.bodyNodes && Check.nodupCheck arm.bodyEntryKeys && Check.nodupCheck arm.bodyExitKeys && Check.allDecide arm.bodyNodes NodeId.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyEntries && AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyExits

Successful select-arm checking proves SelectArmAdmissionArtifact.Valid.

theorem selectArmValidCheck_sound {arm : SelectArmAdmissionArtifact} (hCheck : selectArmValidCheck arm = true) : arm.Valid := arm:SelectArmAdmissionArtifacthCheck:selectArmValidCheck arm = true⊢ arm.Valid arm:SelectArmAdmissionArtifacthCheck:(decide arm.sourceKey.Valid && decide arm.canonicalKey.Valid && boundaryPortsClosedCheck arm.bodyNodes arm.bodyEntries && boundaryPortsClosedCheck arm.bodyNodes arm.bodyExits && Check.nodupCheck arm.bodyNodes && Check.nodupCheck arm.bodyEntryKeys && Check.nodupCheck arm.bodyExitKeys && Check.allDecide arm.bodyNodes NodeId.Valid && AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyEntries && AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyExits) = true⊢ arm.Valid arm:SelectArmAdmissionArtifacthCheck:((((((((decide arm.sourceKey.Valid = true ∧ decide arm.canonicalKey.Valid = true) ∧ boundaryPortsClosedCheck arm.bodyNodes arm.bodyEntries = true) ∧ boundaryPortsClosedCheck arm.bodyNodes arm.bodyExits = true) ∧ Check.nodupCheck arm.bodyNodes = true) ∧ Check.nodupCheck arm.bodyEntryKeys = true) ∧ Check.nodupCheck arm.bodyExitKeys = true) ∧ Check.allDecide arm.bodyNodes NodeId.Valid = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyEntries = true) ∧ AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyExits = true⊢ arm.Valid arm:SelectArmAdmissionArtifacthBodyExitsValid:AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyExits = truehBodyEntriesValid:AdmissionArtifactCheck.boundaryPortsValidCheck arm.bodyEntries = truehBodyNodesValid:Check.allDecide arm.bodyNodes NodeId.Valid = truehBodyExitsUnique:Check.nodupCheck arm.bodyExitKeys = truehBodyEntriesUnique:Check.nodupCheck arm.bodyEntryKeys = truehBodyNodesUnique:Check.nodupCheck arm.bodyNodes = truehBodyExitsClosed:boundaryPortsClosedCheck arm.bodyNodes arm.bodyExits = truehBodyEntriesClosed:boundaryPortsClosedCheck arm.bodyNodes arm.bodyEntries = truehSourceKey:decide arm.sourceKey.Valid = truehCanonicalKey:decide arm.canonicalKey.Valid = true⊢ arm.Valid All goals completed! 🐙

Executable checker that all variant ports share one exclusive output group.

def selectVariantsShareExclusiveGroupCheck : List SelectVariantArtifact → Bool | [] => false | variant :: variants => match variant.port.exclusiveGroup with | none => false | some group => Check.allDecide variants fun other => other.port.exclusiveGroup = some group

Successful exclusive-group checking proves VariantsShareExclusiveGroup.

theorem selectVariantsShareExclusiveGroupCheck_sound {variants : List SelectVariantArtifact} (hCheck : selectVariantsShareExclusiveGroupCheck variants = true) : ∃ owner index, ∀ variant, variant ∈ variants → variant.port.exclusiveGroup = some (owner, index) := variants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck variants = true⊢ ∃ owner index, ∀ variant ∈ variants, variant.port.exclusiveGroup = some (owner, index) cases variants with hCheck:selectVariantsShareExclusiveGroupCheck [] = true⊢ ∃ owner index, ∀ variant ∈ [], variant.port.exclusiveGroup = some (owner, index) All goals completed! 🐙 variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = true⊢ ∃ owner index, ∀ variant_1 ∈ variant :: variants, variant_1.port.exclusiveGroup = some (owner, index) cases hGroup : variant.port.exclusiveGroup with variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = truehGroup:variant.port.exclusiveGroup = none⊢ ∃ owner index, ∀ variant_1 ∈ variant :: variants, variant_1.port.exclusiveGroup = some (owner, index) All goals completed! 🐙 variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = truegroup:NodeId × ℕhGroup:variant.port.exclusiveGroup = some group⊢ ∃ owner index, ∀ variant_1 ∈ variant :: variants, variant_1.port.exclusiveGroup = some (owner, index) cases group with variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)⊢ ∃ owner index, ∀ variant_1 ∈ variant :: variants, variant_1.port.exclusiveGroup = some (owner, index) have hTail : Check.allDecide variants (fun other => other.port.exclusiveGroup = some (owner, index)) = true := variants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck variants = true⊢ ∃ owner index, ∀ variant ∈ variants, variant.port.exclusiveGroup = some (owner, index) All goals completed! 🐙 variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = true⊢ ∀ variant_1 ∈ variant :: variants, variant_1.port.exclusiveGroup = some (owner, index) intro candidate variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthCandidate:candidate ∈ variant :: variants⊢ candidate.port.exclusiveGroup = some (owner, index) variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthCandidate:candidate = variant ∨ candidate ∈ variants⊢ candidate.port.exclusiveGroup = some (owner, index) variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthHead:candidate = variant⊢ candidate.port.exclusiveGroup = some (owner, index)variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthTailMem:candidate ∈ variants⊢ candidate.port.exclusiveGroup = some (owner, index) variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthHead:candidate = variant⊢ candidate.port.exclusiveGroup = some (owner, index) variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = true⊢ variant.port.exclusiveGroup = some (owner, index) All goals completed! 🐙 variant:SelectVariantArtifactvariants:List SelectVariantArtifacthCheck:selectVariantsShareExclusiveGroupCheck (variant :: variants) = trueowner:NodeIdindex:ℕhGroup:variant.port.exclusiveGroup = some (owner, index)hTail:(Check.allDecide variants fun other => other.port.exclusiveGroup = some (owner, index)) = truecandidate:SelectVariantArtifacthTailMem:candidate ∈ variants⊢ candidate.port.exclusiveGroup = some (owner, index) All goals completed! 🐙

Executable checker for one select arm's persisted resolution mode.

def selectArmResolutionSoundCheck (variants : List SelectVariantArtifact) (arm : SelectArmAdmissionArtifact) : Bool := match arm.mode with | SelectResolutionMode.resolvedByLabel => decide (arm.sourceKey = arm.canonicalKey) && Check.anyDecide variants (fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey) | SelectResolutionMode.resolvedByContract => Check.allDecide variants (fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) && Check.allDecide variants (fun variant => (variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey))

Successful resolution-mode checking proves the relational resolution contract.

theorem selectArmResolutionSoundCheck_sound {variants : List SelectVariantArtifact} {arm : SelectArmAdmissionArtifact} (hCheck : selectArmResolutionSoundCheck variants arm = true) : match arm.mode with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant, variant ∈ variants ∧ variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant, variant ∈ variants → variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ (∀ variant, variant ∈ variants → (variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey)) := variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:selectArmResolutionSoundCheck variants arm = true⊢ match arm.mode with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey cases hMode : arm.mode with variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:selectArmResolutionSoundCheck variants arm = truehMode:arm.mode = SelectResolutionMode.resolvedByLabel⊢ match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(match arm.mode with | SelectResolutionMode.resolvedByLabel => decide (arm.sourceKey = arm.canonicalKey) && Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) && Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByLabel⊢ match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => decide (arm.sourceKey = arm.canonicalKey) && Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) && Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByLabel⊢ match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:decide (arm.sourceKey = arm.canonicalKey) = true ∧ (Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByLabel⊢ match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:decide (arm.sourceKey = arm.canonicalKey) = true ∧ (Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByLabelhResult:arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey⊢ match SelectResolutionMode.resolvedByLabel with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey All goals completed! 🐙 variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:selectArmResolutionSoundCheck variants arm = truehMode:arm.mode = SelectResolutionMode.resolvedByContract⊢ match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(match arm.mode with | SelectResolutionMode.resolvedByLabel => decide (arm.sourceKey = arm.canonicalKey) && Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) && Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByContract⊢ match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => decide (arm.sourceKey = arm.canonicalKey) && Check.anyDecide variants fun variant => variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) && Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByContract⊢ match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) = true ∧ (Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByContract⊢ match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey variants:List SelectVariantArtifactarm:SelectArmAdmissionArtifacthCheck:(Check.allDecide variants fun variant => variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) = true ∧ (Check.allDecide variants fun variant => variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey) = truehMode:arm.mode = SelectResolutionMode.resolvedByContracthResult:(∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey⊢ match SelectResolutionMode.resolvedByContract with | SelectResolutionMode.resolvedByLabel => arm.sourceKey = arm.canonicalKey ∧ ∃ variant ∈ variants, variant.key = arm.canonicalKey ∧ variant.port.label = AdmissionPortLabel.label arm.sourceKey | SelectResolutionMode.resolvedByContract => (∀ variant ∈ variants, variant.port.label ≠ AdmissionPortLabel.label arm.sourceKey) ∧ ∀ variant ∈ variants, variant.port.contract.name = arm.sourceKey.name ↔ variant.key = arm.canonicalKey All goals completed! 🐙

Executable checker for select-admission row-local facts.

def selectAdmissionRowsValidCheck (selectAdmission : SelectAdmissionArtifact) : Bool := decide selectAdmission.owner.Valid && decide selectAdmission.conditionNode.Valid && Check.allBool selectAdmission.variants selectVariantValidCheck && Check.allBool selectAdmission.arms selectArmValidCheck

Successful row-local checking proves SelectAdmissionArtifact.RowsValid.

theorem selectAdmissionRowsValidCheck_sound {selectAdmission : SelectAdmissionArtifact} (hCheck : selectAdmissionRowsValidCheck selectAdmission = true) : selectAdmission.RowsValid := selectAdmission:SelectAdmissionArtifacthCheck:selectAdmissionRowsValidCheck selectAdmission = true⊢ selectAdmission.RowsValid selectAdmission:SelectAdmissionArtifacthCheck:(decide selectAdmission.owner.Valid && decide selectAdmission.conditionNode.Valid && Check.allBool selectAdmission.variants selectVariantValidCheck && Check.allBool selectAdmission.arms selectArmValidCheck) = true⊢ selectAdmission.RowsValid selectAdmission:SelectAdmissionArtifacthCheck:((decide selectAdmission.owner.Valid = true ∧ decide selectAdmission.conditionNode.Valid = true) ∧ Check.allBool selectAdmission.variants selectVariantValidCheck = true) ∧ Check.allBool selectAdmission.arms selectArmValidCheck = true⊢ selectAdmission.RowsValid selectAdmission:SelectAdmissionArtifacthArms:Check.allBool selectAdmission.arms selectArmValidCheck = truehVariants:Check.allBool selectAdmission.variants selectVariantValidCheck = truehOwner:decide selectAdmission.owner.Valid = truehCondition:decide selectAdmission.conditionNode.Valid = true⊢ selectAdmission.RowsValid All goals completed! 🐙

Executable checker for one select-admission artifact.

def selectAdmissionValidCheck (selectAdmission : SelectAdmissionArtifact) : Bool := decide (selectAdmission.owner = selectAdmission.conditionNode) && Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys && Check.nodupCheck selectAdmission.variantKeys && decide (2 ≤ selectAdmission.variants.length) && selectVariantsShareExclusiveGroupCheck selectAdmission.variants && Check.nodupCheck selectAdmission.armCanonicalKeys && Check.nodupCheck selectAdmission.armSourceIndexes && decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) && selectAdmissionRowsValidCheck selectAdmission && Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants)

Successful select-admission checking proves SelectAdmissionArtifact.Valid.

theorem selectAdmissionValidCheck_sound {selectAdmission : SelectAdmissionArtifact} (hCheck : selectAdmissionValidCheck selectAdmission = true) : selectAdmission.Valid := selectAdmission:SelectAdmissionArtifacthCheck:selectAdmissionValidCheck selectAdmission = true⊢ selectAdmission.Valid selectAdmission:SelectAdmissionArtifacthCheck:(decide (selectAdmission.owner = selectAdmission.conditionNode) && Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys && Check.nodupCheck selectAdmission.variantKeys && decide (2 ≤ selectAdmission.variants.length) && selectVariantsShareExclusiveGroupCheck selectAdmission.variants && Check.nodupCheck selectAdmission.armCanonicalKeys && Check.nodupCheck selectAdmission.armSourceIndexes && decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) && selectAdmissionRowsValidCheck selectAdmission && Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants)) = true⊢ selectAdmission.Valid selectAdmission:SelectAdmissionArtifacthCheck:((((((((decide (selectAdmission.owner = selectAdmission.conditionNode) = true ∧ Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true) ∧ Check.nodupCheck selectAdmission.variantKeys = true) ∧ decide (2 ≤ selectAdmission.variants.length) = true) ∧ selectVariantsShareExclusiveGroupCheck selectAdmission.variants = true) ∧ Check.nodupCheck selectAdmission.armCanonicalKeys = true) ∧ Check.nodupCheck selectAdmission.armSourceIndexes = true) ∧ decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = true) ∧ selectAdmissionRowsValidCheck selectAdmission = true) ∧ Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = true⊢ selectAdmission.Valid selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.Valid exact { ownerMatchesCondition := selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.OwnerMatchesCondition selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.owner = selectAdmission.conditionNode All goals completed! 🐙 , keysCovered := Check.permCheck_sound hCovered , variantKeysUnique := Check.nodupCheck_sound hVariantKeys , variantsAtLeastTwo := selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.VariantsAtLeastTwo selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ 2 ≤ selectAdmission.variants.length All goals completed! 🐙 , variantsShareExclusiveGroup := selectVariantsShareExclusiveGroupCheck_sound hExclusiveGroup , armCanonicalKeysUnique := Check.nodupCheck_sound hArmKeys , armSourceIndexesUnique := Check.nodupCheck_sound hArmIndexes , armSourceIndexesCanonical := selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.ArmSourceIndexesCanonical selectAdmission:SelectAdmissionArtifacthResolution:Check.allBool selectAdmission.arms (selectArmResolutionSoundCheck selectAdmission.variants) = truehRows:selectAdmissionRowsValidCheck selectAdmission = truehArmIndexesCanonical:decide (selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length) = truehArmIndexes:Check.nodupCheck selectAdmission.armSourceIndexes = truehArmKeys:Check.nodupCheck selectAdmission.armCanonicalKeys = truehExclusiveGroup:selectVariantsShareExclusiveGroupCheck selectAdmission.variants = truehAtLeastTwo:decide (2 ≤ selectAdmission.variants.length) = truehVariantKeys:Check.nodupCheck selectAdmission.variantKeys = truehOwner:decide (selectAdmission.owner = selectAdmission.conditionNode) = truehCovered:Check.permCheck selectAdmission.armCanonicalKeys selectAdmission.variantKeys = true⊢ selectAdmission.armSourceIndexes = List.range selectAdmission.arms.length All goals completed! 🐙 , rowsValid := selectAdmissionRowsValidCheck_sound hRows , armResolutionSound := Check.allBool_sound hResolution (fun _arm _ hArm => selectArmResolutionSoundCheck_sound hArm) }

Executable checker that all select-admission artifacts are locally valid.

def selectsValidCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects selectAdmissionValidCheck

Successful select-list checking proves SelectsValid.

theorem selectsValidCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectsValidCheck = true) : artifact.SelectsValid := Check.allBool_sound hCheck (fun _selectAdmission _ hSelect => selectAdmissionValidCheck_sound hSelect)

Executable checker for select-admission domain closure over the top-level node summary.

def selectAdmissionDomainClosedCheck (nodes : List NodeId) (selectAdmission : SelectAdmissionArtifact) : Bool := Check.memCheck selectAdmission.owner nodes && Check.memCheck selectAdmission.conditionNode nodes && Check.allDecide selectAdmission.variants fun variant => variant.port.node ∈ nodes

Successful select-domain checking proves SelectAdmissionArtifact.DomainClosed.

theorem selectAdmissionDomainClosedCheck_sound {nodes : List NodeId} {selectAdmission : SelectAdmissionArtifact} (hCheck : selectAdmissionDomainClosedCheck nodes selectAdmission = true) : selectAdmission.DomainClosed nodes := nodes:List NodeIdselectAdmission:SelectAdmissionArtifacthCheck:selectAdmissionDomainClosedCheck nodes selectAdmission = true⊢ SelectAdmissionArtifact.DomainClosed nodes selectAdmission nodes:List NodeIdselectAdmission:SelectAdmissionArtifacthCheck:(Check.memCheck selectAdmission.owner nodes && Check.memCheck selectAdmission.conditionNode nodes && Check.allDecide selectAdmission.variants fun variant => variant.port.node ∈ nodes) = true⊢ SelectAdmissionArtifact.DomainClosed nodes selectAdmission nodes:List NodeIdselectAdmission:SelectAdmissionArtifacthCheck:(Check.memCheck selectAdmission.owner nodes = true ∧ Check.memCheck selectAdmission.conditionNode nodes = true) ∧ (Check.allDecide selectAdmission.variants fun variant => variant.port.node ∈ nodes) = true⊢ SelectAdmissionArtifact.DomainClosed nodes selectAdmission nodes:List NodeIdselectAdmission:SelectAdmissionArtifacthVariants:(Check.allDecide selectAdmission.variants fun variant => variant.port.node ∈ nodes) = truehOwner:Check.memCheck selectAdmission.owner nodes = truehCondition:Check.memCheck selectAdmission.conditionNode nodes = true⊢ SelectAdmissionArtifact.DomainClosed nodes selectAdmission All goals completed! 🐙

Boolean exclusive-group ownership check for select condition-node internal exits.

def selectExitOwnedByConditionCheck (conditionNode : NodeId) (exit : AdmissionBoundaryPort) : Bool := match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)

Successful condition-owner checking returns the serialized exclusive-group index.

theorem selectExitOwnedByConditionCheck_sound {conditionNode : NodeId} {exit : AdmissionBoundaryPort} (hCheck : selectExitOwnedByConditionCheck conditionNode exit = true) : ∃ index, exit.exclusiveGroup = some (conditionNode, index) := conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:selectExitOwnedByConditionCheck conditionNode exit = true⊢ ∃ index, exit.exclusiveGroup = some (conditionNode, index) conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:(match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = true⊢ ∃ index, exit.exclusiveGroup = some (conditionNode, index) cases hGroup : exit.exclusiveGroup with conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:(match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = truehGroup:exit.exclusiveGroup = none⊢ ∃ index, none = some (conditionNode, index) All goals completed! 🐙 conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:(match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = truegroup:NodeId × ℕhGroup:exit.exclusiveGroup = some group⊢ ∃ index, some group = some (conditionNode, index) cases group with conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:(match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = trueowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)⊢ ∃ index_1, some (owner, index) = some (conditionNode, index_1) have hOwner : owner = conditionNode := conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:selectExitOwnedByConditionCheck conditionNode exit = true⊢ ∃ index, exit.exclusiveGroup = some (conditionNode, index) have hOwnerCheck : decide (owner = conditionNode) = true := conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:selectExitOwnedByConditionCheck conditionNode exit = true⊢ ∃ index, exit.exclusiveGroup = some (conditionNode, index) All goals completed! 🐙 All goals completed! 🐙 exact ⟨index, conditionNode:NodeIdexit:AdmissionBoundaryPorthCheck:(match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = trueowner:NodeIdindex:ℕhGroup:exit.exclusiveGroup = some (owner, index)hOwner:owner = conditionNode⊢ some (owner, index) = some (conditionNode, index) All goals completed! 🐙⟩

Serialized condition-owned exits are accepted by the boolean owner check.

theorem selectExitOwnedByConditionCheck_complete {conditionNode : NodeId} {exit : AdmissionBoundaryPort} (hGroup : ∃ index, exit.exclusiveGroup = some (conditionNode, index)) : selectExitOwnedByConditionCheck conditionNode exit = true := conditionNode:NodeIdexit:AdmissionBoundaryPorthGroup:∃ index, exit.exclusiveGroup = some (conditionNode, index)⊢ selectExitOwnedByConditionCheck conditionNode exit = true conditionNode:NodeIdexit:AdmissionBoundaryPortindex:ℕhGroupEq:exit.exclusiveGroup = some (conditionNode, index)⊢ selectExitOwnedByConditionCheck conditionNode exit = true conditionNode:NodeIdexit:AdmissionBoundaryPortindex:ℕhGroupEq:exit.exclusiveGroup = some (conditionNode, index)⊢ (match exit.exclusiveGroup with | none => false | some (owner, _index) => decide (owner = conditionNode)) = true conditionNode:NodeIdexit:AdmissionBoundaryPortindex:ℕhGroupEq:exit.exclusiveGroup = some (conditionNode, index)⊢ (match some (conditionNode, index) with | none => false | some (owner, _index) => decide (owner = conditionNode)) = true All goals completed! 🐙

Boolean check that a finite list contains exactly one row satisfying matchCheck.

def uniqueBoolCheck {α : Type} [DecidableEq α] (items : List α) (matchCheck : α → Bool) : Bool := match items.find? matchCheck with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected

List.find? over a boolean predicate returns an item from the scanned list.

theorem find?_bool_mem {α : Type} {items : List α} {matchCheck : α → Bool} {selected : α} (hFind : items.find? matchCheck = some selected) : selected ∈ items ∧ matchCheck selected = true := α:Typeitems:List αmatchCheck:α → Boolselected:αhFind:List.find? matchCheck items = some selected⊢ selected ∈ items ∧ matchCheck selected = true induction items with α:TypematchCheck:α → Boolselected:αhFind:List.find? matchCheck [] = some selected⊢ selected ∈ [] ∧ matchCheck selected = true All goals completed! 🐙 α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:List.find? matchCheck (head :: tail) = some selected⊢ selected ∈ head :: tail ∧ matchCheck selected = true α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match matchCheck head with | true => some head | false => List.find? matchCheck tail) = some selected⊢ selected ∈ head :: tail ∧ matchCheck selected = true cases hHead : matchCheck head with α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match matchCheck head with | true => some head | false => List.find? matchCheck tail) = some selectedhHead:matchCheck head = false⊢ selected ∈ head :: tail ∧ matchCheck selected = true α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match false with | true => some head | false => List.find? matchCheck tail) = some selectedhHead:matchCheck head = false⊢ selected ∈ head :: tail ∧ matchCheck selected = true α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match false with | true => some head | false => List.find? matchCheck tail) = some selectedhHead:matchCheck head = falsehTail:selected ∈ tail ∧ matchCheck selected = true⊢ selected ∈ head :: tail ∧ matchCheck selected = true All goals completed! 🐙 α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match matchCheck head with | true => some head | false => List.find? matchCheck tail) = some selectedhHead:matchCheck head = true⊢ selected ∈ head :: tail ∧ matchCheck selected = true α:TypematchCheck:α → Boolselected:αhead:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehFind:(match true with | true => some head | false => List.find? matchCheck tail) = some selectedhHead:matchCheck head = true⊢ selected ∈ head :: tail ∧ matchCheck selected = true α:TypematchCheck:α → Boolselected:αtail:List αih:List.find? matchCheck tail = some selected → selected ∈ tail ∧ matchCheck selected = truehHead:matchCheck selected = true⊢ selected ∈ selected :: tail ∧ matchCheck selected = true All goals completed! 🐙

Successful finite uniqueness checking returns the unique matched item.

theorem uniqueBoolCheck_sound {α : Type} [DecidableEq α] {items : List α} {matchCheck : α → Bool} (hCheck : uniqueBoolCheck items matchCheck = true) : ∃ selected, selected ∈ items ∧ matchCheck selected = true ∧ ∀ item, item ∈ items → matchCheck item = true → item = selected := α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → BoolhCheck:uniqueBoolCheck items matchCheck = true⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → BoolhCheck:(match List.find? matchCheck items with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = true⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected cases hFind : items.find? matchCheck with α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → BoolhCheck:(match List.find? matchCheck items with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = truehFind:List.find? matchCheck items = none⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → BoolhCheck:(match none with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = truehFind:List.find? matchCheck items = none⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected All goals completed! 🐙 α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → BoolhCheck:(match List.find? matchCheck items with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = trueselected:αhFind:List.find? matchCheck items = some selected⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → Boolselected:αhCheck:(match some selected with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = truehFind:List.find? matchCheck items = some selected⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected α:Typeinst✝:DecidableEq αitems:List αmatchCheck:α → Boolselected:αhCheck:(match some selected with | none => false | some selected => Check.allDecide items fun item => matchCheck item = true → item = selected) = truehFind:List.find? matchCheck items = some selectedhSelected:selected ∈ items ∧ matchCheck selected = true⊢ ∃ selected ∈ items, matchCheck selected = true ∧ ∀ item ∈ items, matchCheck item = true → item = selected All goals completed! 🐙

Boolean predicate for a variant-compatible select bridge entry.

def selectBridgeEntryMatchCheck (variant : SelectVariantArtifact) (entry : AdmissionBoundaryPort) : Bool := decide (variant.port.CompatibleWith entry)

Executable checker for unique select bridge entries.

def selectBridgeEntryUniqueCheck (variant : SelectVariantArtifact) (entries : List AdmissionBoundaryPort) : Bool := uniqueBoolCheck entries (selectBridgeEntryMatchCheck variant)

Successful bridge-entry uniqueness checking proves SelectBridgeEntryUnique.

theorem selectBridgeEntryUniqueCheck_sound {variant : SelectVariantArtifact} {entries : List AdmissionBoundaryPort} (hCheck : selectBridgeEntryUniqueCheck variant entries = true) : SelectBridgeEntryUnique variant entries := variant:SelectVariantArtifactentries:List AdmissionBoundaryPorthCheck:selectBridgeEntryUniqueCheck variant entries = true⊢ SelectBridgeEntryUnique variant entries variant:SelectVariantArtifactentries:List AdmissionBoundaryPorthCheck:selectBridgeEntryUniqueCheck variant entries = trueentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshMatch:selectBridgeEntryMatchCheck variant entry = truehUnique:∀ item ∈ entries, selectBridgeEntryMatchCheck variant item = true → item = entry⊢ SelectBridgeEntryUnique variant entries variant:SelectVariantArtifactentries:List AdmissionBoundaryPorthCheck:selectBridgeEntryUniqueCheck variant entries = trueentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshMatch:selectBridgeEntryMatchCheck variant entry = truehUnique:∀ item ∈ entries, selectBridgeEntryMatchCheck variant item = true → item = entryhCompatible:variant.port.CompatibleWith entry⊢ SelectBridgeEntryUnique variant entries All goals completed! 🐙

Boolean predicate for a variant-compatible, condition-owned select bridge exit.

def selectBridgeInternalExitMatchCheck (conditionNode : NodeId) (variant : SelectVariantArtifact) (exit : AdmissionBoundaryPort) : Bool := decide (variant.port.CompatibleWith exit) && selectExitOwnedByConditionCheck conditionNode exit

Executable checker for unique select internal branch-choice exits.

def selectBridgeInternalExitUniqueCheck (conditionNode : NodeId) (variant : SelectVariantArtifact) (exits : List AdmissionBoundaryPort) : Bool := uniqueBoolCheck exits (selectBridgeInternalExitMatchCheck conditionNode variant)

Successful internal-exit uniqueness checking proves SelectBridgeInternalExitUnique.

theorem selectBridgeInternalExitUniqueCheck_sound {conditionNode : NodeId} {variant : SelectVariantArtifact} {exits : List AdmissionBoundaryPort} (hCheck : selectBridgeInternalExitUniqueCheck conditionNode variant exits = true) : SelectBridgeInternalExitUnique conditionNode variant exits := conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = true⊢ SelectBridgeInternalExitUnique conditionNode variant exits conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:selectBridgeInternalExitMatchCheck conditionNode variant exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exit⊢ SelectBridgeInternalExitUnique conditionNode variant exits conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:(decide (variant.port.CompatibleWith exit) && selectExitOwnedByConditionCheck conditionNode exit) = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exit⊢ SelectBridgeInternalExitUnique conditionNode variant exits conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exit⊢ SelectBridgeInternalExitUnique conditionNode variant exits conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exithCompatible:variant.port.CompatibleWith exit⊢ SelectBridgeInternalExitUnique conditionNode variant exits conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exithCompatible:variant.port.CompatibleWith exithGroup:∃ index, exit.exclusiveGroup = some (conditionNode, index)⊢ SelectBridgeInternalExitUnique conditionNode variant exits exact ⟨ exit , hExit , hCompatible , hGroup , fun other hOther hOtherCompatible hOtherGroup => hUnique other hOther (conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exithCompatible:variant.port.CompatibleWith exithGroup:∃ index, exit.exclusiveGroup = some (conditionNode, index)other:AdmissionBoundaryPorthOther:other ∈ exitshOtherCompatible:variant.port.CompatibleWith otherhOtherGroup:∃ index, other.exclusiveGroup = some (conditionNode, index)⊢ selectBridgeInternalExitMatchCheck conditionNode variant other = true conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exithCompatible:variant.port.CompatibleWith exithGroup:∃ index, exit.exclusiveGroup = some (conditionNode, index)other:AdmissionBoundaryPorthOther:other ∈ exitshOtherCompatible:variant.port.CompatibleWith otherhOtherGroup:∃ index, other.exclusiveGroup = some (conditionNode, index)⊢ (decide (variant.port.CompatibleWith other) && selectExitOwnedByConditionCheck conditionNode other) = true conditionNode:NodeIdvariant:SelectVariantArtifactexits:List AdmissionBoundaryPorthCheck:selectBridgeInternalExitUniqueCheck conditionNode variant exits = trueexit:AdmissionBoundaryPorthExit:exit ∈ exitshMatch:decide (variant.port.CompatibleWith exit) = true ∧ selectExitOwnedByConditionCheck conditionNode exit = truehUnique:∀ item ∈ exits, selectBridgeInternalExitMatchCheck conditionNode variant item = true → item = exithCompatible:variant.port.CompatibleWith exithGroup:∃ index, exit.exclusiveGroup = some (conditionNode, index)other:AdmissionBoundaryPorthOther:other ∈ exitshOtherCompatible:variant.port.CompatibleWith otherhOtherGroup:∃ index, other.exclusiveGroup = some (conditionNode, index)⊢ decide (variant.port.CompatibleWith other) = true ∧ selectExitOwnedByConditionCheck conditionNode other = true All goals completed! 🐙) ⟩

Row checker for one select condition-node primitive frontier row.

def selectBridgeFrontiersPrimitiveStepCheck (selectAdmission : SelectAdmissionArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant _entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false

Executable checker for one select row's primitive bridge frontier backing.

def selectBridgeFrontiersBackedByPrimitiveRowCheck (artifact : WireAdmissionArtifact) (selectAdmission : SelectAdmissionArtifact) : Bool := artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission)

Successful row checking proves primitive bridge frontier backing for one select row.

theorem selectBridgeFrontiersBackedByPrimitiveRowCheck_sound {artifact : WireAdmissionArtifact} {selectAdmission : SelectAdmissionArtifact} (hCheck : selectBridgeFrontiersBackedByPrimitiveRowCheck artifact selectAdmission = true) : ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant, variant ∈ selectAdmission.variants → SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits := artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.selectBridgeFrontiersBackedByPrimitiveRowCheck selectAdmission = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveStep:PrimitiveGraphStephPrimitiveStep:primitiveStep ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission primitiveStep = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits cases primitiveStep with artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = truehPrimitiveStep:PrimitiveGraphStep.empty ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission PrimitiveGraphStep.empty = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = true_binding:BindingNamehPrimitiveStep:PrimitiveGraphStep.bindingRef _binding ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.bindingRef _binding) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = true_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehPrimitiveStep:PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = true_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:selectBridgeFrontiersPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.node primitiveNode entries exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(match PrimitiveGraphStep.node primitiveNode entries exits with | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant _entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsartifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits intro variant artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNodevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variants⊢ SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits have hVariantCheck := Check.allBool_sound hPrimitiveCheck.right (fun checkedVariant _ hCheck => show SelectBridgeEntryUnique checkedVariant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode checkedVariant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.selectBridgeFrontiersBackedByPrimitiveRowCheck selectAdmission = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ variant ∈ selectAdmission.variants, SelectBridgeEntryUnique variant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode variant exits artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck✝:artifact.primitiveSteps.any (selectBridgeFrontiersPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.variants fun variant => selectBridgeEntryUniqueCheck variant entries && selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode variant exits) = truehNode:primitiveNode = selectAdmission.conditionNodevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantscheckedVariant:SelectVariantArtifactx✝:checkedVariant ∈ selectAdmission.variantshCheck:selectBridgeEntryUniqueCheck checkedVariant entries = true ∧ selectBridgeInternalExitUniqueCheck selectAdmission.conditionNode checkedVariant exits = true⊢ SelectBridgeEntryUnique checkedVariant entries ∧ SelectBridgeInternalExitUnique selectAdmission.conditionNode checkedVariant exits All goals completed! 🐙) variant hVariant All goals completed! 🐙

Executable checker for primitive backing of all select condition bridge frontiers.

def selectBridgeFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects (selectBridgeFrontiersBackedByPrimitiveRowCheck artifact)

Successful select bridge-frontier checking proves SelectBridgeFrontiersBackedByPrimitive.

theorem selectBridgeFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) : artifact.SelectBridgeFrontiersBackedByPrimitive := Check.allBool_sound hCheck (fun _selectAdmission _ hSelect => selectBridgeFrontiersBackedByPrimitiveRowCheck_sound hSelect)

Row checker for condition-node bridge entries being consumed by primitive replay.

def selectBridgeEntriesConsumedPrimitiveStepCheck (artifact : WireAdmissionArtifact) (selectAdmission : SelectAdmissionArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node entries _exits => if node = selectAdmission.conditionNode then let matchedConnections := PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps Check.allBool selectAdmission.variants fun variant => Check.allDecide entries fun entry => variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ matchedConnections else true | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => true

Executable checker for consumed select bridge entries.

def selectBridgeEntriesConsumedCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects fun selectAdmission => Check.allBool artifact.primitiveSteps (selectBridgeEntriesConsumedPrimitiveStepCheck artifact selectAdmission)

Successful select bridge-entry consumption checking proves SelectBridgeEntriesConsumed.

theorem selectBridgeEntriesConsumedCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectBridgeEntriesConsumedCheck = true) : artifact.SelectBridgeEntriesConsumed := artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = true⊢ artifact.SelectBridgeEntriesConsumed intro selectAdmission artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selects⊢ ∀ (entries exits : List AdmissionBoundaryPort), PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps → ∀ variant ∈ selectAdmission.variants, ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPort⊢ ∀ (exits : List AdmissionBoundaryPort), PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps → ∀ variant ∈ selectAdmission.variants, ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPort⊢ PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps → ∀ variant ∈ selectAdmission.variants, ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps⊢ ∀ variant ∈ selectAdmission.variants, ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifact⊢ variant ∈ selectAdmission.variants → ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variants⊢ ∀ entry ∈ entries, variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPort⊢ entry ∈ entries → variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entries⊢ variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshCompatible:variant.port.CompatibleWith entry⊢ { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps have hSelectCheck := Check.allBool_sound hCheck (fun checkedSelect _ hCheckedSelect => Check.allBool_sound hCheckedSelect (fun primitiveStep _ hPrimitiveStep => show selectBridgeEntriesConsumedPrimitiveStepCheck artifact checkedSelect primitiveStep = true artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = true⊢ artifact.SelectBridgeEntriesConsumed All goals completed! 🐙)) selectAdmission hSelect artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshCompatible:variant.port.CompatibleWith entryhSelectCheck:∀ item ∈ artifact.primitiveSteps, artifact.selectBridgeEntriesConsumedPrimitiveStepCheck selectAdmission item = truehStepCheck:artifact.selectBridgeEntriesConsumedPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.node selectAdmission.conditionNode entries exits) = true⊢ { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshCompatible:variant.port.CompatibleWith entryhSelectCheck:∀ item ∈ artifact.primitiveSteps, artifact.selectBridgeEntriesConsumedPrimitiveStepCheck selectAdmission item = truehStepCheck:(match PrimitiveGraphStep.node selectAdmission.conditionNode entries exits with | PrimitiveGraphStep.node node entries _exits => if node = selectAdmission.conditionNode then have matchedConnections := PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps; Check.allBool selectAdmission.variants fun variant => Check.allDecide entries fun entry => variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ matchedConnections else true | PrimitiveGraphStep.empty => true | PrimitiveGraphStep.bindingRef _binding => true | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => true | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => true) = true⊢ { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshCompatible:variant.port.CompatibleWith entryhSelectCheck:∀ item ∈ artifact.primitiveSteps, artifact.selectBridgeEntriesConsumedPrimitiveStepCheck selectAdmission item = truehStepCheck:(Check.allBool selectAdmission.variants fun variant => Check.allDecide entries fun entry => variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) = true⊢ { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifacthCheck:artifact.selectBridgeEntriesConsumedCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthNode:PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsvariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantsentry:AdmissionBoundaryPorthEntry:entry ∈ entrieshCompatible:variant.port.CompatibleWith entryhSelectCheck:∀ item ∈ artifact.primitiveSteps, artifact.selectBridgeEntriesConsumedPrimitiveStepCheck selectAdmission item = truehStepCheck:(Check.allBool selectAdmission.variants fun variant => Check.allDecide entries fun entry => variant.port.CompatibleWith entry → { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) = truehVariantCheck:∀ item ∈ entries, variant.port.CompatibleWith item → { fromPort := variant.port, toPort := item } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps⊢ { fromPort := variant.port, toPort := entry } ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps All goals completed! 🐙

Executable checker for the select identity-arm bridge-output branch.

def selectArmIdentityBodyShapeCheck (selectAdmission : SelectAdmissionArtifact) (exits : List AdmissionBoundaryPort) (arm : SelectArmAdmissionArtifact) (variant : SelectVariantArtifact) : Bool := decide (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) && decide (SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape])

Successful identity-arm shape checking proves the identity branch.

theorem selectArmIdentityBodyShapeCheck_sound {selectAdmission : SelectAdmissionArtifact} {exits : List AdmissionBoundaryPort} {arm : SelectArmAdmissionArtifact} {variant : SelectVariantArtifact} (hCheck : selectArmIdentityBodyShapeCheck selectAdmission exits arm variant = true) : (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] := selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:selectArmIdentityBodyShapeCheck selectAdmission exits arm variant = true⊢ (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:(decide (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) && decide (SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape])) = true⊢ (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) = true ∧ decide (SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape]) = true⊢ (arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] All goals completed! 🐙

Executable checker for the non-identity select-arm bridge-output branch.

def selectArmNonIdentityBodyShapeCheck (selectAdmission : SelectAdmissionArtifact) (exits : List AdmissionBoundaryPort) (arm : SelectArmAdmissionArtifact) (variant : SelectVariantArtifact) : Bool := decide (arm.bodyEntries.map AdmissionBoundaryPort.compatibilityShape = [variant.port.compatibilityShape]) && Check.permCheck (arm.bodyExits.map AdmissionBoundaryPort.outputShape) (SelectConditionBridgeOutputShapes selectAdmission exits)

Successful non-identity arm shape checking proves the body-boundary branch.

theorem selectArmNonIdentityBodyShapeCheck_sound {selectAdmission : SelectAdmissionArtifact} {exits : List AdmissionBoundaryPort} {arm : SelectArmAdmissionArtifact} {variant : SelectVariantArtifact} (hCheck : selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant = true) : arm.bodyEntries.map AdmissionBoundaryPort.compatibilityShape = [variant.port.compatibilityShape] ∧ (arm.bodyExits.map AdmissionBoundaryPort.outputShape).Perm (SelectConditionBridgeOutputShapes selectAdmission exits) := selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant = true⊢ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits) selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:(decide (List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape]) && Check.permCheck (List.map AdmissionBoundaryPort.outputShape arm.bodyExits) (SelectConditionBridgeOutputShapes selectAdmission exits)) = true⊢ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits) selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape]) = true ∧ Check.permCheck (List.map AdmissionBoundaryPort.outputShape arm.bodyExits) (SelectConditionBridgeOutputShapes selectAdmission exits) = true⊢ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits) All goals completed! 🐙

Executable checker for one select arm's body boundary shape.

def selectArmBodyBoundaryShapeCheck (selectAdmission : SelectAdmissionArtifact) (exits : List AdmissionBoundaryPort) (arm : SelectArmAdmissionArtifact) (variant : SelectVariantArtifact) : Bool := decide (variant.key = arm.canonicalKey) && (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant)

Successful arm-boundary shape checking proves the relational branch shape.

theorem selectArmBodyBoundaryShapeCheck_sound {selectAdmission : SelectAdmissionArtifact} {exits : List AdmissionBoundaryPort} {arm : SelectArmAdmissionArtifact} {variant : SelectVariantArtifact} (hCheck : selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant = true) : variant.key = arm.canonicalKey ∧ (((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape]) ∨ (arm.bodyEntries.map AdmissionBoundaryPort.compatibilityShape = [variant.port.compatibilityShape] ∧ (arm.bodyExits.map AdmissionBoundaryPort.outputShape).Perm (SelectConditionBridgeOutputShapes selectAdmission exits))) := selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant = true⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:(decide (variant.key = arm.canonicalKey) && (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant)) = true⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (variant.key = arm.canonicalKey) = true ∧ (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant) = true⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (variant.key = arm.canonicalKey) = true ∧ (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant) = truehKey:variant.key = arm.canonicalKey⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) cases hIdentity : selectArmIdentityBodyShapeCheck selectAdmission exits arm variant with selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (variant.key = arm.canonicalKey) = true ∧ (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant) = truehKey:variant.key = arm.canonicalKeyhIdentity:selectArmIdentityBodyShapeCheck selectAdmission exits arm variant = true⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:decide (variant.key = arm.canonicalKey) = true ∧ (selectArmIdentityBodyShapeCheck selectAdmission exits arm variant || selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant) = truehKey:variant.key = arm.canonicalKeyhIdentity:selectArmIdentityBodyShapeCheck selectAdmission exits arm variant = false⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) have hBody : selectArmNonIdentityBodyShapeCheck selectAdmission exits arm variant = true := selectAdmission:SelectAdmissionArtifactexits:List AdmissionBoundaryPortarm:SelectArmAdmissionArtifactvariant:SelectVariantArtifacthCheck:selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant = true⊢ variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 All goals completed! 🐙

Row checker for all select-arm bodies against one condition-node primitive row.

def selectArmBodyBoundariesPrimitiveStepCheck (selectAdmission : SelectAdmissionArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false

Executable checker for one select row's latent arm body boundary facts.

def selectArmBodyBoundariesMatchConditionRowCheck (artifact : WireAdmissionArtifact) (selectAdmission : SelectAdmissionArtifact) : Bool := artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission)

Successful row checking proves body-boundary facts for one select row.

theorem selectArmBodyBoundariesMatchConditionRowCheck_sound {artifact : WireAdmissionArtifact} {selectAdmission : SelectAdmissionArtifact} (hCheck : selectArmBodyBoundariesMatchConditionRowCheck artifact selectAdmission = true) : ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm, arm ∈ selectAdmission.arms → ∃ variant, variant ∈ selectAdmission.variants ∧ variant.key = arm.canonicalKey ∧ (((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape]) ∨ (arm.bodyEntries.map AdmissionBoundaryPort.compatibilityShape = [variant.port.compatibilityShape] ∧ (arm.bodyExits.map AdmissionBoundaryPort.outputShape).Perm (SelectConditionBridgeOutputShapes selectAdmission exits))) := artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.selectArmBodyBoundariesMatchConditionRowCheck selectAdmission = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveStep:PrimitiveGraphStephPrimitiveStep:primitiveStep ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission primitiveStep = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) cases primitiveStep with artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = truehPrimitiveStep:PrimitiveGraphStep.empty ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission PrimitiveGraphStep.empty = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = true_binding:BindingNamehPrimitiveStep:PrimitiveGraphStep.bindingRef _binding ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.bindingRef _binding) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = true_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehPrimitiveStep:PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = true_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:selectArmBodyBoundariesPrimitiveStepCheck selectAdmission (PrimitiveGraphStep.node primitiveNode entries exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(match PrimitiveGraphStep.node primitiveNode entries exits with | PrimitiveGraphStep.node node _entries exits => decide (node = selectAdmission.conditionNode) && Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveStepsartifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNode⊢ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) intro arm artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNodearm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.arms⊢ ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) have hArmCheck := Check.allBool_sound hPrimitiveCheck.right (fun checkedArm _ hCheckedArm => show ∃ variant, variant ∈ selectAdmission.variants ∧ variant.key = checkedArm.canonicalKey ∧ (((checkedArm.bodyNodes = [] ∧ checkedArm.bodyEntries = [] ∧ checkedArm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape]) ∨ (checkedArm.bodyEntries.map AdmissionBoundaryPort.compatibilityShape = [variant.port.compatibilityShape] ∧ (checkedArm.bodyExits.map AdmissionBoundaryPort.outputShape).Perm (SelectConditionBridgeOutputShapes selectAdmission exits))) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.selectArmBodyBoundariesMatchConditionRowCheck selectAdmission = true⊢ ∃ entries exits, PrimitiveGraphStep.node selectAdmission.conditionNode entries exits ∈ artifact.primitiveSteps ∧ ∀ arm ∈ selectAdmission.arms, ∃ variant ∈ selectAdmission.variants, variant.key = arm.canonicalKey ∧ ((arm.bodyNodes = [] ∧ arm.bodyEntries = [] ∧ arm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape arm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape arm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) artifact:WireAdmissionArtifactselectAdmission:SelectAdmissionArtifacthCheck:artifact.primitiveSteps.any (selectArmBodyBoundariesPrimitiveStepCheck selectAdmission) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:decide (primitiveNode = selectAdmission.conditionNode) = true ∧ (Check.allBool selectAdmission.arms fun arm => selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits arm variant) = truehNode:primitiveNode = selectAdmission.conditionNodearm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.armscheckedArm:SelectArmAdmissionArtifactx✝:checkedArm ∈ selectAdmission.armshCheckedArm:(selectAdmission.variants.any fun variant => selectArmBodyBoundaryShapeCheck selectAdmission exits checkedArm variant) = truevariant:SelectVariantArtifacthVariant:variant ∈ selectAdmission.variantshVariantCheck:selectArmBodyBoundaryShapeCheck selectAdmission exits checkedArm variant = true⊢ ∃ variant ∈ selectAdmission.variants, variant.key = checkedArm.canonicalKey ∧ ((checkedArm.bodyNodes = [] ∧ checkedArm.bodyEntries = [] ∧ checkedArm.bodyExits = []) ∧ SelectConditionBridgeOutputShapes selectAdmission exits = [variant.port.identityOutputShape] ∨ List.map AdmissionBoundaryPort.compatibilityShape checkedArm.bodyEntries = [variant.port.compatibilityShape] ∧ (List.map AdmissionBoundaryPort.outputShape checkedArm.bodyExits).Perm (SelectConditionBridgeOutputShapes selectAdmission exits)) All goals completed! 🐙) arm hArm All goals completed! 🐙

Executable checker for all select arm body boundary facts.

def selectArmBodyBoundariesMatchConditionCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects (selectArmBodyBoundariesMatchConditionRowCheck artifact)

Successful select arm body-boundary checking proves SelectArmBodyBoundariesMatchCondition.

theorem selectArmBodyBoundariesMatchConditionCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectArmBodyBoundariesMatchConditionCheck = true) : artifact.SelectArmBodyBoundariesMatchCondition := Check.allBool_sound hCheck (fun _selectAdmission _ hSelect => selectArmBodyBoundariesMatchConditionRowCheck_sound hSelect)

Executable checker that latent select body nodes are fresh from the top-level summary.

def selectArmBodyNodesFreshFromSummaryCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects fun selectAdmission => Check.allBool selectAdmission.arms fun arm => Check.allDecide arm.bodyNodes fun node => node ∉ artifact.nodes

Successful freshness checking proves SelectArmBodyNodesFreshFromSummary.

theorem selectArmBodyNodesFreshFromSummaryCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectArmBodyNodesFreshFromSummaryCheck = true) : artifact.SelectArmBodyNodesFreshFromSummary := artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = true⊢ artifact.SelectArmBodyNodesFreshFromSummary intro selectAdmission artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selects⊢ ∀ arm ∈ selectAdmission.arms, ∀ node ∈ arm.bodyNodes, node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifact⊢ arm ∈ selectAdmission.arms → ∀ node ∈ arm.bodyNodes, node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.arms⊢ ∀ node ∈ arm.bodyNodes, node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.armsnode:NodeId⊢ node ∈ arm.bodyNodes → node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.armsnode:NodeIdhNode:node ∈ arm.bodyNodes⊢ node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.armsnode:NodeIdhNode:node ∈ arm.bodyNodeshSelectCheck:∀ item ∈ selectAdmission.arms, ∀ item_1 ∈ item.bodyNodes, item_1 ∉ artifact.nodes⊢ node ∉ artifact.nodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesFreshFromSummaryCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsarm:SelectArmAdmissionArtifacthArm:arm ∈ selectAdmission.armsnode:NodeIdhNode:node ∈ arm.bodyNodeshSelectCheck:∀ item ∈ selectAdmission.arms, ∀ item_1 ∈ item.bodyNodes, item_1 ∉ artifact.nodeshArmCheck:∀ item ∈ arm.bodyNodes, item ∉ artifact.nodes⊢ node ∉ artifact.nodes All goals completed! 🐙

Row-pair checker that latent select arm body nodes are pairwise disjoint.

def selectArmBodyNodesDisjointPairCheck (left right : SelectArmAdmissionArtifact) : Bool := if left.canonicalKey = right.canonicalKey then true else Check.allDecide left.bodyNodes fun node => node ∉ right.bodyNodes

Successful row-pair checking proves body-node disjointness for distinct canonical keys.

theorem selectArmBodyNodesDisjointPairCheck_sound {left right : SelectArmAdmissionArtifact} (hCheck : selectArmBodyNodesDisjointPairCheck left right = true) (hKeys : left.canonicalKey ≠ right.canonicalKey) : ∀ node, node ∈ left.bodyNodes → node ∉ right.bodyNodes := left:SelectArmAdmissionArtifactright:SelectArmAdmissionArtifacthCheck:selectArmBodyNodesDisjointPairCheck left right = truehKeys:left.canonicalKey ≠ right.canonicalKey⊢ ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes left:SelectArmAdmissionArtifactright:SelectArmAdmissionArtifacthCheck:(if left.canonicalKey = right.canonicalKey then true else Check.allDecide left.bodyNodes fun node => node ∉ right.bodyNodes) = truehKeys:left.canonicalKey ≠ right.canonicalKey⊢ ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes left:SelectArmAdmissionArtifactright:SelectArmAdmissionArtifacthCheck:(Check.allDecide left.bodyNodes fun node => node ∉ right.bodyNodes) = truehKeys:left.canonicalKey ≠ right.canonicalKey⊢ ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes All goals completed! 🐙

Executable checker that latent select arm body-node domains are pairwise disjoint.

def selectArmBodyNodesPairwiseDisjointCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.selects fun selectAdmission => Check.allBool selectAdmission.arms fun left => Check.allBool selectAdmission.arms fun right => selectArmBodyNodesDisjointPairCheck left right

Successful body-node disjointness checking proves SelectArmBodyNodesPairwiseDisjoint.

theorem selectArmBodyNodesPairwiseDisjointCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.selectArmBodyNodesPairwiseDisjointCheck = true) : artifact.SelectArmBodyNodesPairwiseDisjoint := artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = true⊢ artifact.SelectArmBodyNodesPairwiseDisjoint intro selectAdmission artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selects⊢ ∀ left ∈ selectAdmission.arms, ∀ right ∈ selectAdmission.arms, left.canonicalKey ≠ right.canonicalKey → ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifact⊢ left ∈ selectAdmission.arms → ∀ right ∈ selectAdmission.arms, left.canonicalKey ≠ right.canonicalKey → ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.arms⊢ ∀ right ∈ selectAdmission.arms, left.canonicalKey ≠ right.canonicalKey → ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifact⊢ right ∈ selectAdmission.arms → left.canonicalKey ≠ right.canonicalKey → ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.arms⊢ left.canonicalKey ≠ right.canonicalKey → ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.armshKeys:left.canonicalKey ≠ right.canonicalKey⊢ ∀ node ∈ left.bodyNodes, node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.armshKeys:left.canonicalKey ≠ right.canonicalKeynode:NodeId⊢ node ∈ left.bodyNodes → node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.armshKeys:left.canonicalKey ≠ right.canonicalKeynode:NodeIdhNode:node ∈ left.bodyNodes⊢ node ∉ right.bodyNodes have hSelectCheck := Check.allBool_sound hCheck (fun checkedSelect _ hCheckedSelect => Check.allBool_sound hCheckedSelect (fun checkedLeft _ hCheckedLeft => Check.allBool_sound hCheckedLeft (fun checkedRight _ hCheckedRight => show selectArmBodyNodesDisjointPairCheck checkedLeft checkedRight = true artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = true⊢ artifact.SelectArmBodyNodesPairwiseDisjoint All goals completed! 🐙))) selectAdmission hSelect artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.armshKeys:left.canonicalKey ≠ right.canonicalKeynode:NodeIdhNode:node ∈ left.bodyNodeshSelectCheck:∀ item ∈ selectAdmission.arms, ∀ item_1 ∈ selectAdmission.arms, selectArmBodyNodesDisjointPairCheck item item_1 = truehLeftCheck:∀ item ∈ selectAdmission.arms, selectArmBodyNodesDisjointPairCheck left item = true⊢ node ∉ right.bodyNodes artifact:WireAdmissionArtifacthCheck:artifact.selectArmBodyNodesPairwiseDisjointCheck = trueselectAdmission:SelectAdmissionArtifacthSelect:selectAdmission ∈ artifact.selectsleft:SelectArmAdmissionArtifacthLeft:left ∈ selectAdmission.armsright:SelectArmAdmissionArtifacthRight:right ∈ selectAdmission.armshKeys:left.canonicalKey ≠ right.canonicalKeynode:NodeIdhNode:node ∈ left.bodyNodeshSelectCheck:∀ item ∈ selectAdmission.arms, ∀ item_1 ∈ selectAdmission.arms, selectArmBodyNodesDisjointPairCheck item item_1 = truehLeftCheck:∀ item ∈ selectAdmission.arms, selectArmBodyNodesDisjointPairCheck left item = truehRightCheck:selectArmBodyNodesDisjointPairCheck left right = true⊢ node ∉ right.bodyNodes All goals completed! 🐙

Component Frontier Cross-Reference Checks

Executable checker that generated-child frontiers are primitive-backed.

def generatedChildComponentFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) (child : GeneratedChildArtifact) : Bool := let exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps let entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps (Check.allDecide child.outputs fun output => output.key ∈ exitKeys) && (Check.allDecide child.inputs fun input => input.key ∈ entryKeys)

Successful generated-child component-frontier checking proves primitive backing.

theorem generatedChildComponentFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} {child : GeneratedChildArtifact} (hCheck : generatedChildComponentFrontiersBackedByPrimitiveCheck artifact child = true) : (∀ output, output ∈ child.outputs → output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ (∀ input, input ∈ child.inputs → input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) := artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.generatedChildComponentFrontiersBackedByPrimitiveCheck child = true⊢ (∀ output ∈ child.outputs, output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ input ∈ child.inputs, input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:(have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; (Check.allDecide child.outputs fun output => output.key ∈ exitKeys) && Check.allDecide child.inputs fun input => input.key ∈ entryKeys) = true⊢ (∀ output ∈ child.outputs, output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ input ∈ child.inputs, input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:(Check.allDecide child.outputs fun output => output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide child.inputs fun input => input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) = true⊢ (∀ output ∈ child.outputs, output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ ∀ input ∈ child.inputs, input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps All goals completed! 🐙

Executable checker that all used children in one generated row are primitive-backed.

def generatedFormComponentFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) (generated : GeneratedFormArtifact) : Bool := Check.allBool generated.usedChildren (generatedChildComponentFrontiersBackedByPrimitiveCheck artifact)

Successful generated-row checking proves primitive backing for every used child.

theorem generatedFormComponentFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} {generated : GeneratedFormArtifact} (hCheck : generatedFormComponentFrontiersBackedByPrimitiveCheck artifact generated = true) : ∀ child, child ∈ generated.usedChildren → (∀ output, output ∈ child.outputs → output.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) ∧ (∀ input, input ∈ child.inputs → input.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) := Check.allBool_sound hCheck (fun _child _ hChild => generatedChildComponentFrontiersBackedByPrimitiveCheck_sound hChild)

Executable checker that source-visible phantom frontiers are primitive-backed.

def phantomAdapterComponentFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) (phantom : PhantomAdapterArtifact) : Bool := let entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps let exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps match phantom.direction with | PhantomAdapterDirection.gather => decide (phantom.singular.key ∈ entryKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ exitKeys | PhantomAdapterDirection.scatter => decide (phantom.singular.key ∈ exitKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ entryKeys

Successful phantom component-frontier checking proves primitive backing.

theorem phantomAdapterComponentFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} {phantom : PhantomAdapterArtifact} (hCheck : phantomAdapterComponentFrontiersBackedByPrimitiveCheck artifact phantom = true) : match phantom.direction with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi, multi ∈ phantom.multi → multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi, multi ∈ phantom.multi → multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps := artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck phantom = true⊢ match phantom.direction with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps cases hDirection : phantom.direction with artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck phantom = truehDirection:phantom.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; match phantom.direction with | PhantomAdapterDirection.gather => decide (phantom.singular.key ∈ entryKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ exitKeys | PhantomAdapterDirection.scatter => decide (phantom.singular.key ∈ exitKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ entryKeys) = truehDirection:phantom.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => decide (phantom.singular.key ∈ entryKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ exitKeys | PhantomAdapterDirection.scatter => decide (phantom.singular.key ∈ exitKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ entryKeys) = truehDirection:phantom.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:decide (phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide phantom.multi fun multi => multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) = truehDirection:phantom.direction = PhantomAdapterDirection.gather⊢ match PhantomAdapterDirection.gather with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck phantom = truehDirection:phantom.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; match phantom.direction with | PhantomAdapterDirection.gather => decide (phantom.singular.key ∈ entryKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ exitKeys | PhantomAdapterDirection.scatter => decide (phantom.singular.key ∈ exitKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ entryKeys) = truehDirection:phantom.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => decide (phantom.singular.key ∈ entryKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ exitKeys | PhantomAdapterDirection.scatter => decide (phantom.singular.key ∈ exitKeys) && Check.allDecide phantom.multi fun multi => multi.key ∈ entryKeys) = truehDirection:phantom.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:decide (phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide phantom.multi fun multi => multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) = truehDirection:phantom.direction = PhantomAdapterDirection.scatter⊢ match PhantomAdapterDirection.scatter with | PhantomAdapterDirection.gather => phantom.singular.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps | PhantomAdapterDirection.scatter => phantom.singular.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps ∧ ∀ multi ∈ phantom.multi, multi.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps All goals completed! 🐙

Executable checker that select variant frontiers are primitive-backed.

def selectVariantsComponentFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) (selectAdmission : SelectAdmissionArtifact) : Bool := let exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps Check.allDecide selectAdmission.variants fun variant => variant.port.key ∈ exitKeys

Successful select-row checking proves primitive backing for every variant.

theorem selectVariantsComponentFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} {selectAdmission : SelectAdmissionArtifact} (hCheck : selectVariantsComponentFrontiersBackedByPrimitiveCheck artifact selectAdmission = true) : ∀ variant, variant ∈ selectAdmission.variants → variant.port.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps := Check.allDecide_sound hCheck

Executable checker for component-specific primitive frontier backing.

def componentFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.generatedForms (generatedFormComponentFrontiersBackedByPrimitiveCheck artifact) && Check.allBool artifact.phantomAdapters (phantomAdapterComponentFrontiersBackedByPrimitiveCheck artifact) && Check.allBool artifact.selects (selectVariantsComponentFrontiersBackedByPrimitiveCheck artifact)

Successful component-frontier checking proves ComponentFrontiersBackedByPrimitive.

theorem componentFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.componentFrontiersBackedByPrimitiveCheck = true) : artifact.ComponentFrontiersBackedByPrimitive := artifact:WireAdmissionArtifacthCheck:artifact.componentFrontiersBackedByPrimitiveCheck = true⊢ artifact.ComponentFrontiersBackedByPrimitive artifact:WireAdmissionArtifacthCheck:(Check.allBool artifact.generatedForms artifact.generatedFormComponentFrontiersBackedByPrimitiveCheck && Check.allBool artifact.phantomAdapters artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck && Check.allBool artifact.selects artifact.selectVariantsComponentFrontiersBackedByPrimitiveCheck) = true⊢ artifact.ComponentFrontiersBackedByPrimitive artifact:WireAdmissionArtifacthCheck:(Check.allBool artifact.generatedForms artifact.generatedFormComponentFrontiersBackedByPrimitiveCheck && Check.allBool artifact.phantomAdapters artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck) = true ∧ Check.allBool artifact.selects artifact.selectVariantsComponentFrontiersBackedByPrimitiveCheck = true⊢ artifact.ComponentFrontiersBackedByPrimitive artifact:WireAdmissionArtifacthCheck:(Check.allBool artifact.generatedForms artifact.generatedFormComponentFrontiersBackedByPrimitiveCheck = true ∧ Check.allBool artifact.phantomAdapters artifact.phantomAdapterComponentFrontiersBackedByPrimitiveCheck = true) ∧ Check.allBool artifact.selects artifact.selectVariantsComponentFrontiersBackedByPrimitiveCheck = true⊢ artifact.ComponentFrontiersBackedByPrimitive All goals completed! 🐙

Row checker for the primitive node frontier row behind a generated child.

def generatedChildFrontiersPrimitiveStepCheck (child : GeneratedChildArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node entries exits => decide (node = child.node) && Check.permCheck child.inputKeys (entries.map AdmissionBoundaryPort.key) && Check.permCheck child.outputKeys (exits.map AdmissionBoundaryPort.key) | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false

Executable checker that one generated child matches its primitive node frontier row.

def generatedChildFrontiersMatchPrimitiveChildCheck (artifact : WireAdmissionArtifact) (child : GeneratedChildArtifact) : Bool := artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child)

Successful child checking proves exact primitive frontier matching.

theorem generatedChildFrontiersMatchPrimitiveChildCheck_sound {artifact : WireAdmissionArtifact} {child : GeneratedChildArtifact} (hCheck : generatedChildFrontiersMatchPrimitiveChildCheck artifact child = true) : ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (entries.map AdmissionBoundaryPort.key) ∧ child.outputKeys.Perm (exits.map AdmissionBoundaryPort.key) := artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.generatedChildFrontiersMatchPrimitiveChildCheck child = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveStep:PrimitiveGraphStephPrimitiveStep:primitiveStep ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child primitiveStep = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) cases primitiveStep with artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = truehPrimitiveStep:PrimitiveGraphStep.empty ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child PrimitiveGraphStep.empty = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = true_binding:BindingNamehPrimitiveStep:PrimitiveGraphStep.bindingRef _binding ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child (PrimitiveGraphStep.bindingRef _binding) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = true_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehPrimitiveStep:PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = true_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:generatedChildFrontiersPrimitiveStepCheck child (PrimitiveGraphStep.node primitiveNode entries exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(match PrimitiveGraphStep.node primitiveNode entries exits with | PrimitiveGraphStep.node node entries exits => decide (node = child.node) && Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) && Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(decide (primitiveNode = child.node) = true ∧ Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = true) ∧ Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveStepsartifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries)artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ child.inputKeys.Perm (List.map AdmissionBoundaryPort.key entries) All goals completed! 🐙 artifact:WireAdmissionArtifactchild:GeneratedChildArtifacthCheck:artifact.primitiveSteps.any (generatedChildFrontiersPrimitiveStepCheck child) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshOutputs:Check.permCheck child.outputKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = child.node) = truehInputs:Check.permCheck child.inputKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = child.node⊢ child.outputKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙

Executable checker that all used children in one generated row match primitive rows.

def generatedFormChildFrontiersMatchPrimitiveCheck (artifact : WireAdmissionArtifact) (generated : GeneratedFormArtifact) : Bool := Check.allBool generated.usedChildren (generatedChildFrontiersMatchPrimitiveChildCheck artifact)

Successful generated-row checking proves primitive frontier exactness for every child.

theorem generatedFormChildFrontiersMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} {generated : GeneratedFormArtifact} (hCheck : generatedFormChildFrontiersMatchPrimitiveCheck artifact generated = true) : ∀ child, child ∈ generated.usedChildren → ∃ entries exits, PrimitiveGraphStep.node child.node entries exits ∈ artifact.primitiveSteps ∧ child.inputKeys.Perm (entries.map AdmissionBoundaryPort.key) ∧ child.outputKeys.Perm (exits.map AdmissionBoundaryPort.key) := Check.allBool_sound hCheck (fun _child _ hChild => generatedChildFrontiersMatchPrimitiveChildCheck_sound hChild)

Executable checker for generated-child primitive frontier exactness.

def generatedChildFrontiersMatchPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.generatedForms (generatedFormChildFrontiersMatchPrimitiveCheck artifact)

Successful generated-frontier checking proves GeneratedChildFrontiersMatchPrimitive.

theorem generatedChildFrontiersMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.generatedChildFrontiersMatchPrimitiveCheck = true) : artifact.GeneratedChildFrontiersMatchPrimitive := Check.allBool_sound hCheck (fun _generated _ hGenerated => generatedFormChildFrontiersMatchPrimitiveCheck_sound hGenerated)

Phantom Bridge Cross-Reference Checks

Executable checker that one phantom row's internal bridge endpoints are primitive-backed.

def phantomBridgeFrontiersBackedByPrimitiveRowCheck (artifact : WireAdmissionArtifact) (phantom : PhantomAdapterArtifact) : Bool := let entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps let exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps (Check.allDecide phantom.leftBulk fun pair => pair.toPort.key ∈ entryKeys) && (Check.allDecide phantom.rightBulk fun pair => pair.fromPort.key ∈ exitKeys)

Successful phantom bridge-frontier backing checking proves one phantom row.

theorem phantomBridgeFrontiersBackedByPrimitiveRowCheck_sound {artifact : WireAdmissionArtifact} {phantom : PhantomAdapterArtifact} (hCheck : phantomBridgeFrontiersBackedByPrimitiveRowCheck artifact phantom = true) : (∀ pair, pair ∈ phantom.leftBulk → pair.toPort.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) ∧ (∀ pair, pair ∈ phantom.rightBulk → pair.fromPort.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) := artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomBridgeFrontiersBackedByPrimitiveRowCheck phantom = true⊢ (∀ pair ∈ phantom.leftBulk, pair.toPort.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair.fromPort.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have entryKeys := PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps; have exitKeys := PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps; (Check.allDecide phantom.leftBulk fun pair => pair.toPort.key ∈ entryKeys) && Check.allDecide phantom.rightBulk fun pair => pair.fromPort.key ∈ exitKeys) = true⊢ (∀ pair ∈ phantom.leftBulk, pair.toPort.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair.fromPort.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(Check.allDecide phantom.leftBulk fun pair => pair.toPort.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) = true ∧ (Check.allDecide phantom.rightBulk fun pair => pair.fromPort.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps) = true⊢ (∀ pair ∈ phantom.leftBulk, pair.toPort.key ∈ PrimitiveGraphStep.nodeEntryKeysList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair.fromPort.key ∈ PrimitiveGraphStep.nodeExitKeysList artifact.primitiveSteps All goals completed! 🐙

Executable checker for all phantom bridge endpoint primitive backing.

def phantomBridgeFrontiersBackedByPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.phantomAdapters (phantomBridgeFrontiersBackedByPrimitiveRowCheck artifact)

Successful backing checking proves PhantomBridgeFrontiersBackedByPrimitive.

theorem phantomBridgeFrontiersBackedByPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = true) : artifact.PhantomBridgeFrontiersBackedByPrimitive := Check.allBool_sound hCheck (fun _phantom _ hPhantom => phantomBridgeFrontiersBackedByPrimitiveRowCheck_sound hPhantom)

Row checker for the primitive node frontier row behind one phantom adapter.

def phantomBridgeFrontiersPrimitiveStepCheck (phantom : PhantomAdapterArtifact) : PrimitiveGraphStep → Bool | PrimitiveGraphStep.node node entries exits => decide (node = phantom.node) && Check.permCheck phantom.leftBulkTargetKeys (entries.map AdmissionBoundaryPort.key) && Check.permCheck phantom.rightBulkSourceKeys (exits.map AdmissionBoundaryPort.key) | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false

Executable checker that one phantom row exactly matches its primitive node frontier row.

def phantomBridgeFrontiersMatchPrimitiveRowCheck (artifact : WireAdmissionArtifact) (phantom : PhantomAdapterArtifact) : Bool := artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom)

Successful row checking proves one phantom bridge frontier match.

theorem phantomBridgeFrontiersMatchPrimitiveRowCheck_sound {artifact : WireAdmissionArtifact} {phantom : PhantomAdapterArtifact} (hCheck : phantomBridgeFrontiersMatchPrimitiveRowCheck artifact phantom = true) : ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (entries.map AdmissionBoundaryPort.key) ∧ phantom.rightBulkSourceKeys.Perm (exits.map AdmissionBoundaryPort.key) := artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomBridgeFrontiersMatchPrimitiveRowCheck phantom = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveStep:PrimitiveGraphStephPrimitiveStep:primitiveStep ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom primitiveStep = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) cases primitiveStep with artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = truehPrimitiveStep:PrimitiveGraphStep.empty ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom PrimitiveGraphStep.empty = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = true_binding:BindingNamehPrimitiveStep:PrimitiveGraphStep.bindingRef _binding ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom (PrimitiveGraphStep.bindingRef _binding) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = true_leftNodes:List NodeId_rightNodes:List NodeId_leftBindings:List BindingName_rightBindings:List BindingNamehPrimitiveStep:PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom (PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = true_leftExits:List AdmissionBoundaryPort_rightEntries:List AdmissionBoundaryPort_matchedPairs:List AdmissionConnection_unmatchedLeftExits:List AdmissionBoundaryPort_unmatchedRightEntries:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom (PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:phantomBridgeFrontiersPrimitiveStepCheck phantom (PrimitiveGraphStep.node primitiveNode entries exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(match PrimitiveGraphStep.node primitiveNode entries exits with | PrimitiveGraphStep.node node entries exits => decide (node = phantom.node) && Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) && Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) | PrimitiveGraphStep.empty => false | PrimitiveGraphStep.bindingRef _binding => false | PrimitiveGraphStep.overlay _leftNodes _rightNodes _leftBindings _rightBindings => false | PrimitiveGraphStep.connect _leftExits _rightEntries _matchedPairs _unmatchedLeftExits _unmatchedRightEntries => false) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshPrimitiveCheck:(decide (primitiveNode = phantom.node) = true ∧ Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = true) ∧ Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = true⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ ∃ entries exits, PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps ∧ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) ∧ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveStepsartifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries)artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ PrimitiveGraphStep.node phantom.node entries exits ∈ artifact.primitiveSteps All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ phantom.leftBulkTargetKeys.Perm (List.map AdmissionBoundaryPort.key entries) All goals completed! 🐙 artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.primitiveSteps.any (phantomBridgeFrontiersPrimitiveStepCheck phantom) = trueprimitiveNode:NodeIdentries:List AdmissionBoundaryPortexits:List AdmissionBoundaryPorthPrimitiveStep:PrimitiveGraphStep.node primitiveNode entries exits ∈ artifact.primitiveStepshRight:Check.permCheck phantom.rightBulkSourceKeys (List.map AdmissionBoundaryPort.key exits) = truehNode:decide (primitiveNode = phantom.node) = truehLeft:Check.permCheck phantom.leftBulkTargetKeys (List.map AdmissionBoundaryPort.key entries) = truehNodeEq:primitiveNode = phantom.node⊢ phantom.rightBulkSourceKeys.Perm (List.map AdmissionBoundaryPort.key exits) All goals completed! 🐙

Executable checker for all phantom bridge frontier exactness rows.

def phantomBridgeFrontiersMatchPrimitiveCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.phantomAdapters (phantomBridgeFrontiersMatchPrimitiveRowCheck artifact)

Successful frontier-match checking proves PhantomBridgeFrontiersMatchPrimitive.

theorem phantomBridgeFrontiersMatchPrimitiveCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.phantomBridgeFrontiersMatchPrimitiveCheck = true) : artifact.PhantomBridgeFrontiersMatchPrimitive := Check.allBool_sound hCheck (fun _phantom _ hPhantom => phantomBridgeFrontiersMatchPrimitiveRowCheck_sound hPhantom)

Executable checker that one phantom row's bulk contractions were replayed.

def phantomBridgeBulkConnectionsReplayedRowCheck (artifact : WireAdmissionArtifact) (phantom : PhantomAdapterArtifact) : Bool := let matchedConnections := PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps (Check.allDecide phantom.leftBulk fun pair => pair ∈ matchedConnections) && (Check.allDecide phantom.rightBulk fun pair => pair ∈ matchedConnections)

Successful replay checking proves one phantom row's bulk contractions were replayed.

theorem phantomBridgeBulkConnectionsReplayedRowCheck_sound {artifact : WireAdmissionArtifact} {phantom : PhantomAdapterArtifact} (hCheck : phantomBridgeBulkConnectionsReplayedRowCheck artifact phantom = true) : (∀ pair, pair ∈ phantom.leftBulk → pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) ∧ (∀ pair, pair ∈ phantom.rightBulk → pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) := artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:artifact.phantomBridgeBulkConnectionsReplayedRowCheck phantom = true⊢ (∀ pair ∈ phantom.leftBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(have matchedConnections := PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps; (Check.allDecide phantom.leftBulk fun pair => pair ∈ matchedConnections) && Check.allDecide phantom.rightBulk fun pair => pair ∈ matchedConnections) = true⊢ (∀ pair ∈ phantom.leftBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps artifact:WireAdmissionArtifactphantom:PhantomAdapterArtifacthCheck:(Check.allDecide phantom.leftBulk fun pair => pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) = true ∧ (Check.allDecide phantom.rightBulk fun pair => pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) = true⊢ (∀ pair ∈ phantom.leftBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps) ∧ ∀ pair ∈ phantom.rightBulk, pair ∈ PrimitiveGraphStep.matchedConnectionsList artifact.primitiveSteps All goals completed! 🐙

Executable checker for all phantom bridge bulk replay rows.

def phantomBridgeBulkConnectionsReplayedCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.phantomAdapters (phantomBridgeBulkConnectionsReplayedRowCheck artifact)

Successful replay checking proves PhantomBridgeBulkConnectionsReplayed.

theorem phantomBridgeBulkConnectionsReplayedCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.phantomBridgeBulkConnectionsReplayedCheck = true) : artifact.PhantomBridgeBulkConnectionsReplayed := Check.allBool_sound hCheck (fun _phantom _ hPhantom => phantomBridgeBulkConnectionsReplayedRowCheck_sound hPhantom)

Executable checker for all component-domain closure obligations.

def componentDomainsClosedCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.primitiveSteps (primitiveStepDomainClosedCheck artifact.nodes artifact.bindingRefs) && Check.allBool artifact.generatedForms (generatedFormDomainClosedCheck artifact.nodes) && Check.allBool artifact.phantomAdapters (phantomAdapterDomainClosedCheck artifact.nodes) && Check.allBool artifact.selects (selectAdmissionDomainClosedCheck artifact.nodes)

Successful component-domain checking proves ComponentDomainsClosed.

theorem componentDomainsClosedCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.componentDomainsClosedCheck = true) : artifact.ComponentDomainsClosed := artifact:WireAdmissionArtifacthCheck:artifact.componentDomainsClosedCheck = true⊢ artifact.ComponentDomainsClosed artifact:WireAdmissionArtifacthCheck:(Check.allBool artifact.primitiveSteps (primitiveStepDomainClosedCheck artifact.nodes artifact.bindingRefs) && Check.allBool artifact.generatedForms (generatedFormDomainClosedCheck artifact.nodes) && Check.allBool artifact.phantomAdapters (phantomAdapterDomainClosedCheck artifact.nodes) && Check.allBool artifact.selects (selectAdmissionDomainClosedCheck artifact.nodes)) = true⊢ artifact.ComponentDomainsClosed artifact:WireAdmissionArtifacthCheck:((Check.allBool artifact.primitiveSteps (primitiveStepDomainClosedCheck artifact.nodes artifact.bindingRefs) = true ∧ Check.allBool artifact.generatedForms (generatedFormDomainClosedCheck artifact.nodes) = true) ∧ Check.allBool artifact.phantomAdapters (phantomAdapterDomainClosedCheck artifact.nodes) = true) ∧ Check.allBool artifact.selects (selectAdmissionDomainClosedCheck artifact.nodes) = true⊢ artifact.ComponentDomainsClosed artifact:WireAdmissionArtifacthSelects:Check.allBool artifact.selects (selectAdmissionDomainClosedCheck artifact.nodes) = truehPhantom:Check.allBool artifact.phantomAdapters (phantomAdapterDomainClosedCheck artifact.nodes) = truehPrimitive:Check.allBool artifact.primitiveSteps (primitiveStepDomainClosedCheck artifact.nodes artifact.bindingRefs) = truehGenerated:Check.allBool artifact.generatedForms (generatedFormDomainClosedCheck artifact.nodes) = true⊢ artifact.ComponentDomainsClosed All goals completed! 🐙

Executable checker that generated-form rows are replay-addressable.

def generatedFormsReferencedCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.generatedForms (generatedFormReferencedCheck artifact.bindingRefs)

Successful generated-form reference checking proves GeneratedFormsReferenced.

theorem generatedFormsReferencedCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.generatedFormsReferencedCheck = true) : artifact.GeneratedFormsReferenced := Check.allBool_sound hCheck (fun _generated _ hGenerated => generatedFormReferencedCheck_sound hGenerated)

Executable checker that all generated-form rows are locally valid.

def generatedFormsValidCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.generatedForms generatedFormValidCheck

Successful generated-form list checking proves GeneratedFormsValid.

theorem generatedFormsValidCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.generatedFormsValidCheck = true) : artifact.GeneratedFormsValid := Check.allBool_sound hCheck (fun _generated _ hGenerated => generatedFormValidCheck_sound hGenerated)

Executable checker that all phantom-adapter rows are locally valid.

def phantomAdaptersValidCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.phantomAdapters phantomAdapterValidCheck

Successful phantom-adapter list checking proves PhantomAdaptersValid.

theorem phantomAdaptersValidCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.phantomAdaptersValidCheck = true) : artifact.PhantomAdaptersValid := Check.allBool_sound hCheck (fun _phantom _ hPhantom => phantomAdapterValidCheck_sound hPhantom)

Executable checker for component-row identity uniqueness.

def componentRowsUniqueCheck (artifact : WireAdmissionArtifact) : Bool := Check.nodupMapCheck artifact.generatedForms GeneratedFormArtifact.binding && Check.nodupMapCheck artifact.phantomAdapters PhantomAdapterArtifact.node && Check.nodupMapCheck artifact.selects SelectAdmissionArtifact.conditionNode && Check.nodupCheck artifact.componentRoleNodes

Successful component-row checking proves ComponentRowsUnique.

theorem componentRowsUniqueCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.componentRowsUniqueCheck = true) : artifact.ComponentRowsUnique := artifact:WireAdmissionArtifacthCheck:artifact.componentRowsUniqueCheck = true⊢ artifact.ComponentRowsUnique artifact:WireAdmissionArtifacthCheck:(Check.nodupMapCheck artifact.generatedForms GeneratedFormArtifact.binding && Check.nodupMapCheck artifact.phantomAdapters PhantomAdapterArtifact.node && Check.nodupMapCheck artifact.selects SelectAdmissionArtifact.conditionNode && Check.nodupCheck artifact.componentRoleNodes) = true⊢ artifact.ComponentRowsUnique artifact:WireAdmissionArtifacthCheck:((Check.nodupMapCheck artifact.generatedForms GeneratedFormArtifact.binding = true ∧ Check.nodupMapCheck artifact.phantomAdapters PhantomAdapterArtifact.node = true) ∧ Check.nodupMapCheck artifact.selects SelectAdmissionArtifact.conditionNode = true) ∧ Check.nodupCheck artifact.componentRoleNodes = true⊢ artifact.ComponentRowsUnique artifact:WireAdmissionArtifacthRoles:Check.nodupCheck artifact.componentRoleNodes = truehSelect:Check.nodupMapCheck artifact.selects SelectAdmissionArtifact.conditionNode = truehGenerated:Check.nodupMapCheck artifact.generatedForms GeneratedFormArtifact.binding = truehPhantom:Check.nodupMapCheck artifact.phantomAdapters PhantomAdapterArtifact.node = true⊢ artifact.ComponentRowsUnique All goals completed! 🐙

Executable checker for primitive graph-step row-local validity.

def primitiveStepsValidCheck (artifact : WireAdmissionArtifact) : Bool := Check.allBool artifact.primitiveSteps PrimitiveGraphStep.validCheck

Successful primitive-step checking proves PrimitiveStepsValid.

theorem primitiveStepsValidCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.primitiveStepsValidCheck = true) : artifact.PrimitiveStepsValid := artifact:WireAdmissionArtifacthCheck:artifact.primitiveStepsValidCheck = true⊢ artifact.PrimitiveStepsValid All goals completed! 🐙

Executable checker-record counterpart of ValidatorReady.

The name is retained from the earlier staged checker slices. At this point it contains every field needed to construct ValidatorReady.

structure ValidatorReadyCore (artifact : WireAdmissionArtifact) : Prop where schemaCurrent : artifact.SchemaCurrent summaryKeysUnique : artifact.SummaryKeysUnique summaryRowsValid : artifact.SummaryRowsValid summaryDomainClosed : artifact.SummaryDomainClosed summaryIdentitiesMatchPrimitive : artifact.SummaryIdentitiesMatchPrimitive summaryFrontiersBackedByPrimitive : artifact.SummaryFrontiersBackedByPrimitive summaryFrontiersMatchPrimitive : artifact.SummaryFrontiersMatchPrimitive rawConnectionsMatchPrimitive : artifact.RawConnectionsMatchPrimitive componentDomainsClosed : artifact.ComponentDomainsClosed selectsValid : artifact.SelectsValid componentRowsUnique : artifact.ComponentRowsUnique generatedFormsReferenced : artifact.GeneratedFormsReferenced componentFrontiersBackedByPrimitive : artifact.ComponentFrontiersBackedByPrimitive generatedChildFrontiersMatchPrimitive : artifact.GeneratedChildFrontiersMatchPrimitive generatedFormsValid : artifact.GeneratedFormsValid phantomAdaptersValid : artifact.PhantomAdaptersValid primitiveStepsValid : artifact.PrimitiveStepsValid primitiveTraceStackValid : artifact.PrimitiveTraceStackValid primitiveOverlayLedgersPrefixAvailable : artifact.PrimitiveOverlayLedgersPrefixAvailable primitiveConnectFrontiersBackedByNodes : artifact.PrimitiveConnectFrontiersBackedByNodes primitiveConnectFrontiersPrefixAvailable : artifact.PrimitiveConnectFrontiersPrefixAvailable selectBridgeFrontiersBackedByPrimitive : artifact.SelectBridgeFrontiersBackedByPrimitive selectBridgeEntriesConsumed : artifact.SelectBridgeEntriesConsumed selectArmBodyBoundariesMatchCondition : artifact.SelectArmBodyBoundariesMatchCondition selectArmBodyNodesFreshFromSummary : artifact.SelectArmBodyNodesFreshFromSummary selectArmBodyNodesPairwiseDisjoint : artifact.SelectArmBodyNodesPairwiseDisjoint phantomBridgeFrontiersBackedByPrimitive : artifact.PhantomBridgeFrontiersBackedByPrimitive phantomBridgeFrontiersMatchPrimitive : artifact.PhantomBridgeFrontiersMatchPrimitive phantomBridgeBulkConnectionsReplayed : artifact.PhantomBridgeBulkConnectionsReplayed

Full validator readiness implies the executable core contract.

theorem validatorReady_core {artifact : WireAdmissionArtifact} (hReady : artifact.ValidatorReady) : artifact.ValidatorReadyCore where schemaCurrent := hReady.schemaCurrent summaryKeysUnique := hReady.summaryKeysUnique summaryRowsValid := hReady.summaryRowsValid summaryDomainClosed := hReady.summaryDomainClosed summaryIdentitiesMatchPrimitive := hReady.summaryIdentitiesMatchPrimitive summaryFrontiersBackedByPrimitive := hReady.summaryFrontiersBackedByPrimitive summaryFrontiersMatchPrimitive := hReady.summaryFrontiersMatchPrimitive rawConnectionsMatchPrimitive := hReady.rawConnectionsMatchPrimitive componentDomainsClosed := hReady.componentDomainsClosed selectsValid := hReady.selectsValid componentRowsUnique := hReady.componentRowsUnique generatedFormsReferenced := hReady.generatedFormsReferenced componentFrontiersBackedByPrimitive := hReady.componentFrontiersBackedByPrimitive generatedChildFrontiersMatchPrimitive := hReady.generatedChildFrontiersMatchPrimitive generatedFormsValid := hReady.generatedFormsValid phantomAdaptersValid := hReady.phantomAdaptersValid primitiveStepsValid := hReady.primitiveStepsValid primitiveTraceStackValid := hReady.primitiveTraceStackValid primitiveOverlayLedgersPrefixAvailable := hReady.primitiveOverlayLedgersPrefixAvailable primitiveConnectFrontiersBackedByNodes := hReady.primitiveConnectFrontiersBackedByNodes primitiveConnectFrontiersPrefixAvailable := hReady.primitiveConnectFrontiersPrefixAvailable selectBridgeFrontiersBackedByPrimitive := hReady.selectBridgeFrontiersBackedByPrimitive selectBridgeEntriesConsumed := hReady.selectBridgeEntriesConsumed selectArmBodyBoundariesMatchCondition := hReady.selectArmBodyBoundariesMatchCondition selectArmBodyNodesFreshFromSummary := hReady.selectArmBodyNodesFreshFromSummary selectArmBodyNodesPairwiseDisjoint := hReady.selectArmBodyNodesPairwiseDisjoint phantomBridgeFrontiersBackedByPrimitive := hReady.phantomBridgeFrontiersBackedByPrimitive phantomBridgeFrontiersMatchPrimitive := hReady.phantomBridgeFrontiersMatchPrimitive phantomBridgeBulkConnectionsReplayed := hReady.phantomBridgeBulkConnectionsReplayed

Executable checker for the validator-ready checker-record layer.

def validatorReadyCoreCheck (artifact : WireAdmissionArtifact) : Bool := decide artifact.SchemaCurrent && artifact.summaryKeysUniqueCheck && artifact.summaryRowsValidCheck && artifact.summaryDomainClosedCheck && artifact.summaryIdentitiesMatchPrimitiveCheck && artifact.summaryFrontiersBackedByPrimitiveCheck && artifact.summaryFrontiersMatchPrimitiveCheck && artifact.rawConnectionsMatchPrimitiveCheck && artifact.componentDomainsClosedCheck && artifact.selectsValidCheck && artifact.componentRowsUniqueCheck && artifact.generatedFormsReferencedCheck && artifact.componentFrontiersBackedByPrimitiveCheck && artifact.generatedChildFrontiersMatchPrimitiveCheck && artifact.generatedFormsValidCheck && artifact.phantomAdaptersValidCheck && artifact.primitiveStepsValidCheck && artifact.primitiveTraceStackValidCheck && artifact.primitiveOverlayLedgersPrefixAvailableCheck && artifact.primitiveConnectFrontiersBackedByNodesCheck && artifact.primitiveConnectFrontiersPrefixAvailableCheck && artifact.selectBridgeFrontiersBackedByPrimitiveCheck && artifact.selectBridgeEntriesConsumedCheck && artifact.selectArmBodyBoundariesMatchConditionCheck && artifact.selectArmBodyNodesFreshFromSummaryCheck && artifact.selectArmBodyNodesPairwiseDisjointCheck && artifact.phantomBridgeFrontiersBackedByPrimitiveCheck && artifact.phantomBridgeFrontiersMatchPrimitiveCheck && artifact.phantomBridgeBulkConnectionsReplayedCheck

Successful core checking proves the validator-ready checker-record layer.

theorem validatorReadyCoreCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.validatorReadyCoreCheck = true) : artifact.ValidatorReadyCore := artifact:WireAdmissionArtifacthCheck:artifact.validatorReadyCoreCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthCheck:(decide artifact.SchemaCurrent && artifact.summaryKeysUniqueCheck && artifact.summaryRowsValidCheck && artifact.summaryDomainClosedCheck && artifact.summaryIdentitiesMatchPrimitiveCheck && artifact.summaryFrontiersBackedByPrimitiveCheck && artifact.summaryFrontiersMatchPrimitiveCheck && artifact.rawConnectionsMatchPrimitiveCheck && artifact.componentDomainsClosedCheck && artifact.selectsValidCheck && artifact.componentRowsUniqueCheck && artifact.generatedFormsReferencedCheck && artifact.componentFrontiersBackedByPrimitiveCheck && artifact.generatedChildFrontiersMatchPrimitiveCheck && artifact.generatedFormsValidCheck && artifact.phantomAdaptersValidCheck && artifact.primitiveStepsValidCheck && artifact.primitiveTraceStackValidCheck && artifact.primitiveOverlayLedgersPrefixAvailableCheck && artifact.primitiveConnectFrontiersBackedByNodesCheck && artifact.primitiveConnectFrontiersPrefixAvailableCheck && artifact.selectBridgeFrontiersBackedByPrimitiveCheck && artifact.selectBridgeEntriesConsumedCheck && artifact.selectArmBodyBoundariesMatchConditionCheck && artifact.selectArmBodyNodesFreshFromSummaryCheck && artifact.selectArmBodyNodesPairwiseDisjointCheck && artifact.phantomBridgeFrontiersBackedByPrimitiveCheck && artifact.phantomBridgeFrontiersMatchPrimitiveCheck && artifact.phantomBridgeBulkConnectionsReplayedCheck) = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthCheck:(((((((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = true) ∧ artifact.selectArmBodyNodesFreshFromSummaryCheck = true) ∧ artifact.selectArmBodyNodesPairwiseDisjointCheck = true) ∧ artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.phantomBridgeFrontiersMatchPrimitiveCheck = true) ∧ artifact.phantomBridgeBulkConnectionsReplayedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthCheck:((((((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = true) ∧ artifact.selectArmBodyNodesFreshFromSummaryCheck = true) ∧ artifact.selectArmBodyNodesPairwiseDisjointCheck = true) ∧ artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehCheck:(((((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = true) ∧ artifact.selectArmBodyNodesFreshFromSummaryCheck = true) ∧ artifact.selectArmBodyNodesPairwiseDisjointCheck = true) ∧ artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehCheck:((((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = true) ∧ artifact.selectArmBodyNodesFreshFromSummaryCheck = true) ∧ artifact.selectArmBodyNodesPairwiseDisjointCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehCheck:(((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = true) ∧ artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehCheck:((((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = true) ∧ artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehCheck:(((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true) ∧ artifact.selectBridgeEntriesConsumedCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehCheck:((((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = true) ∧ artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehCheck:(((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = true) ∧ artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehCheck:((((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = true) ∧ artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehCheck:(((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = true) ∧ artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehCheck:((((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = true) ∧ artifact.primitiveTraceStackValidCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehCheck:(((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = true) ∧ artifact.primitiveStepsValidCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehCheck:((((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = true) ∧ artifact.phantomAdaptersValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehCheck:(((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = true) ∧ artifact.generatedFormsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehCheck:((((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = true) ∧ artifact.generatedChildFrontiersMatchPrimitiveCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehCheck:(((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = true) ∧ artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehCheck:((((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = true) ∧ artifact.generatedFormsReferencedCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehCheck:(((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = true) ∧ artifact.componentRowsUniqueCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehCheck:((((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = true) ∧ artifact.selectsValidCheck = truehComponentRows:artifact.componentRowsUniqueCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehCheck:(((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = true) ∧ artifact.componentDomainsClosedCheck = truehSelects:artifact.selectsValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehCheck:((((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = true) ∧ artifact.rawConnectionsMatchPrimitiveCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehCheck:(((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = true) ∧ artifact.summaryFrontiersMatchPrimitiveCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehCheck:((((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = true) ∧ artifact.summaryFrontiersBackedByPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = truehCheck:(((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = true) ∧ artifact.summaryIdentitiesMatchPrimitiveCheck = truehSummaryBacked:artifact.summaryFrontiersBackedByPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = truehSummaryBacked:artifact.summaryFrontiersBackedByPrimitiveCheck = truehCheck:((decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = true) ∧ artifact.summaryDomainClosedCheck = truehSummaryIdentities:artifact.summaryIdentitiesMatchPrimitiveCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = truehSummaryBacked:artifact.summaryFrontiersBackedByPrimitiveCheck = truehSummaryIdentities:artifact.summaryIdentitiesMatchPrimitiveCheck = truehCheck:(decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = true) ∧ artifact.summaryRowsValidCheck = truehSummaryDomain:artifact.summaryDomainClosedCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = truehSummaryBacked:artifact.summaryFrontiersBackedByPrimitiveCheck = truehSummaryIdentities:artifact.summaryIdentitiesMatchPrimitiveCheck = truehSummaryDomain:artifact.summaryDomainClosedCheck = truehCheck:decide artifact.SchemaCurrent = true ∧ artifact.summaryKeysUniqueCheck = truehSummaryRows:artifact.summaryRowsValidCheck = true⊢ artifact.ValidatorReadyCore artifact:WireAdmissionArtifacthPhantomBridgeBulkReplayed:artifact.phantomBridgeBulkConnectionsReplayedCheck = truehPhantomBridgeFrontiersMatch:artifact.phantomBridgeFrontiersMatchPrimitiveCheck = truehPhantomBridgeFrontiersBacked:artifact.phantomBridgeFrontiersBackedByPrimitiveCheck = truehSelectArmBodyDisjoint:artifact.selectArmBodyNodesPairwiseDisjointCheck = truehSelectArmBodyFresh:artifact.selectArmBodyNodesFreshFromSummaryCheck = truehSelectArmBodyBoundaries:artifact.selectArmBodyBoundariesMatchConditionCheck = truehSelectBridgeEntries:artifact.selectBridgeEntriesConsumedCheck = truehSelectBridgeFrontiers:artifact.selectBridgeFrontiersBackedByPrimitiveCheck = truehPrimitiveConnectPrefix:artifact.primitiveConnectFrontiersPrefixAvailableCheck = truehPrimitiveConnectBacked:artifact.primitiveConnectFrontiersBackedByNodesCheck = truehPrimitiveOverlayPrefix:artifact.primitiveOverlayLedgersPrefixAvailableCheck = truehPrimitiveTrace:artifact.primitiveTraceStackValidCheck = truehPrimitiveSteps:artifact.primitiveStepsValidCheck = truehPhantomValid:artifact.phantomAdaptersValidCheck = truehGeneratedValid:artifact.generatedFormsValidCheck = truehGeneratedChildFrontiers:artifact.generatedChildFrontiersMatchPrimitiveCheck = truehComponentFrontiers:artifact.componentFrontiersBackedByPrimitiveCheck = truehGeneratedReferenced:artifact.generatedFormsReferencedCheck = truehComponentRows:artifact.componentRowsUniqueCheck = truehSelects:artifact.selectsValidCheck = truehComponentDomains:artifact.componentDomainsClosedCheck = truehRawConnections:artifact.rawConnectionsMatchPrimitiveCheck = truehSummaryFrontiers:artifact.summaryFrontiersMatchPrimitiveCheck = truehSummaryBacked:artifact.summaryFrontiersBackedByPrimitiveCheck = truehSummaryIdentities:artifact.summaryIdentitiesMatchPrimitiveCheck = truehSummaryDomain:artifact.summaryDomainClosedCheck = truehSummaryRows:artifact.summaryRowsValidCheck = truehSchema:decide artifact.SchemaCurrent = truehSummaryKeys:artifact.summaryKeysUniqueCheck = true⊢ artifact.ValidatorReadyCore All goals completed! 🐙

The executable core now covers every field of ValidatorReady.

theorem validatorReadyCore_toValidatorReady {artifact : WireAdmissionArtifact} (hCore : artifact.ValidatorReadyCore) : artifact.ValidatorReady where schemaCurrent := hCore.schemaCurrent summaryKeysUnique := hCore.summaryKeysUnique summaryRowsValid := hCore.summaryRowsValid summaryDomainClosed := hCore.summaryDomainClosed summaryIdentitiesMatchPrimitive := hCore.summaryIdentitiesMatchPrimitive summaryFrontiersBackedByPrimitive := hCore.summaryFrontiersBackedByPrimitive summaryFrontiersMatchPrimitive := hCore.summaryFrontiersMatchPrimitive rawConnectionsMatchPrimitive := hCore.rawConnectionsMatchPrimitive componentDomainsClosed := hCore.componentDomainsClosed componentRowsUnique := hCore.componentRowsUnique generatedFormsReferenced := hCore.generatedFormsReferenced componentFrontiersBackedByPrimitive := hCore.componentFrontiersBackedByPrimitive generatedChildFrontiersMatchPrimitive := hCore.generatedChildFrontiersMatchPrimitive primitiveTraceStackValid := hCore.primitiveTraceStackValid primitiveOverlayLedgersPrefixAvailable := hCore.primitiveOverlayLedgersPrefixAvailable primitiveConnectFrontiersBackedByNodes := hCore.primitiveConnectFrontiersBackedByNodes primitiveConnectFrontiersPrefixAvailable := hCore.primitiveConnectFrontiersPrefixAvailable selectBridgeFrontiersBackedByPrimitive := hCore.selectBridgeFrontiersBackedByPrimitive selectBridgeEntriesConsumed := hCore.selectBridgeEntriesConsumed selectArmBodyBoundariesMatchCondition := hCore.selectArmBodyBoundariesMatchCondition selectArmBodyNodesFreshFromSummary := hCore.selectArmBodyNodesFreshFromSummary selectArmBodyNodesPairwiseDisjoint := hCore.selectArmBodyNodesPairwiseDisjoint phantomBridgeFrontiersBackedByPrimitive := hCore.phantomBridgeFrontiersBackedByPrimitive phantomBridgeFrontiersMatchPrimitive := hCore.phantomBridgeFrontiersMatchPrimitive phantomBridgeBulkConnectionsReplayed := hCore.phantomBridgeBulkConnectionsReplayed primitiveStepsValid := hCore.primitiveStepsValid generatedFormsValid := hCore.generatedFormsValid phantomAdaptersValid := hCore.phantomAdaptersValid selectsValid := hCore.selectsValid

Full Lean-owned executable checker for decoded Wire admission artifacts.

def validatorReadyCheck (artifact : WireAdmissionArtifact) : Bool := artifact.validatorReadyCoreCheck

Successful executable validator checking proves the full validator-ready contract.

theorem validatorReadyCheck_sound {artifact : WireAdmissionArtifact} (hCheck : artifact.validatorReadyCheck = true) : artifact.ValidatorReady := validatorReadyCore_toValidatorReady (validatorReadyCoreCheck_sound hCheck)

Successful executable validator checking supplies the theorem-facing soundness cutline.

theorem validatorReadyCheck_soundness {artifact : WireAdmissionArtifact} (hCheck : artifact.validatorReadyCheck = true) : artifact.Sound := validatorReady_sound (validatorReadyCheck_sound hCheck)end WireAdmissionArtifactend AdmissionArtifactend Cortex.Wire