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import OAI.Computability.PerfectCompleteness.Foundations.CutSlotOutside
import OAI.Computability.PerfectCompleteness.Foundations.WholeCutExteriorTransportLemmas
import OAI.Computability.PerfectCompleteness.Foundations.WholeCutReplayGroupingTransport
import OAI.Computability.PerfectCompleteness.Foundations.WholeCutReplayLemmas
import OAI.Computability.PerfectCompleteness.Repetition.CleanEndpointSlots
import OAI.Computability.PerfectCompleteness.Repetition.CleanRecordChildBlocks
namespace OAI
section
namespace PerfectCompleteness.CleanPhysicalReplay
open scoped Classical
open RecursiveSpaces DescendantSpaces TreeSourceSpaces HierarchicalArrays
open UniqueGamesTheorem.Foundations.Games
noncomputable section
variable {branch : Nat → Nat} {root h t : Nat}
(rows repeats : Nat → Nat) (p : Path branch root (h + 1))
(outside : Slots branch root → Fin t → MixedSupport.Slot)
(placeholder : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
abbrev Exterior := WholeCutGrouping.Exterior rows repeats p
(CutSlotAssembly.fill p outside placeholder)
def exteriorAt (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(external : Exterior rows repeats p outside placeholder) :
WholeCutGrouping.Exterior rows repeats p (CutSlotAssembly.fill p outside inside) :=
WholeCutExteriorTransport.equiv rows repeats p
(CutSlotAssembly.fill p outside placeholder) (CutSlotAssembly.fill p outside inside)
(CutSlotAssembly.fill_outside_eq p outside placeholder inside) external
theorem cutSlots_fill (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot) :
WholeCutGrouping.cutSlots p (CutSlotAssembly.fill p outside inside) = inside := by
funext s
exact CutSlotAssembly.fill_at_cut p outside inside s
theorem childSlots_fill (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(i : Fin (branch h)) :
childSlots (WholeCutGrouping.cutSlots p (CutSlotAssembly.fill p outside inside)) i =
childSlots inside i :=
congrArg (fun ss => childSlots ss i) (cutSlots_fill p outside inside)
def fillChild (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(i : Fin (branch h))
(block : CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) inside rows i) :
CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p)
(WholeCutGrouping.cutSlots p (CutSlotAssembly.fill p outside inside)) rows i :=
cast (congrArg (SourceChildKernel.Block (WholeCutCalls.Index rows repeats p) rows)
(childSlots_fill p outside inside i).symm) block
theorem fillChild_heq (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(i : Fin (branch h))
(block : CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) inside rows i) :
HEq (fillChild rows repeats p outside inside i block) block :=
cast_heq _ _
private theorem cast_zeroBlock {n : Nat} {C : Type*} [Fintype C]
(slots target : Slots branch n → Fin t → MixedSupport.Slot) (hs : slots = target) :
cast (congrArg (SourceChildKernel.Block C rows) hs)
(SourceChildKernel.zeroBlock (C := C) rows slots) =
SourceChildKernel.zeroBlock rows target := by
cases hs
rfl
theorem fillChild_zero (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(i : Fin (branch h)) :
fillChild rows repeats p outside inside i
(SourceChildKernel.zeroBlock rows (childSlots inside i)) =
SourceChildKernel.zeroBlock rows
(childSlots (WholeCutGrouping.cutSlots p (CutSlotAssembly.fill p outside inside)) i) :=
cast_zeroBlock rows _ _ (childSlots_fill p outside inside i).symm
def retainedAt (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(children : (i : {i : Fin (branch h) // ¬ clean i}) →
CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) inside rows i.val) :
WholeCutReplayGrouping.RetainedChildren rows repeats p
(CutSlotAssembly.fill p outside inside) clean :=
fun i => fillChild rows repeats p outside inside i.val (children i)
def assembleAt (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(external : Exterior rows repeats p outside placeholder)
(children : (i : {i : Fin (branch h) // ¬ clean i}) →
CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) inside rows i.val) :
WholeCutReplay.Tape rows repeats p (CutSlotAssembly.fill p outside inside) clean :=
WholeCutReplayGrouping.assemble rows repeats p (CutSlotAssembly.fill p outside inside) clean
(exteriorAt rows repeats p outside placeholder inside external)
(retainedAt rows repeats p outside inside clean children)
def physicalTape (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(external : Exterior rows repeats p outside placeholder)
(children : CutChildGrouping.Raw (C := WholeCutCalls.Index rows repeats p) inside rows) :
WholeCutSampler.Tape rows repeats p (CutSlotAssembly.fill p outside inside) :=
(WholeCutGrouping.splitTape rows repeats p (CutSlotAssembly.fill p outside inside)).symm
(exteriorAt rows repeats p outside placeholder inside external,
fun i => fillChild rows repeats p outside inside i (children i))
theorem assembleAt_eq_erase (inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(external : Exterior rows repeats p outside placeholder)
(children : CutChildGrouping.Raw (C := WholeCutCalls.Index rows repeats p) inside rows) :
assembleAt rows repeats p outside placeholder inside clean external (fun i => children i.val) =
WholeCutReplay.erase rows repeats p (CutSlotAssembly.fill p outside inside) clean
(physicalTape rows repeats p outside placeholder inside external children) := by
have h := WholeCutReplayGrouping.assemble_splitTape rows repeats p
(CutSlotAssembly.fill p outside inside) clean
(physicalTape rows repeats p outside placeholder inside external children)
change WholeCutReplayGrouping.assemble rows repeats p (CutSlotAssembly.fill p outside inside) clean
(exteriorAt rows repeats p outside placeholder inside external)
(fun child => fillChild rows repeats p outside inside child.val (children child.val)) =
WholeCutReplay.erase rows repeats p (CutSlotAssembly.fill p outside inside) clean
(physicalTape rows repeats p outside placeholder inside external children)
simpa only [physicalTape, Equiv.apply_symm_apply] using h
theorem physicalTape_grouped_zero
(inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(external : Exterior rows repeats p outside placeholder)
(children : CutChildGrouping.Raw (C := WholeCutCalls.Index rows repeats p) inside rows)
(hzero : ∀ i, clean i → children i =
SourceChildKernel.zeroBlock rows (childSlots inside i)) :
WholeCutZero.GroupedAtClean rows repeats p (CutSlotAssembly.fill p outside inside) clean
(physicalTape rows repeats p outside placeholder inside external children) := by
intro i hi
have hz : fillChild rows repeats p outside inside i (children i) =
SourceChildKernel.zeroBlock rows
(childSlots (WholeCutGrouping.cutSlots p (CutSlotAssembly.fill p outside inside)) i) := by
rw [hzero i hi]
exact fillChild_zero rows repeats p outside inside i
change (∀ q, ((WholeCutGrouping.splitTape rows repeats p
(CutSlotAssembly.fill p outside inside)
(physicalTape rows repeats p outside placeholder inside external children)).2 i).1 q = 0) ∧ _
simp only [physicalTape, Equiv.apply_symm_apply]
rw [hz]
exact ⟨fun _ => rfl, fun _ _ => rfl⟩
private theorem exteriorAt_heq
(inside : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(external : Exterior rows repeats p outside placeholder) :
HEq (exteriorAt rows repeats p outside placeholder inside external) external :=
cast_heq _ _
theorem transport_assembleAt
(inside target : Slots branch (h + 1) → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(hs : ∀ i, ¬ clean i → ∀ s, inside (i, s) = target (i, s))
(external : Exterior rows repeats p outside placeholder)
(children : (i : {i : Fin (branch h) // ¬ clean i}) →
CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) inside rows i.val)
(other : (i : {i : Fin (branch h) // ¬ clean i}) →
CutChildGrouping.Child (C := WholeCutCalls.Index rows repeats p) target rows i.val)
(hc : ∀ i, HEq (children i) (other i)) :
WholeCutReplayKeys.transportTape rows repeats p
(CutSlotAssembly.fill p outside inside) (CutSlotAssembly.fill p outside target) clean
(CutSlotAssembly.fill_kept_eq p outside inside target clean hs)
(assembleAt rows repeats p outside placeholder inside clean external children) =
assembleAt rows repeats p outside placeholder target clean external other := by
unfold assembleAt
rw [WholeCutReplayGroupingTransport.transport_assemble]
apply congrArg₂ (WholeCutReplayGrouping.assemble rows repeats p
(CutSlotAssembly.fill p outside target) clean)
· apply eq_of_heq
exact (cast_heq _ _).trans
((exteriorAt_heq rows repeats p outside placeholder inside external).trans
(exteriorAt_heq rows repeats p outside placeholder target external).symm)
· funext i
apply eq_of_heq
exact (WholeCutReplayGroupingTransport.castChildren_apply_heq rows repeats p
(CutSlotAssembly.fill p outside inside) (CutSlotAssembly.fill p outside target) clean
(CutSlotAssembly.fill_kept_eq p outside inside target clean hs)
(retainedAt rows repeats p outside inside clean children) i).trans
((fillChild_heq rows repeats p outside inside i.val (children i)).trans
((hc i).trans (fillChild_heq rows repeats p outside target i.val (other i)).symm))
section Source
variable {v m : Nat} [NeZero m]
(clauses : Fin m → SourceClause.NormalizedClause v)
(designated : Fin (branch h) → Slots branch h)
abbrev Record := CleanRecordChildBlocks.Record
(C := WholeCutCalls.Index rows repeats p) (t := t) rows clauses designated
abbrev Sample := SourceChildKernel.Sample
(C := WholeCutCalls.Index rows repeats p) (t := t) rows clauses designated
def leftRecord (record : Record (t := t) rows repeats p clauses designated)
(external : Exterior rows repeats p outside placeholder) :
WholeCutReplay.Tape rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.leftRef rows clauses designated record))
(CleanRecordChildBlocks.clean rows clauses designated record) :=
assembleAt rows repeats p outside placeholder
(CleanRecordChildBlocks.leftRef rows clauses designated record)
(CleanRecordChildBlocks.clean rows clauses designated record) external
(CleanRecordChildBlocks.leftChild rows clauses designated record)
def rightRecord (record : Record (t := t) rows repeats p clauses designated)
(external : Exterior rows repeats p outside placeholder) :
WholeCutReplay.Tape rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.rightRef rows clauses designated record))
(CleanRecordChildBlocks.clean rows clauses designated record) :=
assembleAt rows repeats p outside placeholder
(CleanRecordChildBlocks.rightRef rows clauses designated record)
(CleanRecordChildBlocks.clean rows clauses designated record) external
(CleanRecordChildBlocks.rightChild rows clauses designated record)
def leftInside (x : Sample (t := t) rows repeats p clauses designated) :
Slots branch (h + 1) → Fin t → MixedSupport.Slot :=
SourceChildKernel.parentLeftSlots clauses designated (fun i => ((x i).1, (x i).2.1))
def rightInside (x : Sample (t := t) rows repeats p clauses designated) :
Slots branch (h + 1) → Fin t → MixedSupport.Slot :=
SourceChildKernel.parentRightSlots rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2)
def leftBlocks (x : Sample (t := t) rows repeats p clauses designated) :
CutChildGrouping.Raw (C := WholeCutCalls.Index rows repeats p)
(leftInside rows repeats p clauses designated x) rows :=
SourceChildKernel.leftChildren rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2)
def rightBlocks (x : Sample (t := t) rows repeats p clauses designated) :
CutChildGrouping.Raw (C := WholeCutCalls.Index rows repeats p)
(rightInside rows repeats p clauses designated x) rows :=
SourceChildKernel.rightChildren rows clauses designated
(fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2)
def leftTape (x : Sample (t := t) rows repeats p clauses designated)
(external : Exterior rows repeats p outside placeholder) :
WholeCutSampler.Tape rows repeats p
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x)) :=
physicalTape rows repeats p outside placeholder (leftInside rows repeats p clauses designated x)
external (leftBlocks rows repeats p clauses designated x)
def rightTape (x : Sample (t := t) rows repeats p clauses designated)
(external : Exterior rows repeats p outside placeholder) :
WholeCutSampler.Tape rows repeats p
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x)) :=
physicalTape rows repeats p outside placeholder (rightInside rows repeats p clauses designated x)
external (rightBlocks rows repeats p clauses designated x)
theorem leftInside_nonclean (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(i : Fin (branch h)) (hi : ¬ CleanRecordChildBlocks.clean rows clauses designated record i)
(s : Slots branch h) :
CleanRecordChildBlocks.leftRef rows clauses designated record (i, s) =
leftInside rows repeats p clauses designated x (i, s) :=
congrFun (CleanRecordChildBlocks.leftRef_childSlots_event
rows clauses designated record x hevent ⟨i, hi⟩) s
theorem rightInside_nonclean (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(i : Fin (branch h)) (hi : ¬ CleanRecordChildBlocks.clean rows clauses designated record i)
(s : Slots branch h) :
CleanRecordChildBlocks.rightRef rows clauses designated record (i, s) =
rightInside rows repeats p clauses designated x (i, s) :=
congrFun (CleanRecordChildBlocks.rightRef_childSlots_event
rows clauses designated record x hevent ⟨i, hi⟩) s
theorem leftRecord_eq_erase (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder) :
WholeCutReplayKeys.transportTape rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.leftRef rows clauses designated record))
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(CutSlotAssembly.fill_kept_eq p outside _ _ _
(leftInside_nonclean rows repeats p clauses designated record x hevent))
(leftRecord rows repeats p outside placeholder clauses designated record external) =
WholeCutReplay.erase rows repeats p
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(leftTape rows repeats p outside placeholder clauses designated x external) := by
exact (transport_assembleAt rows repeats p outside placeholder _ _ _
(leftInside_nonclean rows repeats p clauses designated record x hevent) external _ _
(CleanRecordChildBlocks.leftChild_event_heq rows clauses designated record x hevent)).trans
(assembleAt_eq_erase rows repeats p outside placeholder _ _ external
(leftBlocks rows repeats p clauses designated x))
theorem rightRecord_eq_erase (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder) :
WholeCutReplayKeys.transportTape rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.rightRef rows clauses designated record))
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(CutSlotAssembly.fill_kept_eq p outside _ _ _
(rightInside_nonclean rows repeats p clauses designated record x hevent))
(rightRecord rows repeats p outside placeholder clauses designated record external) =
WholeCutReplay.erase rows repeats p
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(rightTape rows repeats p outside placeholder clauses designated x external) := by
exact (transport_assembleAt rows repeats p outside placeholder _ _ _
(rightInside_nonclean rows repeats p clauses designated record x hevent) external _ _
(CleanRecordChildBlocks.rightChild_event_heq rows clauses designated record x hevent)).trans
(assembleAt_eq_erase rows repeats p outside placeholder _ _ external
(rightBlocks rows repeats p clauses designated x))
variable
(μ : Fin (branch h) → FiniteDistribution (SourceQuestionReconstruction.SourceTuple m t))
(ν : (i : Fin (branch h)) → FiniteDistribution
(SourceChildKernel.Rest (m := m) (t := t) designated i))
(flag : Fin (branch h) → FiniteDistribution Bool)
omit [NeZero m] in
theorem rightBlocks_zero (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(i : Fin (branch h)) (hi : CleanRecordChildBlocks.clean rows clauses designated record i) :
rightBlocks rows repeats p clauses designated x i =
SourceChildKernel.zeroBlock rows
(childSlots (rightInside rows repeats p clauses designated x) i) :=
SourceChildKernel.childrenLaw_clean_zero rows clauses designated μ ν flag x hx i
(CleanRecordChildBlocks.childClean_of_clean rows clauses designated record x hevent i hi)
omit [NeZero m] in
theorem leftBlocks_zero (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(i : Fin (branch h)) (hi : CleanRecordChildBlocks.clean rows clauses designated record i) :
leftBlocks rows repeats p clauses designated x i =
SourceChildKernel.zeroBlock rows
(childSlots (leftInside rows repeats p clauses designated x) i) := by
have hz := rightBlocks_zero rows repeats p clauses designated μ ν flag record x hx hevent i hi
change ChildAssemblyProjection.childPullback rows
(SourceChildKernel.parentProjection rows clauses designated
(fun j => ((x j).1, (x j).2.1)) (fun j => (x j).2.2)) i
(rightBlocks rows repeats p clauses designated x i) = _
rw [hz]
exact map_zero _
omit [NeZero m] in
theorem rightTape_grouped_zero (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder) :
WholeCutZero.GroupedAtClean rows repeats p
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(rightTape rows repeats p outside placeholder clauses designated x external) :=
physicalTape_grouped_zero rows repeats p outside placeholder _ _ external _
(rightBlocks_zero rows repeats p clauses designated μ ν flag record x hx hevent)
omit [NeZero m] in
theorem leftTape_grouped_zero (record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder) :
WholeCutZero.GroupedAtClean rows repeats p
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x))
(CleanRecordChildBlocks.clean rows clauses designated record)
(leftTape rows repeats p outside placeholder clauses designated x external) :=
physicalTape_grouped_zero rows repeats p outside placeholder _ _ external _
(leftBlocks_zero rows repeats p clauses designated μ ν flag record x hx hevent)
private theorem response_of_erase {Y : Type*}
(slots target : Slots branch root → Fin t → MixedSupport.Slot)
(clean : Fin (branch h) → Prop)
(hs : ∀ s, CutSamplerKeyLocality.keptLeaf p clean s → slots s = target s)
(reference : WholeCutReplay.Tape rows repeats p slots clean)
(tape : WholeCutSampler.Tape rows repeats p target)
(htape : WholeCutReplayKeys.transportTape rows repeats p slots target clean hs reference =
WholeCutReplay.erase rows repeats p target clean tape)
(hzero : WholeCutZero.GroupedAtClean rows repeats p target clean tape)
(post : Output branch root rows → Y)
(labeling : KeyStrategy.Strategy (TreeCanonical.locationCount branch root t))
(side : CanonicalKeys.Side) :
KeyStrategy.response labeling side (TreeCanonical.numberedSlots slots)
(WholeCutReplayKeys.query rows repeats p slots clean reference post) =
KeyStrategy.response labeling side (TreeCanonical.numberedSlots target)
(WholeCutKeyLocality.query rows repeats p target tape post) := by
have h := WholeCutReplayKeys.response_eq_transport rows repeats p slots target clean hs
reference post labeling side
rw [htape, WholeCutReplayKeys.query_erase rows repeats p target clean tape post hzero] at h
exact h
theorem leftRecord_response_eq {Y : Type*}
(record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y)
(labeling : KeyStrategy.Strategy (TreeCanonical.locationCount branch root t))
(side : CanonicalKeys.Side) :
KeyStrategy.response labeling side
(TreeCanonical.numberedSlots
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.leftRef rows clauses designated record)))
(WholeCutReplayKeys.query rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.leftRef rows clauses designated record))
(CleanRecordChildBlocks.clean rows clauses designated record)
(leftRecord rows repeats p outside placeholder clauses designated record external) post) =
KeyStrategy.response labeling side
(TreeCanonical.numberedSlots
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x)))
(WholeCutKeyLocality.query rows repeats p
(CutSlotAssembly.fill p outside (leftInside rows repeats p clauses designated x))
(leftTape rows repeats p outside placeholder clauses designated x external) post) :=
response_of_erase rows repeats p _ _ _
(CutSlotAssembly.fill_kept_eq p outside _ _ _
(leftInside_nonclean rows repeats p clauses designated record x hevent)) _ _
(leftRecord_eq_erase rows repeats p outside placeholder clauses designated record x hevent external)
(leftTape_grouped_zero rows repeats p outside placeholder clauses designated μ ν flag
record x hx hevent external) post labeling side
theorem rightRecord_response_eq {Y : Type*}
(record : Record (t := t) rows repeats p clauses designated)
(x : Sample (t := t) rows repeats p clauses designated)
(hx : (SourceChildKernel.childrenLaw rows clauses designated μ ν flag).weight x ≠ 0)
(hevent : CleanRecordChildBlocks.event rows clauses designated record x = true)
(external : Exterior rows repeats p outside placeholder)
(post : Output branch root rows → Y)
(labeling : KeyStrategy.Strategy (TreeCanonical.locationCount branch root t))
(side : CanonicalKeys.Side) :
KeyStrategy.response labeling side
(TreeCanonical.numberedSlots
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.rightRef rows clauses designated record)))
(WholeCutReplayKeys.query rows repeats p
(CutSlotAssembly.fill p outside (CleanRecordChildBlocks.rightRef rows clauses designated record))
(CleanRecordChildBlocks.clean rows clauses designated record)
(rightRecord rows repeats p outside placeholder clauses designated record external) post) =
KeyStrategy.response labeling side
(TreeCanonical.numberedSlots
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x)))
(WholeCutKeyLocality.query rows repeats p
(CutSlotAssembly.fill p outside (rightInside rows repeats p clauses designated x))
(rightTape rows repeats p outside placeholder clauses designated x external) post) :=
response_of_erase rows repeats p _ _ _
(CutSlotAssembly.fill_kept_eq p outside _ _ _
(rightInside_nonclean rows repeats p clauses designated record x hevent)) _ _
(rightRecord_eq_erase rows repeats p outside placeholder clauses designated record x hevent external)
(rightTape_grouped_zero rows repeats p outside placeholder clauses designated μ ν flag
record x hx hevent external) post labeling side
end Source
section OwnReplay
variable {v m : Nat} [NeZero m]
(clauses : Fin m → SourceClause.NormalizedClause v)
(designated : Fin (branch h) → Slots branch h)
(record : Record (t := t) rows repeats p clauses designated)
(external : Exterior rows repeats p outside placeholder)
def leftReplay
(own : {i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} →
Fin t → Fin m) :=
CleanEndpointSlots.leftReplay clauses designated
(CleanRecordChildBlocks.clean rows clauses designated record)
(CleanRecordChildBlocks.visible rows clauses designated record) rows repeats p outside
(leftRecord rows repeats p outside placeholder clauses designated record external) own
def rightReplay
(own : {i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} →
Fin t → Fin v) :=
CleanEndpointSlots.rightReplay clauses designated
(CleanRecordChildBlocks.clean rows clauses designated record)
(CleanRecordChildBlocks.visible rows clauses designated record) rows repeats p outside
(CleanRecordChildBlocks.projected rows clauses designated record)
(rightRecord rows repeats p outside placeholder clauses designated record external) own
end OwnReplay
end
end PerfectCompleteness.CleanPhysicalReplay
end
end OAI
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