openAI-math-dataset / lean /OAI /Computability /PerfectCompleteness /Repetition /CleanRecordObservation.lean
| import OAI.Computability.PerfectCompleteness.Repetition.CleanRecordChildBlocks | |
| import OAI.Computability.PerfectCompleteness.Repetition.CutChildCleanLawLemmas | |
| namespace OAI | |
| section | |
| namespace PerfectCompleteness.CleanRecordObservation | |
| noncomputable section | |
| open scoped Classical | |
| open RecursiveSpaces TreeSourceSpaces SourceQuestionReconstruction | |
| variable {branch : Nat → Nat} {h t v m : Nat} {C : Type*} [Fintype C] | |
| (rows : Nat → Nat) (clauses : Fin m → SourceClause.NormalizedClause v) | |
| (designated : Fin (branch h) → Slots branch h) | |
| abbrev Record := CleanRecordChildBlocks.Record (C := C) (t := t) rows clauses designated | |
| abbrev Sample := SourceChildKernel.Sample (C := C) (t := t) rows clauses designated | |
| def observe (x : Sample (C := C) (t := t) rows clauses designated) : | |
| Record (C := C) (t := t) rows clauses designated := | |
| UniformCleanSoundness.observations | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.zero (C := C) (t := t) rows clauses designated) x | |
| theorem event_eq (record : Record (C := C) (t := t) rows clauses designated) | |
| (x : Sample (C := C) (t := t) rows clauses designated) : | |
| CleanRecordChildBlocks.event rows clauses designated record x = | |
| decide (observe rows clauses designated x = record) := | |
| congrFun (UniformCleanSoundness.recordEvent_eq | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.zero (C := C) (t := t) rows clauses designated) record) x | |
| @[simp] theorem event_observe (x : Sample (C := C) (t := t) rows clauses designated) : | |
| CleanRecordChildBlocks.event rows clauses designated | |
| (observe rows clauses designated x) x = true := by | |
| rw [event_eq] | |
| exact decide_eq_true rfl | |
| def leftQuestions (record : Record (C := C) (t := t) rows clauses designated) | |
| (x : Sample (C := C) (t := t) rows clauses designated) : | |
| {i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} → | |
| Fin t → Fin m := | |
| fun i k => ((x i.val).1 k).1 | |
| def rightQuestions (record : Record (C := C) (t := t) rows clauses designated) | |
| (x : Sample (C := C) (t := t) rows clauses designated) : | |
| {i : Fin (branch h) // CleanRecordChildBlocks.clean rows clauses designated record i} → | |
| Fin t → Fin v := | |
| fun i k => SourceClause.occurrenceVariable clauses ((x i.val).1 k) | |
| theorem leftInside_eq (record : Record (C := C) (t := t) rows clauses designated) | |
| (x : Sample (C := C) (t := t) rows clauses designated) | |
| (hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) : | |
| CleanEndpointSlots.leftInside clauses designated | |
| (CleanRecordChildBlocks.clean rows clauses designated record) | |
| (CleanRecordChildBlocks.visible rows clauses designated record) | |
| (leftQuestions rows clauses designated record x) = | |
| SourceChildKernel.parentLeftSlots clauses designated | |
| (fun i => ((x i).1, (x i).2.1)) := by | |
| have h := CleanSourceRecord.reconstructLeft_eq designated | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.zero (C := C) (t := t) rows clauses designated) | |
| (v := v) record x hevent | |
| funext s k | |
| exact congrArg (fun f => SourceKeys.slot clauses (f s.1 s.2 k)) h | |
| theorem rightInside_eq (record : Record (C := C) (t := t) rows clauses designated) | |
| (x : Sample (C := C) (t := t) rows clauses designated) | |
| (hevent : CleanRecordChildBlocks.event rows clauses designated record x = true) : | |
| CleanEndpointSlots.rightInside clauses designated | |
| (CleanRecordChildBlocks.clean rows clauses designated record) | |
| (CleanRecordChildBlocks.visible rows clauses designated record) | |
| (CleanRecordChildBlocks.projected rows clauses designated record) | |
| (rightQuestions rows clauses designated record x) = | |
| SourceChildKernel.parentRightSlots rows clauses designated | |
| (fun i => ((x i).1, (x i).2.1)) (fun i => (x i).2.2) := by | |
| have h := CleanSourceRecord.reconstructRight_eq designated | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.zero (C := C) (t := t) rows clauses designated) | |
| clauses record x hevent | |
| funext s k | |
| refine (congrArg (fun f => SourceKeys.slot clauses (f s.1 s.2 k)) h).trans ?_ | |
| have hflag : CleanSourceRecord.rawProjected designated | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) | |
| s.1 (x s.1).2.2 = | |
| SourceChildKernel.rawProjected rows clauses designated s.1 (x s.1).2.2 := by | |
| cases (x s.1).2.2 <;> rfl | |
| exact (congrArg (fun projected : Bool => SourceKeys.slot clauses | |
| (rightTuple clauses projected | |
| (CleanSourceRecord.sourceTree designated | |
| (D := SourceChildKernel.D (C := C) (t := t) rows clauses designated) | |
| (SourceChildKernel.Factors (C := C) (t := t) rows clauses designated) x s.1 s.2) k)) hflag).trans | |
| (SourceChildKernel.mixedSlots_eq_rightTuple clauses designated s.1 | |
| ((x s.1).1, (x s.1).2.1) | |
| (SourceChildKernel.rawProjected rows clauses designated s.1 (x s.1).2.2) s.2 k).symm | |
| end | |
| end PerfectCompleteness.CleanRecordObservation | |
| end | |
| end OAI | |