| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Algorithm.GuardProbability |
| import OAI.Combinatorics.MatchingCount.Algorithm.TreeGeneratedUpdate |
|
|
| namespace OAI |
|
|
| namespace MatchingFPRAS.ExecutableSource |
| open TreeTyped TreeFraction TreeTyped.Numbered ExecutableBottleneck ExecutableHierarchy ExecutableRefresh Enlargement RealGeometry NumericLadder |
| open ExecutableLadder UnitRefresh Replica.Ladder Transport NumericMarking ExecutableStatistics ExecutableScaling ExecutableAdaptive |
|
|
| attribute [local instance] NumberedHierarchy.labelOrder |
| attribute [local instance] Transport.sym2Order Transport.bagEdgeOrder Transport.bagEdgeFintype |
| attribute [local instance] UnitRefresh.Computable.allowedDec Transport.prodOrder Transport.sumOrder |
|
|
| lemma generatedSourceSample_support {n : ℕ} [Nontrivial (Fin n)] |
| (he : Even n) (w : Fin n→Fin n→ℚ) (hw : ∀ a b,0<w a b) (K D : ℕ) (hD : 0<D) |
| (hu : ∀ a b,a≠b→BottleneckAlgorithm.edge w a b≤(4:ℚ)^K) |
| (ft fq : List Bool) (hq : 0<fq.length) {k r km : ℕ} |
| (bits : Fin r→ScanBits (SourceVertex (Fin n) K) k) |
| (mb : BagEdge (RationalSource.bags w K)→Fin km→Bool) : |
| 0<sourceLaw (fun a b=>(w a b:ℝ)) K D ((RationalSource.sourceMarkedEquiv w K).symm |
| (generatedSourceSample he w hw K D hD hu ft fq hq bits mb)) := by |
| let x:=generatedSourceSample he w hw K D hD hu ft fq hq bits mb |
| have hs:=RationalSource.source_draw_support w hw K D km hD |
| (fun _ : Unit=>x.1) ((),mb) |
| exact hs |
|
|
| lemma generated_certificate_zero {G : GraphInput} [Nontrivial (Fin G.n)] |
| (he : Even G.n) {j : ℕ} (s : FiniteTrial.ScaleState G j) (hZ : Z G=0) |
| (K D : ℕ) (hD : 0<D) |
| (hu : ∀ a b,a≠b→BottleneckAlgorithm.edge s.activity a b≤(4:ℚ)^K) |
| (ft fq : List Bool) (hq : 0<fq.length) {k r km : ℕ} |
| (bits : Fin r→ScanBits (SourceVertex (Fin G.n) K) k) |
| (mb : BagEdge (RationalSource.bags s.activity K)→Fin km→Bool) : |
| RationalSource.observableD s.activity s.certificateActivity K |
| (generatedSourceSample he s.activity s.activity_pos K D hD hu ft fq hq bits mb)=0 := by |
| let x:=generatedSourceSample he s.activity s.activity_pos K D hD hu ft fq hq bits mb |
| let a:=(RationalSource.sourceMarkedEquiv s.activity K).symm x |
| have hs:=generatedSourceSample_support he s.activity s.activity_pos K D hD hu ft fq hq bits mb |
| have hc:=s.toReal.certificate_zero (K:=K) he hZ D |
| rw [←s.activity_cast,←s.certificateActivity_cast] at hc |
| have hh:=hc a hs |
| have hv:=RationalSource.observableD_cast s.activity s.certificateActivity K a |
| simp only [a,Equiv.apply_symm_apply] at hv |
| rw [←hv] at hh |
| exact_mod_cast hh |
| end MatchingFPRAS.ExecutableSource |
|
|
| end OAI |
|
|
