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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | 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
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