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lines changed Original file line number Diff line number Diff line change @@ -11,7 +11,6 @@ import LeanCamCombi.GrowthInGroups.Lecture3
1111import LeanCamCombi.GrowthInGroups.Lecture4
1212import LeanCamCombi.Mathlib.Combinatorics.Additive.ApproximateSubgroup
1313import LeanCamCombi.Mathlib.Combinatorics.SetFamily.LYM
14- import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Copy
1514import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Density
1615import LeanCamCombi.Mathlib.Probability.ProbabilityMassFunction.Constructions
1716import LeanCamCombi.PlainCombi.KatonaCircle
Original file line number Diff line number Diff line change @@ -69,12 +69,14 @@ protected nonrec lemma meas [IsProbabilityMeasure μ] [Fintype α] [DecidableEq
6969 [DecidableRel H.Adj] :
7070 μ {ω | G ω = H} =
7171 p ^ #H.edgeFinset * (1 - p) ^ (Fintype.card {e : Sym2 α // ¬ e.IsDiag} - #H.edgeFinset) := by
72- have := hG.meas
73- (H.edgeFinset.attach.map <| ⟨Set.inclusion fun e he ↦
74- not_isDiag_of_mem_edgeSet _ <| mem_edgeFinset.1 he, Set.inclusion_injective _⟩)
75- simp at this
76- rw [Finset.card_attach, ← Fintype.card_subtype_compl] at this
77- convert this
78- sorry
72+ have hHaux : H.edgeFinset = ({e | e ∈ H.edgeSet} : Finset _) := by ext; simp
73+ have hGHaux ω : G ω = H ↔ {e : {e : Sym2 α // ¬ e.IsDiag} | e.1 ∈ (G ω).edgeSet} =
74+ Set.range fun a : H.edgeFinset ↦
75+ Set.inclusion (fun e he ↦ not_isDiag_of_mem_edgeSet H (mem_edgeFinset.mp he)) a := by
76+ simp only [Set.ext_iff, ← edgeSet_inj]
77+ simpa [Sym2.forall] using forall₂_congr fun u v ↦ by simp +contextual [or_iff_not_imp_left]
78+ simpa [hGHaux, hHaux, ← Fintype.card_subtype_compl] using
79+ hG.meas <| H.edgeFinset.attach.map <| ⟨Set.inclusion fun e he ↦
80+ not_isDiag_of_mem_edgeSet _ <| mem_edgeFinset.1 he, Set.inclusion_injective _⟩
7981
8082end IsBinomialRandomGraph
Original file line number Diff line number Diff line change @@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
44Authors: Yaël Dillies
55-/
66import Mathlib.Analysis.SpecialFunctions.Pow.Real
7+ import Mathlib.Combinatorics.SimpleGraph.Copy
78import Mathlib.MeasureTheory.Measure.Typeclasses
89import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Density
910import LeanCamCombi.ExtrProbCombi.BinomialRandomGraph
10- import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Copy
1111
1212/-!
1313# Bollobás' graph containment lemma
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