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LeanCamCombi.lean

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import LeanCamCombi.Archive.CauchyDavenportFromKneser
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import LeanCamCombi.CauchyFunctionalEquation
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import LeanCamCombi.ConvexityRefactor.Defs
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import LeanCamCombi.ConvexityRefactor.StdSimplex
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import LeanCamCombi.Corners.CombiDegen
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import LeanCamCombi.GrowthInGroups.Lecture2
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import LeanCamCombi.GrowthInGroups.Lecture3
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import LeanCamCombi.GrowthInGroups.Lecture4
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import LeanCamCombi.GrowthInGroups.LinearLowerBound
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import LeanCamCombi.Impact
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import LeanCamCombi.Kneser.Kneser
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import LeanCamCombi.Kneser.KneserRuzsa
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import LeanCamCombi.Kneser.MulStab
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Basic
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Degrees
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Equiv
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import LeanCamCombi.Mathlib.Algebra.Ring.Hom.Defs
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import LeanCamCombi.Mathlib.Analysis.Convex.Exposed
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import LeanCamCombi.Mathlib.Analysis.Convex.Extreme
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import LeanCamCombi.Mathlib.Analysis.Convex.Independence
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import LeanCamCombi.Mathlib.Analysis.Convex.SimplicialComplex.Basic
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import LeanCamCombi.Mathlib.Analysis.RCLike.Basic
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import LeanCamCombi.Mathlib.Combinatorics.Schnirelmann
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import LeanCamCombi.Mathlib.Combinatorics.SetFamily.Shatter
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import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Basic
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import LeanCamCombi.Mathlib.Combinatorics.SimpleGraph.Subgraph
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import LeanCamCombi.Mathlib.Data.List.DropRight
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import LeanCamCombi.Mathlib.Data.Multiset.Basic
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import LeanCamCombi.Mathlib.Data.Prod.Lex
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import LeanCamCombi.Mathlib.Data.Set.Image
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import LeanCamCombi.Mathlib.Data.Set.Pointwise.SMul
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import LeanCamCombi.Mathlib.GroupTheory.OrderOfElement
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import LeanCamCombi.Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional
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import LeanCamCombi.Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable
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import LeanCamCombi.Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic
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import LeanCamCombi.Mathlib.MeasureTheory.Function.ConditionalExpectation.Real
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import LeanCamCombi.Mathlib.MeasureTheory.Function.L1Space
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import LeanCamCombi.Mathlib.MeasureTheory.Function.LpSeminorm.Basic
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import LeanCamCombi.Mathlib.MeasureTheory.Measure.Haar.NormedSpace
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import LeanCamCombi.Mathlib.MeasureTheory.Measure.Typeclasses
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import LeanCamCombi.Mathlib.Order.BooleanSubalgebra
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import LeanCamCombi.Mathlib.Order.Flag
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import LeanCamCombi.Mathlib.Order.Partition.Finpartition
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import LeanCamCombi.Mathlib.Order.RelIso.Group
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import LeanCamCombi.Mathlib.Probability.ProbabilityMassFunction.Constructions
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import LeanCamCombi.Mathlib.Probability.Variance
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import LeanCamCombi.Mathlib.RingTheory.FinitePresentation
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import LeanCamCombi.Mathlib.RingTheory.Spectrum.Prime.Topology
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import LeanCamCombi.Mathlib.Topology.MetricSpace.MetricSeparated
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import LeanCamCombi.MetricBetween

LeanCamCombi/CauchyFunctionalEquation.lean

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LeanCamCombi/GrowthInGroups/Chevalley.lean

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import Mathlib.Data.DFinsupp.WellFounded
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import Mathlib.RingTheory.Localization.Algebra
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import Mathlib.RingTheory.Spectrum.Prime.Polynomial
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import LeanCamCombi.Mathlib.Data.Prod.Lex
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import LeanCamCombi.Mathlib.RingTheory.FinitePresentation
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import LeanCamCombi.GrowthInGroups.ConstructiblePrimeSpectrum
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open Polynomial PrimeSpectrum TensorProduct Topology

LeanCamCombi/GrowthInGroups/ChevalleyComplex.lean

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@@ -5,7 +5,6 @@ import Mathlib.RingTheory.Spectrum.Prime.Polynomial
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Basic
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Degrees
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import LeanCamCombi.Mathlib.Algebra.MvPolynomial.Equiv
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import LeanCamCombi.Mathlib.Data.Prod.Lex
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import LeanCamCombi.Mathlib.Data.Set.Image
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import LeanCamCombi.Mathlib.RingTheory.Spectrum.Prime.Topology
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import LeanCamCombi.GrowthInGroups.ConstructibleSetData
@@ -149,7 +148,7 @@ lemma foo_induction (n : ℕ)
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-- We replace `R` by `R ⧸ Ideal.span {(e i).leadingCoeff}` where `(e i).degree` is lowered
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-- and `Away (e i).leadingCoeff` where `(e i).leadingCoeff` becomes invertible.
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apply hP _ _ i e rfl (by simpa using hi) (H_IH _ ?_ _ rfl) (H_IH _ ?_ _ rfl)
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· rw [hv, Prod.Lex.lt_iff'']
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· rw [hv, Prod.Lex.lt_iff']
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constructor
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· intro j
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simp only [coe_mapRingHom, InductionObj.ofLex_degree_fst, Pi.smul_apply,

LeanCamCombi/GrowthInGroups/Constructible.lean

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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Yaël Dillies
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-/
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import Mathlib.Order.BooleanSubalgebra
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import Mathlib.Topology.Spectral.Hom
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import LeanCamCombi.Mathlib.Order.BooleanSubalgebra
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/-!
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# Constructible sets
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basis.isConstructible' compact_inter _))
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(union : ∀ s hs t ht, P s hs → P t ht → P (s ∪ t) (hs.union ht))
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(s : Set X) (hs : IsConstructible s) : P s hs := by
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induction s, hs using BooleanSubalgebra.closure_sdiff_sup_induction' with
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induction s, hs using BooleanSubalgebra.closure_sdiff_sup_induction with
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| isSublattice =>
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exact ⟨fun s hs t ht ↦ ⟨hs.1.union ht.1, hs.2.union ht.2⟩,
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fun s hs t ht ↦ ⟨hs.1.inter ht.1, hs.2.inter_isOpen ht.2 ht.1⟩⟩

LeanCamCombi/GrowthInGroups/Lecture1.lean

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import Mathlib.Analysis.SpecialFunctions.Log.Basic
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import Mathlib.Combinatorics.Additive.DoublingConst
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import Mathlib.Combinatorics.Additive.VerySmallDoubling
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import Mathlib.Geometry.Group.Growth.LinearLowerBound
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import Mathlib.GroupTheory.Nilpotent
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import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
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import LeanCamCombi.GrowthInGroups.LinearLowerBound
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import LeanCamCombi.Util
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open Finset Fintype Group MulOpposite Real

LeanCamCombi/GrowthInGroups/LinearLowerBound.lean

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LeanCamCombi/Kneser/Kneser.lean

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exfalso
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have : ¬s * t * H ⊆ s * t := by
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rw [mul_subset_left_iff (hs.mul ht), hstab, ← coe_subset, coe_one]
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exact hCstab.not_subset_singleton
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exact hCstab.coe.not_subset_singleton
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simp_rw [mul_subset_iff_left, Classical.not_forall, mem_mul] at this
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obtain ⟨_, ⟨a, ha, b, hb, rfl⟩, hab⟩ := this
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set s₁ := s ∩ a • H with hs₁

LeanCamCombi/Mathlib/Algebra/Ring/Hom/Defs.lean

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LeanCamCombi/Mathlib/Analysis/RCLike/Basic.lean

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