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LeanCamCombi.lean

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@@ -12,7 +12,6 @@ import LeanCamCombi.GraphTheory.ExampleSheet1
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import LeanCamCombi.GraphTheory.ExampleSheet2
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import LeanCamCombi.GrowthInGroups.ApproximateSubgroup
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import LeanCamCombi.GrowthInGroups.BooleanSubalgebra
15-
import LeanCamCombi.GrowthInGroups.CharPolyBaseChange
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import LeanCamCombi.GrowthInGroups.Chevalley
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import LeanCamCombi.GrowthInGroups.ChevalleyComplex
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import LeanCamCombi.GrowthInGroups.Constructible
@@ -65,7 +64,6 @@ import LeanCamCombi.Mathlib.Data.Set.Pointwise.Interval
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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.Order.Interval.Finset.Defs
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import LeanCamCombi.Mathlib.Order.Partition.Finpartition
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import LeanCamCombi.Mathlib.Order.RelClasses
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import LeanCamCombi.Mathlib.Order.SupClosed
@@ -74,8 +72,6 @@ import LeanCamCombi.Mathlib.RingTheory.FinitePresentation
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import LeanCamCombi.Mathlib.RingTheory.Ideal.Span
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import LeanCamCombi.Mathlib.RingTheory.LocalRing.ResidueField.Ideal
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import LeanCamCombi.Mathlib.RingTheory.Polynomial.Basic
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import LeanCamCombi.Mathlib.Topology.Defs.Induced
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import LeanCamCombi.Mathlib.Topology.Spectral.Hom
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import LeanCamCombi.MetricBetween
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import LeanCamCombi.MinkowskiCaratheodory
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import LeanCamCombi.OrderShatter

LeanCamCombi/GrowthInGroups/BooleanSubalgebra.lean

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@@ -81,10 +81,10 @@ instance instBotCoe : Bot L where bot := ⟨⊥, bot_mem⟩
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instance instTopCoe : Top L where top := ⟨⊤, top_mem⟩
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/-- A boolean subalgebra of a lattice inherits a supremum. -/
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instance instSupCoe : Sup L where sup a b := ⟨a ⊔ b, L.supClosed a.2 b.2
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instance instSupCoe : Max L where max a b := ⟨a ⊔ b, L.supClosed a.2 b.2
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/-- A boolean subalgebra of a lattice inherits an infimum. -/
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instance instInfCoe : Inf L where inf a b := ⟨a ⊓ b, L.infClosed a.2 b.2
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instance instInfCoe : Min L where min a b := ⟨a ⊓ b, L.infClosed a.2 b.2
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/-- A boolean subalgebra of a lattice inherits a complement. -/
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instance instHasComplCoe : HasCompl L where compl a := ⟨aᶜ, compl_mem a.2
@@ -166,8 +166,8 @@ instance instBot : Bot (BooleanSubalgebra α) where
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bot.infClosed' _ := by aesop
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/-- The inf of two boolean subalgebras is their intersection. -/
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instance instInf : Inf (BooleanSubalgebra α) where
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inf L M := { carrier := L ∩ M
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instance instInf : Min (BooleanSubalgebra α) where
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min L M := { carrier := L ∩ M
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bot_mem' := ⟨bot_mem, bot_mem⟩
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compl_mem' := fun ha ↦ ⟨compl_mem ha.1, compl_mem ha.2
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supClosed' := L.supClosed.inter M.supClosed

LeanCamCombi/GrowthInGroups/CharPolyBaseChange.lean

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This file was deleted.

LeanCamCombi/GrowthInGroups/Constructible.lean

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@@ -3,19 +3,15 @@ Copyright (c) 2024 Yaël Dillies. All rights reserved.
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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.Tactic.StacksAttribute
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import Mathlib.Topology.Compactness.Compact
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import Mathlib.Topology.Separation.Basic
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import Mathlib.Topology.Spectral.Hom
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import LeanCamCombi.Mathlib.Data.Set.Image
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import LeanCamCombi.Mathlib.Topology.Defs.Induced
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import LeanCamCombi.GrowthInGroups.BooleanSubalgebra
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import LeanCamCombi.Mathlib.Data.Set.Image
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/-!
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# Constructible sets
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-/
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open Set TopologicalSpace
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open Set TopologicalSpace Topology
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variable {ι : Sort*} {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] {f : α → β}
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{s t U : Set α} {a : α}

LeanCamCombi/GrowthInGroups/PrimeSpectrumPolynomial.lean

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@@ -1,11 +1,11 @@
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import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
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import Mathlib.LinearAlgebra.Dual
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import Mathlib.LinearAlgebra.Charpoly.BaseChange
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import Mathlib.LinearAlgebra.Eigenspace.Zero
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import Mathlib.LinearAlgebra.FreeModule.PID
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import Mathlib.Order.CompletePartialOrder
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import Mathlib.RingTheory.AdjoinRoot
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import Mathlib.RingTheory.SimpleRing.Basic
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import LeanCamCombi.GrowthInGroups.CharPolyBaseChange
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import LeanCamCombi.Mathlib.RingTheory.LocalRing.ResidueField.Ideal
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open Polynomial TensorProduct PrimeSpectrum
@@ -149,4 +149,3 @@ lemma isOpen_image_comap_of_monic (f g : R[X]) (hg : g.Monic) :
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exact (isClosed_zeroLocus (R := R) t).isOpen_compl
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end PrimeSpectrum
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#min_imports

LeanCamCombi/GrowthInGroups/VerySmallDoubling.lean

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Original file line numberDiff line numberDiff line change
@@ -127,8 +127,8 @@ def symmetricSubgroup (A : Finset G) (h : #(A * A) < (3 / 2 : ℚ) * #A) : Subgr
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rw [← coe_mul_comm_of_doubling (weaken_doubling h)]
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exact ⟨a * b * t, by simp [ht, mul_assoc], ((c * d)⁻¹ * t)⁻¹, by simp [ht, mul_assoc]⟩
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lemma coe_symmetricSubgroup (A : Finset G) (h) : (symmetricSubgroup A h : Set G) = A * A⁻¹ := by
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rw [symmetricSubgroup_coe, eq_comm]
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lemma coe_symmetricSubgroup' (A : Finset G) (h) : (symmetricSubgroup A h : Set G) = A * A⁻¹ := by
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rw [coe_symmetricSubgroup, eq_comm]
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norm_cast
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exact mul_comm_of_doubling (by qify at h ⊢; linarith)
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@@ -180,7 +180,7 @@ lemma A_subset_aH (a : G) (ha : a ∈ A) : A ⊆ a • (A⁻¹ * A) := by
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lemma subgroup_strong_bound_left (h : #(A * A) < (3 / 2 : ℚ) * #A) (a : G) (ha : a ∈ A) :
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A * A ⊆ a • op a • (A⁻¹ * A) := by
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have h₁ : (A⁻¹ * A) * (A⁻¹ * A) = A⁻¹ * A := by
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rw [← coe_inj, coe_mul, coe_mul, ← symmetricSubgroup_coe _ h, coe_mul_coe]
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rw [← coe_inj, coe_mul, coe_mul, ← coe_symmetricSubgroup _ h, coe_mul_coe]
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have h₂ : a • op a • (A⁻¹ * A) = (a • (A⁻¹ * A)) * (op a • (A⁻¹ * A)) := by
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rw [mul_smul_comm, smul_mul_assoc, h₁, smul_comm]
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rw [h₂]
@@ -246,19 +246,19 @@ theorem very_small_doubling (h : #(A * A) < (3 / 2 : ℚ) * #A) :
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refine ⟨H, inferInstance, ?_, fun a ha ↦ ⟨?_, subset_antisymm ?_ ?_⟩⟩
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· simp [← Nat.card_eq_fintype_card, symmetricSubgroup, ← coe_mul, ← coe_inv, H]
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rwa [Nat.card_eq_finsetCard, subgroup_strong_bound h]
249-
· rw [symmetricSubgroup_coe]
249+
· rw [coe_symmetricSubgroup]
250250
exact_mod_cast A_subset_aH a ha
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· rw [Set.subset_set_smul_iff, ← op_inv]
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calc
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a •> (H : Set G) <• a⁻¹ ⊆ a •> (H : Set G) * A⁻¹ := Set.op_smul_set_subset_mul (by simpa)
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_ ⊆ A * (H : Set G) * A⁻¹ := by gcongr; exact Set.smul_set_subset_mul (by simpa)
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_ = H := by
256-
rw [symmetricSubgroup_coe, ← mul_assoc, ← coe_symmetricSubgroup _ h, mul_assoc,
257-
← coe_symmetricSubgroup _ h, ← symmetricSubgroup_coe _ h, coe_mul_coe]
256+
rw [coe_symmetricSubgroup, ← mul_assoc, ← coe_symmetricSubgroup' _ h, mul_assoc,
257+
← coe_symmetricSubgroup' _ h, ← coe_symmetricSubgroup _ h, coe_mul_coe]
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· rw [Set.subset_set_smul_iff]
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calc
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a⁻¹ •> ((H : Set G) <• a) ⊆ A⁻¹ * (H : Set G) <• a := Set.smul_set_subset_mul (by simpa)
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_ ⊆ A⁻¹ * ((H : Set G) * A) := by gcongr; exact Set.op_smul_set_subset_mul (by simpa)
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_ = H := by
263-
rw [coe_symmetricSubgroup, mul_assoc, ← symmetricSubgroup_coe _ h, ← mul_assoc,
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symmetricSubgroup_coe _ h, ← coe_symmetricSubgroup _ h, coe_mul_coe]
263+
rw [coe_symmetricSubgroup', mul_assoc, ← coe_symmetricSubgroup _ h, ← mul_assoc,
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coe_symmetricSubgroup _ h, ← coe_symmetricSubgroup' _ h, coe_mul_coe]

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