measure_theory.group.geometry_of_numbers ⟷ Mathlib.MeasureTheory.Group.GeometryOfNumbers

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -66,7 +66,7 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure /-
 /-- The **Minkowksi Convex Body Theorem**. If `s` is a convex symmetric domain of `E` whose volume
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -87,9 +87,9 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
     exists_pair_mem_lattice_not_disjoint_vadd fund ((h_conv.smul _).NullMeasurableSet _) h_vol
   obtain ⟨_, ⟨v, hv, rfl⟩, w, hw, hvw⟩ := not_disjoint_iff.mp h
   refine' ⟨x - y, sub_ne_zero.2 hxy, _⟩
-  rw [mem_inv_smul_set_iff₀ (two_ne_zero' ℝ)] at hv hw 
+  rw [mem_inv_smul_set_iff₀ (two_ne_zero' ℝ)] at hv hw
   simp_rw [AddSubgroup.vadd_def, vadd_eq_add, add_comm _ w, ← sub_eq_sub_iff_add_eq_add, ←
-    AddSubgroup.coe_sub] at hvw 
+    AddSubgroup.coe_sub] at hvw
   rw [← hvw, ← inv_smul_smul₀ (two_ne_zero' ℝ) (_ - _), smul_sub, sub_eq_add_neg, smul_add]
   refine' h_conv hw (h_symm _ hv) _ _ _ <;> norm_num
 #align measure_theory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,9 +3,9 @@ Copyright (c) 2021 Alex J. Best. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
 -/
-import Mathbin.Analysis.Convex.Measure
-import Mathbin.MeasureTheory.Group.FundamentalDomain
-import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
+import Analysis.Convex.Measure
+import MeasureTheory.Group.FundamentalDomain
+import MeasureTheory.Measure.Lebesgue.EqHaar
 
 #align_import measure_theory.group.geometry_of_numbers from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
 
@@ -66,7 +66,7 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure /-
 /-- The **Minkowksi Convex Body Theorem**. If `s` is a convex symmetric domain of `E` whose volume
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Alex J. Best. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
-
-! This file was ported from Lean 3 source module measure_theory.group.geometry_of_numbers
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Measure
 import Mathbin.MeasureTheory.Group.FundamentalDomain
 import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
 
+#align_import measure_theory.group.geometry_of_numbers from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Geometry of numbers
 
@@ -69,7 +66,7 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 #print MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure /-
 /-- The **Minkowksi Convex Body Theorem**. If `s` is a convex symmetric domain of `E` whose volume
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -50,6 +50,7 @@ open scoped Pointwise
 
 variable {E L : Type _} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 
+#print MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd /-
 /-- **Blichfeldt's Theorem**. If the volume of the set `s` is larger than the covolume of the
 countable subgroup `L` of `E`, then there exists two distincts points `x, y ∈ L` such that `(x + s)`
 and `(y + s)` are not disjoint. -/
@@ -66,8 +67,10 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
               fun _ => (hS.vadd _).inter fund.null_measurable_set).symm).trans_le
       (measure_mono <| Union_subset fun _ => inter_subset_right _ _)
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+#print MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure /-
 /-- The **Minkowksi Convex Body Theorem**. If `s` is a convex symmetric domain of `E` whose volume
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero
 lattice point of `L`.  -/
@@ -93,6 +96,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
   rw [← hvw, ← inv_smul_smul₀ (two_ne_zero' ℝ) (_ - _), smul_sub, sub_eq_add_neg, smul_add]
   refine' h_conv hw (h_symm _ hv) _ _ _ <;> norm_num
 #align measure_theory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure
+-/
 
 end MeasureTheory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
 
 ! This file was ported from Lean 3 source module measure_theory.group.geometry_of_numbers
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
 /-!
 # Geometry of numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove some of the fundamental theorems in the geometry of numbers, as studied by
 Hermann Minkowski.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -64,7 +64,7 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
       (measure_mono <| Union_subset fun _ => inter_subset_right _ _)
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » 0) -/
 /-- The **Minkowksi Convex Body Theorem**. If `s` is a convex symmetric domain of `E` whose volume
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero
 lattice point of `L`.  -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -69,9 +69,10 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero
 lattice point of `L`.  -/
 theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddCommGroup E]
-    [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [AddHaarMeasure μ] {L : AddSubgroup E}
-    [Countable L] (fund : IsAddFundamentalDomain L F μ) (h : μ F * 2 ^ finrank ℝ E < μ s)
-    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) : ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s :=
+    [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [IsAddHaarMeasure μ]
+    {L : AddSubgroup E} [Countable L] (fund : IsAddFundamentalDomain L F μ)
+    (h : μ F * 2 ^ finrank ℝ E < μ s) (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) :
+    ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s :=
   by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rwa [add_haar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -71,7 +71,7 @@ lattice point of `L`.  -/
 theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddCommGroup E]
     [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [AddHaarMeasure μ] {L : AddSubgroup E}
     [Countable L] (fund : IsAddFundamentalDomain L F μ) (h : μ F * 2 ^ finrank ℝ E < μ s)
-    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) : ∃ (x : _)(_ : x ≠ 0), ((x : L) : E) ∈ s :=
+    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) : ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s :=
   by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rwa [add_haar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
@@ -83,9 +83,9 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
     exists_pair_mem_lattice_not_disjoint_vadd fund ((h_conv.smul _).NullMeasurableSet _) h_vol
   obtain ⟨_, ⟨v, hv, rfl⟩, w, hw, hvw⟩ := not_disjoint_iff.mp h
   refine' ⟨x - y, sub_ne_zero.2 hxy, _⟩
-  rw [mem_inv_smul_set_iff₀ (two_ne_zero' ℝ)] at hv hw
+  rw [mem_inv_smul_set_iff₀ (two_ne_zero' ℝ)] at hv hw 
   simp_rw [AddSubgroup.vadd_def, vadd_eq_add, add_comm _ w, ← sub_eq_sub_iff_add_eq_add, ←
-    AddSubgroup.coe_sub] at hvw
+    AddSubgroup.coe_sub] at hvw 
   rw [← hvw, ← inv_smul_smul₀ (two_ne_zero' ℝ) (_ - _), smul_sub, sub_eq_add_neg, smul_add]
   refine' h_conv hw (h_symm _ hv) _ _ _ <;> norm_num
 #align measure_theory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -51,7 +51,7 @@ variable {E L : Type _} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 countable subgroup `L` of `E`, then there exists two distincts points `x, y ∈ L` such that `(x + s)`
 and `(y + s)` are not disjoint. -/
 theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L] [AddAction L E]
-    [MeasurableSpace L] [MeasurableVAdd L E] [VaddInvariantMeasure L E μ]
+    [MeasurableSpace L] [MeasurableVAdd L E] [VAddInvariantMeasure L E μ]
     (fund : IsAddFundamentalDomain L F μ) (hS : NullMeasurableSet s μ) (h : μ F < μ s) :
     ∃ x y : L, x ≠ y ∧ ¬Disjoint (x +ᵥ s) (y +ᵥ s) :=
   by
@@ -69,10 +69,9 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
 is large enough compared to the covolume of a lattice `L` of `E`, then it contains a non-zero
 lattice point of `L`.  -/
 theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddCommGroup E]
-    [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [IsAddHaarMeasure μ]
-    {L : AddSubgroup E} [Countable L] (fund : IsAddFundamentalDomain L F μ)
-    (h : μ F * 2 ^ finrank ℝ E < μ s) (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) :
-    ∃ (x : _)(_ : x ≠ 0), ((x : L) : E) ∈ s :=
+    [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [AddHaarMeasure μ] {L : AddSubgroup E}
+    [Countable L] (fund : IsAddFundamentalDomain L F μ) (h : μ F * 2 ^ finrank ℝ E < μ s)
+    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) : ∃ (x : _)(_ : x ≠ 0), ((x : L) : E) ∈ s :=
   by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rwa [add_haar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -43,7 +43,7 @@ namespace MeasureTheory
 
 open ENNReal FiniteDimensional MeasureTheory MeasureTheory.Measure Set
 
-open Pointwise
+open scoped Pointwise
 
 variable {E L : Type _} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
 
 ! This file was ported from Lean 3 source module measure_theory.group.geometry_of_numbers
-! leanprover-community/mathlib commit 02e095b22be8a3731542041cdc1266b7f588377c
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Measure
 import Mathbin.MeasureTheory.Group.FundamentalDomain
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
+import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
 
 /-!
 # Geometry of numbers

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -51,7 +51,7 @@ variable {E L : Type _} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 countable subgroup `L` of `E`, then there exists two distincts points `x, y ∈ L` such that `(x + s)`
 and `(y + s)` are not disjoint. -/
 theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L] [AddAction L E]
-    [MeasurableSpace L] [HasMeasurableVadd L E] [VaddInvariantMeasure L E μ]
+    [MeasurableSpace L] [MeasurableVAdd L E] [VaddInvariantMeasure L E μ]
     (fund : IsAddFundamentalDomain L F μ) (hS : NullMeasurableSet s μ) (h : μ F < μ s) :
     ∃ x y : L, x ≠ y ∧ ¬Disjoint (x +ᵥ s) (y +ᵥ s) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -59,7 +59,7 @@ theorem exists_pair_mem_lattice_not_disjoint_vadd [AddCommGroup L] [Countable L]
   exact
     ((fund.measure_eq_tsum _).trans
           (measure_Union₀
-              (Pairwise.mono h fun i j hij => (hij.mono inf_le_left inf_le_left).AeDisjoint)
+              (Pairwise.mono h fun i j hij => (hij.mono inf_le_left inf_le_left).AEDisjoint)
               fun _ => (hS.vadd _).inter fund.null_measurable_set).symm).trans_le
       (measure_mono <| Union_subset fun _ => inter_subset_right _ _)
 #align measure_theory.exists_pair_mem_lattice_not_disjoint_vadd MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcb83fe7996142dfcfe7368d31304a9adc874a

The iInter version of Cantor's intersection theorem is already present: IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed. The proof of the added sInter version takes advantage of the iInter version.

Much of the addition due to conversation with Sebastien Gouezel on Zulip.

@@ -120,7 +120,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure [NormedAddC
     · rw [sdiff_eq_sdiff_iff_inf_eq_inf (z := U).mpr (by simp [Set.inter_comm .. ▸ hU.2, zero_mem])]
       exact AddSubgroup.isClosed_of_discrete.sdiff hU.1
     exact isOpen_inter_eq_singleton_of_mem_discrete (zero_mem L)
-  refine IsCompact.nonempty_iInter_of_sequence_nonempty_compact_closed Z (fun n => ?_)
+  refine IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosed Z (fun n => ?_)
     (fun n => ?_) ((S 0).isCompact.inter_right h_clos) (fun n => (S n).isClosed.inter h_clos)
   · refine Set.inter_subset_inter_left _ (SetLike.coe_subset_coe.mpr ?_)
     refine ConvexBody.smul_le_of_le K h_zero ?_

I am keeping some 1 / p lemmas behind to keep the diff small but the goal is to get rid of them entirely.

@@ -69,7 +69,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rw [addHaar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
       mul_lt_mul_right (pow_ne_zero (finrank ℝ E) (two_ne_zero' _)) (pow_ne_top two_ne_top),
-      mul_right_comm, ofReal_pow (by norm_num : 0 ≤ (2 : ℝ)⁻¹), ← ofReal_inv_of_pos zero_lt_two]
+      mul_right_comm, ofReal_pow (by norm_num : 0 ≤ (2 : ℝ)⁻¹), ofReal_inv_of_pos zero_lt_two]
     norm_num
     rwa [← mul_pow, ENNReal.inv_mul_cancel two_ne_zero two_ne_top, one_pow, one_mul]
   obtain ⟨x, y, hxy, h⟩ :=

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -99,7 +99,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure [NormedAddC
     intro hμ
     suffices μ F = 0 from fund.measure_ne_zero (NeZero.ne μ) this
     rw [hμ, le_zero_iff, mul_eq_zero] at h
-    exact h.resolve_right <| (pow_ne_zero_iff finrank_pos).mpr two_ne_zero
+    exact h.resolve_right <| pow_ne_zero _ two_ne_zero
   have h_nemp : s.Nonempty := nonempty_of_measure_ne_zero h_mes
   let u : ℕ → ℝ≥0 := (exists_seq_strictAnti_tendsto 0).choose
   let K : ConvexBody E := ⟨s, h_conv, h_cpt, h_nemp⟩

@@ -65,7 +65,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
     [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [IsAddHaarMeasure μ]
     {L : AddSubgroup E} [Countable L] (fund : IsAddFundamentalDomain L F μ)
     (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) (h : μ F * 2 ^ finrank ℝ E < μ s) :
-    ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s := by
+    ∃ x ≠ 0, ((x : L) : E) ∈ s := by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rw [addHaar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
       mul_lt_mul_right (pow_ne_zero (finrank ℝ E) (two_ne_zero' _)) (pow_ne_top two_ne_top),
@@ -94,12 +94,12 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure [NormedAddC
     {L : AddSubgroup E} [Countable L] [DiscreteTopology L] (fund : IsAddFundamentalDomain L F μ)
     (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) (h_cpt : IsCompact s)
     (h : μ F * 2 ^ finrank ℝ E ≤ μ s) :
-    ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s := by
+    ∃ x ≠ 0, ((x : L) : E) ∈ s := by
   have h_mes : μ s ≠ 0 := by
-    by_contra hμ
-    suffices μ F = 0 by exact fund.measure_ne_zero (NeZero.ne μ) this
+    intro hμ
+    suffices μ F = 0 from fund.measure_ne_zero (NeZero.ne μ) this
     rw [hμ, le_zero_iff, mul_eq_zero] at h
-    exact h.resolve_right <| (pow_eq_zero_iff finrank_pos).not.mpr two_ne_zero
+    exact h.resolve_right <| (pow_ne_zero_iff finrank_pos).mpr two_ne_zero
   have h_nemp : s.Nonempty := nonempty_of_measure_ne_zero h_mes
   let u : ℕ → ℝ≥0 := (exists_seq_strictAnti_tendsto 0).choose
   let K : ConvexBody E := ⟨s, h_conv, h_cpt, h_nemp⟩

@@ -3,9 +3,9 @@ Copyright (c) 2021 Alex J. Best. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
 -/
+import Mathlib.Analysis.Convex.Body
 import Mathlib.Analysis.Convex.Measure
 import Mathlib.MeasureTheory.Group.FundamentalDomain
-import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
 
 #align_import measure_theory.group.geometry_of_numbers from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
 
@@ -38,9 +38,9 @@ Hermann Minkowski.
 
 namespace MeasureTheory
 
-open ENNReal FiniteDimensional MeasureTheory MeasureTheory.Measure Set
+open ENNReal FiniteDimensional MeasureTheory MeasureTheory.Measure Set Filter
 
-open scoped Pointwise
+open scoped Pointwise NNReal
 
 variable {E L : Type*} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 
@@ -64,7 +64,7 @@ lattice point of `L`.  -/
 theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddCommGroup E]
     [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [IsAddHaarMeasure μ]
     {L : AddSubgroup E} [Countable L] (fund : IsAddFundamentalDomain L F μ)
-    (h : μ F * 2 ^ finrank ℝ E < μ s) (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) :
+    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) (h : μ F * 2 ^ finrank ℝ E < μ s) :
     ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s := by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
     rw [addHaar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
@@ -83,4 +83,62 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
   refine' h_conv hw (h_symm _ hv) _ _ _ <;> norm_num
 #align measure_theory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure
 
+/-- The **Minkowski Convex Body Theorem for compact domain**. If `s` is a convex compact symmetric
+domain of `E` whose volume is large enough compared to the covolume of a lattice `L` of `E`, then it
+contains a non-zero lattice point of `L`. Compared to
+`exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure`, this version requires in addition
+that `s` is compact and `L` is discrete but provides a weaker inequality rather than a strict
+inequality. -/
+theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure [NormedAddCommGroup E]
+    [NormedSpace ℝ E] [BorelSpace E] [FiniteDimensional ℝ E] [Nontrivial E] [IsAddHaarMeasure μ]
+    {L : AddSubgroup E} [Countable L] [DiscreteTopology L] (fund : IsAddFundamentalDomain L F μ)
+    (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) (h_cpt : IsCompact s)
+    (h : μ F * 2 ^ finrank ℝ E ≤ μ s) :
+    ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s := by
+  have h_mes : μ s ≠ 0 := by
+    by_contra hμ
+    suffices μ F = 0 by exact fund.measure_ne_zero (NeZero.ne μ) this
+    rw [hμ, le_zero_iff, mul_eq_zero] at h
+    exact h.resolve_right <| (pow_eq_zero_iff finrank_pos).not.mpr two_ne_zero
+  have h_nemp : s.Nonempty := nonempty_of_measure_ne_zero h_mes
+  let u : ℕ → ℝ≥0 := (exists_seq_strictAnti_tendsto 0).choose
+  let K : ConvexBody E := ⟨s, h_conv, h_cpt, h_nemp⟩
+  let S : ℕ → ConvexBody E := fun n => (1 + u n) • K
+  let Z : ℕ → Set E := fun n => (S n) ∩ (L \ {0})
+  -- The convex bodies `S n` have volume strictly larger than `μ s` and thus we can apply
+  -- `exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure` to them and obtain that
+  -- `S n` contains a nonzero point of `L`. Since the intersection of the `S n` is equal to `s`,
+  -- it follows that `s` contains a nonzero point of `L`.
+  have h_zero : 0 ∈ K := K.zero_mem_of_symmetric h_symm
+  suffices Set.Nonempty (⋂ n, Z n) by
+    erw [← Set.iInter_inter, K.iInter_smul_eq_self h_zero] at this
+    · obtain ⟨x, hx⟩ := this
+      exact ⟨⟨x, by aesop⟩, by aesop⟩
+    · exact (exists_seq_strictAnti_tendsto (0:ℝ≥0)).choose_spec.2.2
+  have h_clos : IsClosed ((L : Set E) \ {0}) := by
+    rsuffices ⟨U, hU⟩ : ∃ U : Set E, IsOpen U ∧  U ∩ L = {0}
+    · rw [sdiff_eq_sdiff_iff_inf_eq_inf (z := U).mpr (by simp [Set.inter_comm .. ▸ hU.2, zero_mem])]
+      exact AddSubgroup.isClosed_of_discrete.sdiff hU.1
+    exact isOpen_inter_eq_singleton_of_mem_discrete (zero_mem L)
+  refine IsCompact.nonempty_iInter_of_sequence_nonempty_compact_closed Z (fun n => ?_)
+    (fun n => ?_) ((S 0).isCompact.inter_right h_clos) (fun n => (S n).isClosed.inter h_clos)
+  · refine Set.inter_subset_inter_left _ (SetLike.coe_subset_coe.mpr ?_)
+    refine ConvexBody.smul_le_of_le K h_zero ?_
+    rw [add_le_add_iff_left]
+    exact le_of_lt <| (exists_seq_strictAnti_tendsto (0:ℝ≥0)).choose_spec.1 (Nat.lt.base n)
+  · suffices μ F * 2 ^ finrank ℝ E < μ (S n : Set E) by
+      have h_symm' : ∀ x ∈ S n, -x ∈ S n := by
+        rintro _ ⟨y, hy, rfl⟩
+        exact ⟨-y, h_symm _ hy, by simp⟩
+      obtain ⟨x, hx_nz, hx_mem⟩ := exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure
+        fund h_symm' (S n).convex this
+      exact ⟨x, hx_mem, by aesop⟩
+    refine lt_of_le_of_lt h ?_
+    rw [ConvexBody.coe_smul', NNReal.smul_def, addHaar_smul_of_nonneg _ (NNReal.coe_nonneg _)]
+    rw [show μ s < _ ↔ 1 * μ s < _ by rw [one_mul]]
+    refine (mul_lt_mul_right h_mes (ne_of_lt h_cpt.measure_lt_top)).mpr ?_
+    rw [ofReal_pow (NNReal.coe_nonneg _)]
+    refine one_lt_pow ?_ (ne_of_gt finrank_pos)
+    simp [(exists_seq_strictAnti_tendsto (0:ℝ≥0)).choose_spec.2.1 n]
+
 end MeasureTheory

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -42,7 +42,7 @@ open ENNReal FiniteDimensional MeasureTheory MeasureTheory.Measure Set
 
 open scoped Pointwise
 
-variable {E L : Type _} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
+variable {E L : Type*} [MeasurableSpace E] {μ : Measure E} {F s : Set E}
 
 /-- **Blichfeldt's Theorem**. If the volume of the set `s` is larger than the covolume of the
 countable subgroup `L` of `E`, then there exist two distinct points `x, y ∈ L` such that `(x + s)`

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Alex J. Best. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex J. Best
-
-! This file was ported from Lean 3 source module measure_theory.group.geometry_of_numbers
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Measure
 import Mathlib.MeasureTheory.Group.FundamentalDomain
 import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
 
+#align_import measure_theory.group.geometry_of_numbers from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Geometry of numbers
 

This is supposed to mean "an additive Haar measure", not adding something to Haar, so it should be one word and not two.

@@ -70,7 +70,7 @@ theorem exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure [NormedAddC
     (h : μ F * 2 ^ finrank ℝ E < μ s) (h_symm : ∀ x ∈ s, -x ∈ s) (h_conv : Convex ℝ s) :
     ∃ (x : _) (_ : x ≠ 0), ((x : L) : E) ∈ s := by
   have h_vol : μ F < μ ((2⁻¹ : ℝ) • s) := by
-    rw [add_haar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
+    rw [addHaar_smul_of_nonneg μ (by norm_num : 0 ≤ (2 : ℝ)⁻¹) s, ←
       mul_lt_mul_right (pow_ne_zero (finrank ℝ E) (two_ne_zero' _)) (pow_ne_top two_ne_top),
       mul_right_comm, ofReal_pow (by norm_num : 0 ≤ (2 : ℝ)⁻¹), ← ofReal_inv_of_pos zero_lt_two]
     norm_num