measure_theory.measure.haar.of_basis ⟷ Mathlib.MeasureTheory.Measure.Haar.OfBasis

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

@@ -194,7 +194,7 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
       cases' eq_or_ne (a i) 0 with hai hai
       · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
         rw [hai, ← h, zero_div, MulZeroClass.zero_mul]
-      · rw [div_mul_cancel _ hai]
+      · rw [div_mul_cancel₀ _ hai]
 #align parallelepiped_single parallelepiped_single
 -/
 

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

@@ -140,7 +140,7 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
   · rintro ⟨t, ht, rfl⟩
     exact ⟨t • v, fun i => ⟨t i, ht _, by simp⟩, rfl⟩
   rintro ⟨g, hg, rfl⟩
-  change ∀ i, _ at hg 
+  change ∀ i, _ at hg
   choose t ht hg using hg
   refine' ⟨t, ht, _⟩
   simp_rw [hg]
@@ -185,14 +185,14 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
     refine' ⟨fun i => x i / a i, fun i => _, funext fun i => _⟩
     · specialize h i
       cases' le_total (a i) 0 with hai hai
-      · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai] at h 
+      · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai] at h
         exact ⟨div_nonneg_of_nonpos h.2 hai, div_le_one_of_ge h.1 hai⟩
-      · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai] at h 
+      · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai] at h
         exact ⟨div_nonneg h.1 hai, div_le_one_of_le h.2 hai⟩
     · specialize h i
       simp only [smul_eq_mul, Pi.mul_apply]
       cases' eq_or_ne (a i) 0 with hai hai
-      · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h 
+      · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
         rw [hai, ← h, zero_div, MulZeroClass.zero_mul]
       · rw [div_mul_cancel _ hai]
 #align parallelepiped_single parallelepiped_single

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

@@ -63,7 +63,7 @@ theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
   by
   simp only [parallelepiped, ← image_comp]
   congr 1 with t
-  simp only [Function.comp_apply, LinearMap.map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
+  simp only [Function.comp_apply, map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
 #align image_parallelepiped image_parallelepiped
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.MeasureTheory.Measure.Haar.Basic
-import Mathbin.Analysis.InnerProductSpace.PiL2
+import MeasureTheory.Measure.Haar.Basic
+import Analysis.InnerProductSpace.PiL2
 
 #align_import measure_theory.measure.haar.of_basis from "leanprover-community/mathlib"@"92bd7b1ffeb306a89f450bee126ddd8a284c259d"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
-! leanprover-community/mathlib commit 92bd7b1ffeb306a89f450bee126ddd8a284c259d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.Haar.Basic
 import Mathbin.Analysis.InnerProductSpace.PiL2
 
+#align_import measure_theory.measure.haar.of_basis from "leanprover-community/mathlib"@"92bd7b1ffeb306a89f450bee126ddd8a284c259d"
+
 /-!
 # Additive Haar measure constructed from a basis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

@@ -232,11 +232,13 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E
 #align basis.parallelepiped Basis.parallelepiped
 -/
 
+#print Basis.coe_parallelepiped /-
 @[simp]
 theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
     (b.parallelepiped : Set E) = parallelepiped b :=
   rfl
 #align basis.coe_parallelepiped Basis.coe_parallelepiped
+-/
 
 #print Basis.parallelepiped_reindex /-
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/b01d6eb9d0a308807af54319b264d0994b91774b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
-! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
+! leanprover-community/mathlib commit 92bd7b1ffeb306a89f450bee126ddd8a284c259d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -154,27 +154,15 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
 theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
   by
   rw [parallelepiped_eq_sum_segment]
-  -- TODO: add `convex.sum` to match `convex.add`
-  let this.1 : AddSubmonoid (Set E) :=
-    { carrier := {s | Convex ℝ s}
-      zero_mem' := convex_singleton _
-      add_mem' := fun x y => Convex.add }
-  exact this.sum_mem fun i hi => convex_segment _ _
+  exact convex_sum _ fun i hi => convex_segment _ _
 #align convex_parallelepiped convex_parallelepiped
 -/
 
 #print parallelepiped_eq_convexHull /-
 /-- A `parallelepiped` is the convex hull of its vertices -/
 theorem parallelepiped_eq_convexHull (v : ι → E) :
-    parallelepiped v = convexHull ℝ (∑ i, {(0 : E), v i}) :=
-  by
-  -- TODO: add `convex_hull_sum` to match `convex_hull_add`
-  let this.1 : Set E →+ Set E :=
-    { toFun := convexHull ℝ
-      map_zero' := convexHull_singleton _
-      map_add' := convexHull_add }
-  simp_rw [parallelepiped_eq_sum_segment, ← convexHull_pair]
-  exact (this.map_sum _ _).symm
+    parallelepiped v = convexHull ℝ (∑ i, {(0 : E), v i}) := by
+  simp_rw [convexHull_sum, convexHull_pair, parallelepiped_eq_sum_segment]
 #align parallelepiped_eq_convex_hull parallelepiped_eq_convexHull
 -/
 

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

@@ -53,11 +53,14 @@ def parallelepiped (v : ι → E) : Set E :=
 #align parallelepiped parallelepiped
 -/
 
+#print mem_parallelepiped_iff /-
 theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
     x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ) (ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
   simp [parallelepiped, eq_comm]
 #align mem_parallelepiped_iff mem_parallelepiped_iff
+-/
 
+#print image_parallelepiped /-
 theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
     f '' parallelepiped v = parallelepiped (f ∘ v) :=
   by
@@ -65,7 +68,9 @@ theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
   congr 1 with t
   simp only [Function.comp_apply, LinearMap.map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
 #align image_parallelepiped image_parallelepiped
+-/
 
+#print parallelepiped_comp_equiv /-
 /-- Reindexing a family of vectors does not change their parallelepiped. -/
 @[simp]
 theorem parallelepiped_comp_equiv (v : ι → E) (e : ι' ≃ ι) :
@@ -90,7 +95,9 @@ theorem parallelepiped_comp_equiv (v : ι → E) (e : ι' ≃ ι) :
     Equiv.piCongrLeft'_apply, Equiv.apply_symm_apply] using
     (e.symm.sum_comp fun i : ι' => x i • v (e i)).symm
 #align parallelepiped_comp_equiv parallelepiped_comp_equiv
+-/
 
+#print parallelepiped_orthonormalBasis_one_dim /-
 -- The parallelepiped associated to an orthonormal basis of `ℝ` is either `[0, 1]` or `[-1, 0]`.
 theorem parallelepiped_orthonormalBasis_one_dim (b : OrthonormalBasis ι ℝ ℝ) :
     parallelepiped b = Icc 0 1 ∨ parallelepiped b = Icc (-1) 0 :=
@@ -124,7 +131,9 @@ theorem parallelepiped_orthonormalBasis_one_dim (b : OrthonormalBasis ι ℝ ℝ
     simp only [← image_comp, mul_neg, mul_one, Finset.sum_singleton, image_neg, preimage_neg_Icc,
       neg_zero, Finset.univ_unique]
 #align parallelepiped_orthonormal_basis_one_dim parallelepiped_orthonormalBasis_one_dim
+-/
 
+#print parallelepiped_eq_sum_segment /-
 theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i, segment ℝ 0 (v i) :=
   by
   ext
@@ -139,6 +148,7 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
   refine' ⟨t, ht, _⟩
   simp_rw [hg]
 #align parallelepiped_eq_sum_segment parallelepiped_eq_sum_segment
+-/
 
 #print convex_parallelepiped /-
 theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
@@ -153,6 +163,7 @@ theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
 #align convex_parallelepiped convex_parallelepiped
 -/
 
+#print parallelepiped_eq_convexHull /-
 /-- A `parallelepiped` is the convex hull of its vertices -/
 theorem parallelepiped_eq_convexHull (v : ι → E) :
     parallelepiped v = convexHull ℝ (∑ i, {(0 : E), v i}) :=
@@ -165,7 +176,9 @@ theorem parallelepiped_eq_convexHull (v : ι → E) :
   simp_rw [parallelepiped_eq_sum_segment, ← convexHull_pair]
   exact (this.map_sum _ _).symm
 #align parallelepiped_eq_convex_hull parallelepiped_eq_convexHull
+-/
 
+#print parallelepiped_single /-
 /-- The axis aligned parallelepiped over `ι → ℝ` is a cuboid. -/
 theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
     (parallelepiped fun i => Pi.single i (a i)) = Set.uIcc 0 a :=
@@ -198,6 +211,7 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
         rw [hai, ← h, zero_div, MulZeroClass.zero_mul]
       · rw [div_mul_cancel _ hai]
 #align parallelepiped_single parallelepiped_single
+-/
 
 end AddCommGroup
 
@@ -236,13 +250,16 @@ theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
   rfl
 #align basis.coe_parallelepiped Basis.coe_parallelepiped
 
+#print Basis.parallelepiped_reindex /-
 @[simp]
 theorem Basis.parallelepiped_reindex (b : Basis ι ℝ E) (e : ι ≃ ι') :
     (b.reindex e).parallelepiped = b.parallelepiped :=
   PositiveCompacts.ext <|
     (congr_arg parallelepiped (b.coe_reindex _)).trans (parallelepiped_comp_equiv b e.symm)
 #align basis.parallelepiped_reindex Basis.parallelepiped_reindex
+-/
 
+#print Basis.parallelepiped_map /-
 theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
     (b.map e).parallelepiped =
       b.parallelepiped.map e
@@ -252,6 +269,7 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
         e.to_linear_map.is_open_map_of_finite_dimensional e.surjective :=
   PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
 #align basis.parallelepiped_map Basis.parallelepiped_map
+-/
 
 variable [MeasurableSpace E] [BorelSpace E]
 
@@ -269,9 +287,11 @@ instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure
 #align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 -/
 
+#print Basis.addHaar_self /-
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact add_haar_measure_self
 #align basis.add_haar_self Basis.addHaar_self
+-/
 
 end NormedSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -145,7 +145,7 @@ theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
   by
   rw [parallelepiped_eq_sum_segment]
   -- TODO: add `convex.sum` to match `convex.add`
-  let this : AddSubmonoid (Set E) :=
+  let this.1 : AddSubmonoid (Set E) :=
     { carrier := {s | Convex ℝ s}
       zero_mem' := convex_singleton _
       add_mem' := fun x y => Convex.add }
@@ -158,7 +158,7 @@ theorem parallelepiped_eq_convexHull (v : ι → E) :
     parallelepiped v = convexHull ℝ (∑ i, {(0 : E), v i}) :=
   by
   -- TODO: add `convex_hull_sum` to match `convex_hull_add`
-  let this : Set E →+ Set E :=
+  let this.1 : Set E →+ Set E :=
     { toFun := convexHull ℝ
       map_zero' := convexHull_singleton _
       map_add' := convexHull_add }

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.InnerProductSpace.PiL2
 /-!
 # Additive Haar measure constructed from a basis
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a basis of a finite-dimensional real vector space, we define the corresponding Lebesgue
 measure, which gives measure `1` to the parallelepiped spanned by the basis.
 
@@ -143,7 +146,7 @@ theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
   rw [parallelepiped_eq_sum_segment]
   -- TODO: add `convex.sum` to match `convex.add`
   let this : AddSubmonoid (Set E) :=
-    { carrier := { s | Convex ℝ s }
+    { carrier := {s | Convex ℝ s}
       zero_mem' := convex_singleton _
       add_mem' := fun x y => Convex.add }
   exact this.sum_mem fun i hi => convex_segment _ _
@@ -260,10 +263,10 @@ irreducible_def Basis.addHaar (b : Basis ι ℝ E) : Measure E :=
 #align basis.add_haar Basis.addHaar
 -/
 
-#print AddHaarMeasure_basis_addHaar /-
-instance AddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : AddHaarMeasure b.addHaar := by
+#print IsAddHaarMeasure_basis_addHaar /-
+instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure b.addHaar := by
   rw [Basis.addHaar]; exact measure.is_add_haar_measure_add_haar_measure _
-#align is_add_haar_measure_basis_add_haar AddHaarMeasure_basis_addHaar
+#align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 -/
 
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by

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

@@ -51,7 +51,7 @@ def parallelepiped (v : ι → E) : Set E :=
 -/
 
 theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
-    x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ)(ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
+    x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ) (ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
   simp [parallelepiped, eq_comm]
 #align mem_parallelepiped_iff mem_parallelepiped_iff
 
@@ -131,7 +131,7 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
   · rintro ⟨t, ht, rfl⟩
     exact ⟨t • v, fun i => ⟨t i, ht _, by simp⟩, rfl⟩
   rintro ⟨g, hg, rfl⟩
-  change ∀ i, _ at hg
+  change ∀ i, _ at hg 
   choose t ht hg using hg
   refine' ⟨t, ht, _⟩
   simp_rw [hg]
@@ -184,14 +184,14 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
     refine' ⟨fun i => x i / a i, fun i => _, funext fun i => _⟩
     · specialize h i
       cases' le_total (a i) 0 with hai hai
-      · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai] at h
+      · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai] at h 
         exact ⟨div_nonneg_of_nonpos h.2 hai, div_le_one_of_ge h.1 hai⟩
-      · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai] at h
+      · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai] at h 
         exact ⟨div_nonneg h.1 hai, div_le_one_of_le h.2 hai⟩
     · specialize h i
       simp only [smul_eq_mul, Pi.mul_apply]
       cases' eq_or_ne (a i) 0 with hai hai
-      · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
+      · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h 
         rw [hai, ← h, zero_div, MulZeroClass.zero_mul]
       · rw [div_mul_cancel _ hai]
 #align parallelepiped_single parallelepiped_single

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

@@ -43,10 +43,12 @@ section AddCommGroup
 
 variable [AddCommGroup E] [Module ℝ E] [AddCommGroup F] [Module ℝ F]
 
+#print parallelepiped /-
 /-- The closed parallelepiped spanned by a finite family of vectors. -/
 def parallelepiped (v : ι → E) : Set E :=
   (fun t : ι → ℝ => ∑ i, t i • v i) '' Icc 0 1
 #align parallelepiped parallelepiped
+-/
 
 theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
     x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ)(ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
@@ -135,6 +137,7 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
   simp_rw [hg]
 #align parallelepiped_eq_sum_segment parallelepiped_eq_sum_segment
 
+#print convex_parallelepiped /-
 theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
   by
   rw [parallelepiped_eq_sum_segment]
@@ -145,6 +148,7 @@ theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) :=
       add_mem' := fun x y => Convex.add }
   exact this.sum_mem fun i hi => convex_segment _ _
 #align convex_parallelepiped convex_parallelepiped
+-/
 
 /-- A `parallelepiped` is the convex hull of its vertices -/
 theorem parallelepiped_eq_convexHull (v : ι → E) :
@@ -198,6 +202,7 @@ section NormedSpace
 
 variable [NormedAddCommGroup E] [NormedAddCommGroup F] [NormedSpace ℝ E] [NormedSpace ℝ F]
 
+#print Basis.parallelepiped /-
 /-- The parallelepiped spanned by a basis, as a compact set with nonempty interior. -/
 def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E
     where
@@ -220,6 +225,7 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E
         zero_lt_one, imp_true_iff]
     rwa [← Homeomorph.image_interior, nonempty_image_iff]
 #align basis.parallelepiped Basis.parallelepiped
+-/
 
 @[simp]
 theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
@@ -246,15 +252,19 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
 
 variable [MeasurableSpace E] [BorelSpace E]
 
+#print Basis.addHaar /-
 /-- The Lebesgue measure associated to a basis, giving measure `1` to the parallelepiped spanned
 by the basis. -/
 irreducible_def Basis.addHaar (b : Basis ι ℝ E) : Measure E :=
   Measure.addHaarMeasure b.parallelepiped
 #align basis.add_haar Basis.addHaar
+-/
 
-instance addHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : AddHaarMeasure b.addHaar := by
+#print AddHaarMeasure_basis_addHaar /-
+instance AddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : AddHaarMeasure b.addHaar := by
   rw [Basis.addHaar]; exact measure.is_add_haar_measure_add_haar_measure _
-#align is_add_haar_measure_basis_add_haar addHaarMeasure_basis_addHaar
+#align is_add_haar_measure_basis_add_haar AddHaarMeasure_basis_addHaar
+-/
 
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact add_haar_measure_self
@@ -262,6 +272,7 @@ theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) =
 
 end NormedSpace
 
+#print measureSpaceOfInnerProductSpace /-
 /-- A finite dimensional inner product space has a canonical measure, the Lebesgue measure giving
 volume `1` to the parallelepiped spanned by any orthonormal basis. We define the measure using
 some arbitrary choice of orthonormal basis. The fact that it works with any orthonormal basis
@@ -270,11 +281,14 @@ instance (priority := 100) measureSpaceOfInnerProductSpace [NormedAddCommGroup E
     [InnerProductSpace ℝ E] [FiniteDimensional ℝ E] [MeasurableSpace E] [BorelSpace E] :
     MeasureSpace E where volume := (stdOrthonormalBasis ℝ E).toBasis.addHaar
 #align measure_space_of_inner_product_space measureSpaceOfInnerProductSpace
+-/
 
+#print Real.measureSpace /-
 /- This instance should not be necessary, but Lean has difficulties to find it in product
 situations if we do not declare it explicitly. -/
 instance Real.measureSpace : MeasureSpace ℝ := by infer_instance
 #align real.measure_space Real.measureSpace
+-/
 
 /-! # Miscellaneous instances for `euclidean_space`
 
@@ -293,6 +307,7 @@ instance : MeasurableSpace (EuclideanSpace ℝ ι) :=
 instance : BorelSpace (EuclideanSpace ℝ ι) :=
   Pi.borelSpace
 
+#print EuclideanSpace.measurableEquiv /-
 /-- `pi_Lp.equiv` as a `measurable_equiv`. -/
 @[simps toEquiv]
 protected def measurableEquiv : EuclideanSpace ℝ ι ≃ᵐ (ι → ℝ)
@@ -301,10 +316,13 @@ protected def measurableEquiv : EuclideanSpace ℝ ι ≃ᵐ (ι → ℝ)
   measurable_to_fun := measurable_id
   measurable_inv_fun := measurable_id
 #align euclidean_space.measurable_equiv EuclideanSpace.measurableEquiv
+-/
 
+#print EuclideanSpace.coe_measurableEquiv /-
 theorem coe_measurableEquiv : ⇑(EuclideanSpace.measurableEquiv ι) = PiLp.equiv 2 _ :=
   rfl
 #align euclidean_space.coe_measurable_equiv EuclideanSpace.coe_measurableEquiv
+-/
 
 end EuclideanSpace
 

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

@@ -252,9 +252,9 @@ irreducible_def Basis.addHaar (b : Basis ι ℝ E) : Measure E :=
   Measure.addHaarMeasure b.parallelepiped
 #align basis.add_haar Basis.addHaar
 
-instance isAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure b.addHaar := by
+instance addHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : AddHaarMeasure b.addHaar := by
   rw [Basis.addHaar]; exact measure.is_add_haar_measure_add_haar_measure _
-#align is_add_haar_measure_basis_add_haar isAddHaarMeasure_basis_addHaar
+#align is_add_haar_measure_basis_add_haar addHaarMeasure_basis_addHaar
 
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact add_haar_measure_self

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

@@ -33,7 +33,7 @@ of the basis).
 
 open Set TopologicalSpace MeasureTheory MeasureTheory.Measure FiniteDimensional
 
-open BigOperators Pointwise
+open scoped BigOperators Pointwise
 
 noncomputable section
 

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

@@ -252,16 +252,12 @@ irreducible_def Basis.addHaar (b : Basis ι ℝ E) : Measure E :=
   Measure.addHaarMeasure b.parallelepiped
 #align basis.add_haar Basis.addHaar
 
-instance isAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure b.addHaar :=
-  by
-  rw [Basis.addHaar]
-  exact measure.is_add_haar_measure_add_haar_measure _
+instance isAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure b.addHaar := by
+  rw [Basis.addHaar]; exact measure.is_add_haar_measure_add_haar_measure _
 #align is_add_haar_measure_basis_add_haar isAddHaarMeasure_basis_addHaar
 
-theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 :=
-  by
-  rw [Basis.addHaar]
-  exact add_haar_measure_self
+theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
+  rw [Basis.addHaar]; exact add_haar_measure_self
 #align basis.add_haar_self Basis.addHaar_self
 
 end NormedSpace

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

@@ -3,12 +3,12 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
-! This file was ported from Lean 3 source module measure_theory.measure.haar_of_basis
-! leanprover-community/mathlib commit 4b884eff88bf72d32496b0bc7cc0bfccce77f2fa
+! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
+! 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.MeasureTheory.Measure.Haar
+import Mathbin.MeasureTheory.Measure.Haar.Basic
 import Mathbin.Analysis.InnerProductSpace.PiL2
 
 /-!

@@ -22,7 +22,7 @@ nonempty interior.
 * `Basis.addHaar` is the Lebesgue measure associated to a basis, giving measure `1` to the
 corresponding parallelepiped.
 
-In particular, we declare a `measure_space` instance on any finite-dimensional inner product space,
+In particular, we declare a `MeasureSpace` instance on any finite-dimensional inner product space,
 by using the Lebesgue measure associated to some orthonormal basis (which is in fact independent
 of the basis).
 -/
@@ -324,7 +324,7 @@ instance Real.measureSpace : MeasureSpace ℝ := by infer_instance
 
 /-! # Miscellaneous instances for `EuclideanSpace`
 
-In combination with `measureSpaceOfInnerProductSpace`, these put a `measure_space` structure
+In combination with `measureSpaceOfInnerProductSpace`, these put a `MeasureSpace` structure
 on `EuclideanSpace`. -/
 
 

Prove that the fundamental domain of a ℤ-lattice is almost equal to the corresponding parallelepiped. This is useful because many results in measure theory use the parallelepiped associated to a basis.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -54,6 +54,16 @@ theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
   simp [parallelepiped, eq_comm]
 #align mem_parallelepiped_iff mem_parallelepiped_iff
 
+theorem parallelepiped_basis_eq (b : Basis ι ℝ E) :
+    parallelepiped b = {x | ∀ i, b.repr x i ∈ Set.Icc 0 1} := by
+  classical
+  ext x
+  simp_rw [mem_parallelepiped_iff, mem_setOf_eq, b.ext_elem_iff, _root_.map_sum,
+    _root_.map_smul, Finset.sum_apply', Basis.repr_self, Finsupp.smul_single, smul_eq_mul,
+    mul_one, Finsupp.single_apply, Finset.sum_ite_eq', Finset.mem_univ, ite_true, mem_Icc,
+    Pi.le_def, Pi.zero_apply, Pi.one_apply, ← forall_and]
+  aesop
+
 theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
     f '' parallelepiped v = parallelepiped (f ∘ v) := by
   simp only [parallelepiped, ← image_comp]

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -168,7 +168,7 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
       rcases eq_or_ne (a i) 0 with hai | hai
       · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
         rw [hai, ← h, zero_div, zero_mul]
-      · rw [div_mul_cancel _ hai]
+      · rw [div_mul_cancel₀ _ hai]
 #align parallelepiped_single parallelepiped_single
 
 end AddCommGroup

Also rename *lpBcf to *lpBCF and drop 2 duplicate instances.

@@ -34,7 +34,11 @@ open scoped BigOperators Pointwise
 
 noncomputable section
 
-variable {ι ι' E F : Type*} [Fintype ι] [Fintype ι']
+variable {ι ι' E F : Type*}
+
+section Fintype
+
+variable [Fintype ι] [Fintype ι']
 
 section AddCommGroup
 
@@ -288,6 +292,8 @@ theorem Basis.prod_addHaar (v : Basis ι ℝ E) (w : Basis ι' ℝ F) :
 
 end NormedSpace
 
+end Fintype
+
 /-- A finite dimensional inner product space has a canonical measure, the Lebesgue measure giving
 volume `1` to the parallelepiped spanned by any orthonormal basis. We define the measure using
 some arbitrary choice of orthonormal basis. The fact that it works with any orthonormal basis
@@ -319,7 +325,7 @@ variable (ι)
 -- TODO: do we want these instances for `PiLp` too?
 instance : MeasurableSpace (EuclideanSpace ℝ ι) := MeasurableSpace.pi
 
-instance : BorelSpace (EuclideanSpace ℝ ι) := Pi.borelSpace
+instance [Finite ι] : BorelSpace (EuclideanSpace ℝ ι) := Pi.borelSpace
 
 /-- `WithLp.equiv` as a `MeasurableEquiv`. -/
 @[simps toEquiv]

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -66,7 +66,7 @@ theorem parallelepiped_comp_equiv (v : ι → E) (e : ι' ≃ ι) :
   have : Icc (0 : ι → ℝ) 1 = K '' Icc (0 : ι' → ℝ) 1 := by
     rw [← Equiv.preimage_eq_iff_eq_image]
     ext x
-    simp only [mem_preimage, mem_Icc, Pi.le_def, Pi.zero_apply, Equiv.piCongrLeft'_apply,
+    simp only [K, mem_preimage, mem_Icc, Pi.le_def, Pi.zero_apply, Equiv.piCongrLeft'_apply,
       Pi.one_apply]
     refine'
       ⟨fun h => ⟨fun i => _, fun i => _⟩, fun h =>
@@ -77,7 +77,7 @@ theorem parallelepiped_comp_equiv (v : ι → E) (e : ι' ≃ ι) :
   congr 1 with x
   have := fun z : ι' → ℝ => e.symm.sum_comp fun i => z i • v (e i)
   simp_rw [Equiv.apply_symm_apply] at this
-  simp_rw [Function.comp_apply, mem_image, mem_Icc, Equiv.piCongrLeft'_apply, this]
+  simp_rw [Function.comp_apply, mem_image, mem_Icc, K, Equiv.piCongrLeft'_apply, this]
 #align parallelepiped_comp_equiv parallelepiped_comp_equiv
 
 -- The parallelepiped associated to an orthonormal basis of `ℝ` is either `[0, 1]` or `[-1, 0]`.
@@ -107,7 +107,7 @@ theorem parallelepiped_orthonormalBasis_one_dim (b : OrthonormalBasis ι ℝ ℝ
       ← image_comp, Function.comp_apply, image_id', ge_iff_le, zero_le_one, not_true, gt_iff_lt]
   · right
     simp_rw [H, parallelepiped, Algebra.id.smul_eq_mul, A]
-    simp only [Finset.univ_unique, Fin.default_eq_zero, mul_neg, mul_one, Finset.sum_neg_distrib,
+    simp only [F, Finset.univ_unique, Fin.default_eq_zero, mul_neg, mul_one, Finset.sum_neg_distrib,
       Finset.sum_singleton, ← image_comp, Function.comp, image_neg, preimage_neg_Icc, neg_zero]
 #align parallelepiped_orthonormal_basis_one_dim parallelepiped_orthonormalBasis_one_dim
 
@@ -214,6 +214,7 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
   PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
 #align basis.parallelepiped_map Basis.parallelepiped_map
 
+set_option tactic.skipAssignedInstances false in
 theorem Basis.prod_parallelepiped (v : Basis ι ℝ E) (w : Basis ι' ℝ F) :
     (v.prod w).parallelepiped = v.parallelepiped.prod w.parallelepiped := by
   ext x

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -180,8 +180,8 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E where
       (continuous_finset_sum Finset.univ fun (i : ι) (_H : i ∈ Finset.univ) =>
         (continuous_apply i).smul continuous_const)
   interior_nonempty' := by
-    suffices H : Set.Nonempty (interior (b.equivFunL.symm.toHomeomorph '' Icc 0 1))
-    · dsimp only [_root_.parallelepiped]
+    suffices H : Set.Nonempty (interior (b.equivFunL.symm.toHomeomorph '' Icc 0 1)) by
+      dsimp only [_root_.parallelepiped]
       convert H
       exact (b.equivFun_symm_apply _).symm
     have A : Set.Nonempty (interior (Icc (0 : ι → ℝ) 1)) := by

@@ -214,6 +214,36 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
   PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
 #align basis.parallelepiped_map Basis.parallelepiped_map
 
+theorem Basis.prod_parallelepiped (v : Basis ι ℝ E) (w : Basis ι' ℝ F) :
+    (v.prod w).parallelepiped = v.parallelepiped.prod w.parallelepiped := by
+  ext x
+  simp only [Basis.coe_parallelepiped, TopologicalSpace.PositiveCompacts.coe_prod, Set.mem_prod,
+    mem_parallelepiped_iff]
+  constructor
+  · intro h
+    rcases h with ⟨t, ht1, ht2⟩
+    constructor
+    · use t ∘ Sum.inl
+      constructor
+      · exact ⟨(ht1.1 <| Sum.inl ·), (ht1.2 <| Sum.inl ·)⟩
+      simp [ht2, Prod.fst_sum, Prod.snd_sum]
+    · use t ∘ Sum.inr
+      constructor
+      · exact ⟨(ht1.1 <| Sum.inr ·), (ht1.2 <| Sum.inr ·)⟩
+      simp [ht2, Prod.fst_sum, Prod.snd_sum]
+  intro h
+  rcases h with ⟨⟨t, ht1, ht2⟩, ⟨s, hs1, hs2⟩⟩
+  use Sum.elim t s
+  constructor
+  · constructor
+    · change ∀ x : ι ⊕ ι', 0 ≤ Sum.elim t s x
+      aesop
+    · change ∀ x : ι ⊕ ι', Sum.elim t s x ≤ 1
+      aesop
+  ext
+  · simp [ht2, Prod.fst_sum]
+  · simp [hs2, Prod.snd_sum]
+
 variable [MeasurableSpace E] [BorelSpace E]
 
 /-- The Lebesgue measure associated to a basis, giving measure `1` to the parallelepiped spanned
@@ -226,8 +256,8 @@ instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure
   rw [Basis.addHaar]; exact Measure.isAddHaarMeasure_addHaarMeasure _
 #align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 
-instance [SecondCountableTopology E] (b : Basis ι ℝ E) :
-    SigmaFinite b.addHaar := by
+instance (b : Basis ι ℝ E) : SigmaFinite b.addHaar := by
+  have : FiniteDimensional ℝ E := FiniteDimensional.of_fintype_basis b
   rw [Basis.addHaar_def]; exact sigmaFinite_addHaarMeasure
 
 /-- Let `μ` be a σ-finite left invariant measure on `E`. Then `μ` is equal to the Haar measure
@@ -247,6 +277,14 @@ theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (_root_.parallelepip
   rw [Basis.addHaar]; exact addHaarMeasure_self
 #align basis.add_haar_self Basis.addHaar_self
 
+variable [MeasurableSpace F] [BorelSpace F] [SecondCountableTopologyEither E F]
+
+theorem Basis.prod_addHaar (v : Basis ι ℝ E) (w : Basis ι' ℝ F) :
+    (v.prod w).addHaar = v.addHaar.prod w.addHaar := by
+  have : FiniteDimensional ℝ E := FiniteDimensional.of_fintype_basis v
+  have : FiniteDimensional ℝ F := FiniteDimensional.of_fintype_basis w
+  simp [(v.prod w).addHaar_eq_iff, Basis.prod_parallelepiped, Basis.addHaar_self]
+
 end NormedSpace
 
 /-- A finite dimensional inner product space has a canonical measure, the Lebesgue measure giving

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -188,7 +188,7 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E where
       rw [← pi_univ_Icc, interior_pi_set (@finite_univ ι _)]
       simp only [univ_pi_nonempty_iff, Pi.zero_apply, Pi.one_apply, interior_Icc, nonempty_Ioo,
         zero_lt_one, imp_true_iff]
-    rwa [← Homeomorph.image_interior, nonempty_image_iff]
+    rwa [← Homeomorph.image_interior, image_nonempty]
 #align basis.parallelepiped Basis.parallelepiped
 
 @[simp]

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -46,7 +46,7 @@ def parallelepiped (v : ι → E) : Set E :=
 #align parallelepiped parallelepiped
 
 theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
-    x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ) (_ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
+    x ∈ parallelepiped v ↔ ∃ t ∈ Icc (0 : ι → ℝ) 1, x = ∑ i, t i • v i := by
   simp [parallelepiped, eq_comm]
 #align mem_parallelepiped_iff mem_parallelepiped_iff
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -146,7 +146,7 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
   · rintro ⟨t, ht, rfl⟩ i
     specialize ht i
     simp_rw [smul_eq_mul, Pi.mul_apply]
-    cases' le_total (a i) 0 with hai hai
+    rcases le_total (a i) 0 with hai | hai
     · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai]
       exact ⟨le_mul_of_le_one_left hai ht.2, mul_nonpos_of_nonneg_of_nonpos ht.1 hai⟩
     · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai]
@@ -154,14 +154,14 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
   · intro h
     refine' ⟨fun i => x i / a i, fun i => _, funext fun i => _⟩
     · specialize h i
-      cases' le_total (a i) 0 with hai hai
+      rcases le_total (a i) 0 with hai | hai
       · rw [sup_eq_left.mpr hai, inf_eq_right.mpr hai] at h
         exact ⟨div_nonneg_of_nonpos h.2 hai, div_le_one_of_ge h.1 hai⟩
       · rw [sup_eq_right.mpr hai, inf_eq_left.mpr hai] at h
         exact ⟨div_nonneg h.1 hai, div_le_one_of_le h.2 hai⟩
     · specialize h i
       simp only [smul_eq_mul, Pi.mul_apply]
-      cases' eq_or_ne (a i) 0 with hai hai
+      rcases eq_or_ne (a i) 0 with hai | hai
       · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
         rw [hai, ← h, zero_div, zero_mul]
       · rw [div_mul_cancel _ hai]

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -207,11 +207,10 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
     (b.map e).parallelepiped = b.parallelepiped.map e
     (have := FiniteDimensional.of_fintype_basis b
     -- Porting note: Lean cannot infer the instance above
-    @LinearMap.continuous_of_finiteDimensional _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this (e.toLinearMap))
+    LinearMap.continuous_of_finiteDimensional e.toLinearMap)
     (have := FiniteDimensional.of_fintype_basis (b.map e)
     -- Porting note: Lean cannot infer the instance above
-    @LinearMap.isOpenMap_of_finiteDimensional _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this _
-      e.surjective) :=
+    LinearMap.isOpenMap_of_finiteDimensional _ e.surjective) :=
   PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
 #align basis.parallelepiped_map Basis.parallelepiped_map
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -54,7 +54,7 @@ theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
     f '' parallelepiped v = parallelepiped (f ∘ v) := by
   simp only [parallelepiped, ← image_comp]
   congr 1 with t
-  simp only [Function.comp_apply, map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
+  simp only [Function.comp_apply, _root_.map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
 #align image_parallelepiped image_parallelepiped
 
 /-- Reindexing a family of vectors does not change their parallelepiped. -/

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -193,7 +193,7 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E where
 
 @[simp]
 theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
-   (b.parallelepiped : Set E) = _root_.parallelepiped b := rfl
+    (b.parallelepiped : Set E) = _root_.parallelepiped b := rfl
 #align basis.coe_parallelepiped Basis.coe_parallelepiped
 
 @[simp]

Also _root_.map_smul when in the neighbourhood.

@@ -54,7 +54,7 @@ theorem image_parallelepiped (f : E →ₗ[ℝ] F) (v : ι → E) :
     f '' parallelepiped v = parallelepiped (f ∘ v) := by
   simp only [parallelepiped, ← image_comp]
   congr 1 with t
-  simp only [Function.comp_apply, LinearMap.map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
+  simp only [Function.comp_apply, map_sum, LinearMap.map_smulₛₗ, RingHom.id_apply]
 #align image_parallelepiped image_parallelepiped
 
 /-- Reindexing a family of vectors does not change their parallelepiped. -/

We prove that the two MeasureSpace structures on $\mathbb{R}^\iota$, the one coming from its identification with ι→ ℝ and the one coming from EuclideanSpace ℝ ι, agree in the sense that the measure equivalence between the two corresponding volumes is measure preserving.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -294,4 +294,7 @@ protected def measurableEquiv : EuclideanSpace ℝ ι ≃ᵐ (ι → ℝ) where
 theorem coe_measurableEquiv : ⇑(EuclideanSpace.measurableEquiv ι) = WithLp.equiv 2 _ := rfl
 #align euclidean_space.coe_measurable_equiv EuclideanSpace.coe_measurableEquiv
 
+theorem coe_measurableEquiv_symm :
+    ⇑(EuclideanSpace.measurableEquiv ι).symm = (WithLp.equiv 2 _).symm := rfl
+
 end EuclideanSpace

A linter that throws on seeing a colon at the start of a line, according to the style guideline that says these operators should go before linebreaks.

@@ -210,8 +210,9 @@ theorem Basis.parallelepiped_map (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) :
     @LinearMap.continuous_of_finiteDimensional _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this (e.toLinearMap))
     (have := FiniteDimensional.of_fintype_basis (b.map e)
     -- Porting note: Lean cannot infer the instance above
-    @LinearMap.isOpenMap_of_finiteDimensional _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this _ e.surjective)
-    := PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
+    @LinearMap.isOpenMap_of_finiteDimensional _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this _
+      e.surjective) :=
+  PositiveCompacts.ext (image_parallelepiped e.toLinearMap _).symm
 #align basis.parallelepiped_map Basis.parallelepiped_map
 
 variable [MeasurableSpace E] [BorelSpace E]

We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:

theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
     b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1

theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
     b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
       b.equivFunL.symm.continuous

theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
    map f b.addHaar = (b.map f.toLinearEquiv).addHaar

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -226,6 +226,23 @@ instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure
   rw [Basis.addHaar]; exact Measure.isAddHaarMeasure_addHaarMeasure _
 #align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 
+instance [SecondCountableTopology E] (b : Basis ι ℝ E) :
+    SigmaFinite b.addHaar := by
+  rw [Basis.addHaar_def]; exact sigmaFinite_addHaarMeasure
+
+/-- Let `μ` be a σ-finite left invariant measure on `E`. Then `μ` is equal to the Haar measure
+defined by `b` iff the parallelepiped defined by `b` has measure `1` for `μ`. -/
+theorem Basis.addHaar_eq_iff [SecondCountableTopology E] (b : Basis ι ℝ E) (μ : Measure E)
+    [SigmaFinite μ] [IsAddLeftInvariant μ] :
+    b.addHaar = μ ↔ μ b.parallelepiped = 1 := by
+  rw [Basis.addHaar_def]
+  exact addHaarMeasure_eq_iff b.parallelepiped μ
+
+@[simp]
+theorem Basis.addHaar_reindex (b : Basis ι ℝ E) (e : ι ≃ ι') :
+    (b.reindex e).addHaar = b.addHaar := by
+  rw [Basis.addHaar, b.parallelepiped_reindex e, ← Basis.addHaar]
+
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (_root_.parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact addHaarMeasure_self
 #align basis.add_haar_self Basis.addHaar_self

This removes the (PiLp.equiv 2 fun i => α i) abbreviation, replacing it with its implementation (WithLp.equiv 2 (∀ i, α i)). The same thing is done for PiLp.linearEquiv.

@@ -265,15 +265,15 @@ instance : MeasurableSpace (EuclideanSpace ℝ ι) := MeasurableSpace.pi
 
 instance : BorelSpace (EuclideanSpace ℝ ι) := Pi.borelSpace
 
-/-- `PiLp.equiv` as a `MeasurableEquiv`. -/
+/-- `WithLp.equiv` as a `MeasurableEquiv`. -/
 @[simps toEquiv]
 protected def measurableEquiv : EuclideanSpace ℝ ι ≃ᵐ (ι → ℝ) where
-  toEquiv := PiLp.equiv _ _
+  toEquiv := WithLp.equiv _ _
   measurable_toFun := measurable_id
   measurable_invFun := measurable_id
 #align euclidean_space.measurable_equiv EuclideanSpace.measurableEquiv
 
-theorem coe_measurableEquiv : ⇑(EuclideanSpace.measurableEquiv ι) = PiLp.equiv 2 _ := rfl
+theorem coe_measurableEquiv : ⇑(EuclideanSpace.measurableEquiv ι) = WithLp.equiv 2 _ := rfl
 #align euclidean_space.coe_measurable_equiv EuclideanSpace.coe_measurableEquiv
 
 end EuclideanSpace

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -163,7 +163,7 @@ theorem parallelepiped_single [DecidableEq ι] (a : ι → ℝ) :
       simp only [smul_eq_mul, Pi.mul_apply]
       cases' eq_or_ne (a i) 0 with hai hai
       · rw [hai, inf_idem, sup_idem, ← le_antisymm_iff] at h
-        rw [hai, ← h, zero_div, MulZeroClass.zero_mul]
+        rw [hai, ← h, zero_div, zero_mul]
       · rw [div_mul_cancel _ hai]
 #align parallelepiped_single parallelepiped_single
 

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -77,8 +77,7 @@ theorem parallelepiped_comp_equiv (v : ι → E) (e : ι' ≃ ι) :
   congr 1 with x
   have := fun z : ι' → ℝ => e.symm.sum_comp fun i => z i • v (e i)
   simp_rw [Equiv.apply_symm_apply] at this
-  simp_rw [Function.comp_apply, ge_iff_le, zero_le_one, not_true, gt_iff_lt, mem_image, mem_Icc,
-    Equiv.piCongrLeft'_apply, this]
+  simp_rw [Function.comp_apply, mem_image, mem_Icc, Equiv.piCongrLeft'_apply, this]
 #align parallelepiped_comp_equiv parallelepiped_comp_equiv
 
 -- The parallelepiped associated to an orthonormal basis of `ℝ` is either `[0, 1]` or `[-1, 0]`.
@@ -107,7 +106,7 @@ theorem parallelepiped_orthonormalBasis_one_dim (b : OrthonormalBasis ι ℝ ℝ
     simp only [Finset.univ_unique, Fin.default_eq_zero, smul_eq_mul, mul_one, Finset.sum_singleton,
       ← image_comp, Function.comp_apply, image_id', ge_iff_le, zero_le_one, not_true, gt_iff_lt]
   · right
-    simp_rw [H, parallelepiped, Algebra.id.smul_eq_mul, mul_one, A]
+    simp_rw [H, parallelepiped, Algebra.id.smul_eq_mul, A]
     simp only [Finset.univ_unique, Fin.default_eq_zero, mul_neg, mul_one, Finset.sum_neg_distrib,
       Finset.sum_singleton, ← image_comp, Function.comp, image_neg, preimage_neg_Icc, neg_zero]
 #align parallelepiped_orthonormal_basis_one_dim parallelepiped_orthonormalBasis_one_dim

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

This has nice performance benefits.

@@ -34,7 +34,7 @@ open scoped BigOperators Pointwise
 
 noncomputable section
 
-variable {ι ι' E F : Type _} [Fintype ι] [Fintype ι']
+variable {ι ι' E F : Type*} [Fintype ι] [Fintype ι']
 
 section AddCommGroup
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
-! leanprover-community/mathlib commit 92bd7b1ffeb306a89f450bee126ddd8a284c259d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.Haar.Basic
 import Mathlib.Analysis.InnerProductSpace.PiL2
 
+#align_import measure_theory.measure.haar.of_basis from "leanprover-community/mathlib"@"92bd7b1ffeb306a89f450bee126ddd8a284c259d"
+
 /-!
 # Additive Haar measure constructed from a basis
 

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.measure.haar.of_basis
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 92bd7b1ffeb306a89f450bee126ddd8a284c259d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -130,24 +130,13 @@ theorem parallelepiped_eq_sum_segment (v : ι → E) : parallelepiped v = ∑ i,
 
 theorem convex_parallelepiped (v : ι → E) : Convex ℝ (parallelepiped v) := by
   rw [parallelepiped_eq_sum_segment]
-  -- TODO: add `convex.sum` to match `Convex.add`
-  let A : AddSubmonoid (Set E) :=
-    { carrier := { s | Convex ℝ s }
-      zero_mem' := convex_singleton _
-      add_mem' := Convex.add }
-  refine A.sum_mem (fun i _hi => convex_segment _ _)
+  exact convex_sum _ fun _i _hi => convex_segment _ _
 #align convex_parallelepiped convex_parallelepiped
 
 /-- A `parallelepiped` is the convex hull of its vertices -/
 theorem parallelepiped_eq_convexHull (v : ι → E) :
     parallelepiped v = convexHull ℝ (∑ i, {(0 : E), v i}) := by
-  -- TODO: add `convex_hull_sum` to match `convexHull_add`
-  let A : Set E →+ Set E :=
-    { toFun := convexHull ℝ
-      map_zero' := convexHull_singleton _
-      map_add' := convexHull_add }
-  simp_rw [parallelepiped_eq_sum_segment, ← convexHull_pair]
-  exact (A.map_sum _ _).symm
+  simp_rw [convexHull_sum, convexHull_pair, parallelepiped_eq_sum_segment]
 #align parallelepiped_eq_convex_hull parallelepiped_eq_convexHull
 
 /-- The axis aligned parallelepiped over `ι → ℝ` is a cuboid. -/

@@ -206,11 +206,10 @@ def Basis.parallelepiped (b : Basis ι ℝ E) : PositiveCompacts E where
     rwa [← Homeomorph.image_interior, nonempty_image_iff]
 #align basis.parallelepiped Basis.parallelepiped
 
--- Porting note: lint complains that this result is a tautology and thus unnecessary
--- @[simp]
--- theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
---    (b.parallelepiped : Set E) = parallelepiped b := rfl
--- #align basis.coe_parallelepiped Basis.coe_parallelepiped
+@[simp]
+theorem Basis.coe_parallelepiped (b : Basis ι ℝ E) :
+   (b.parallelepiped : Set E) = _root_.parallelepiped b := rfl
+#align basis.coe_parallelepiped Basis.coe_parallelepiped
 
 @[simp]
 theorem Basis.parallelepiped_reindex (b : Basis ι ℝ E) (e : ι ≃ ι') :
@@ -242,7 +241,7 @@ instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure
   rw [Basis.addHaar]; exact Measure.isAddHaarMeasure_addHaarMeasure _
 #align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 
-theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
+theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (_root_.parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact addHaarMeasure_self
 #align basis.add_haar_self Basis.addHaar_self
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -49,7 +49,7 @@ def parallelepiped (v : ι → E) : Set E :=
 #align parallelepiped parallelepiped
 
 theorem mem_parallelepiped_iff (v : ι → E) (x : E) :
-    x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ)(_ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
+    x ∈ parallelepiped v ↔ ∃ (t : ι → ℝ) (_ht : t ∈ Icc (0 : ι → ℝ) 1), x = ∑ i, t i • v i := by
   simp [parallelepiped, eq_comm]
 #align mem_parallelepiped_iff mem_parallelepiped_iff
 

@@ -257,7 +257,7 @@ instance (priority := 100) measureSpaceOfInnerProductSpace [NormedAddCommGroup E
     MeasureSpace E where volume := (stdOrthonormalBasis ℝ E).toBasis.addHaar
 #align measure_space_of_inner_product_space measureSpaceOfInnerProductSpace
 
-instance IsAddHaarMeasure [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
+instance [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
     [MeasurableSpace E] [BorelSpace E] : IsAddHaarMeasure (volume : Measure E) :=
   IsAddHaarMeasure_basis_addHaar _
 

Lean 3 was able to apply, e.g., instances about measure_theory.measure.prod to the volume on the Cartesian product. Lean 4 can't do this, so we need to duplicate many instances.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp>

@@ -257,6 +257,10 @@ instance (priority := 100) measureSpaceOfInnerProductSpace [NormedAddCommGroup E
     MeasureSpace E where volume := (stdOrthonormalBasis ℝ E).toBasis.addHaar
 #align measure_space_of_inner_product_space measureSpaceOfInnerProductSpace
 
+instance IsAddHaarMeasure [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
+    [MeasurableSpace E] [BorelSpace E] : IsAddHaarMeasure (volume : Measure E) :=
+  IsAddHaarMeasure_basis_addHaar _
+
 /- This instance should not be necessary, but Lean has difficulties to find it in product
 situations if we do not declare it explicitly. -/
 instance Real.measureSpace : MeasureSpace ℝ := by infer_instance

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -238,10 +238,9 @@ irreducible_def Basis.addHaar (b : Basis ι ℝ E) : Measure E :=
   Measure.addHaarMeasure b.parallelepiped
 #align basis.add_haar Basis.addHaar
 
--- Porting note: `is_add_haar_measure` is now called `AddHaarMeasure` in Mathlib4
-instance AddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : AddHaarMeasure b.addHaar := by
-  rw [Basis.addHaar]; exact Measure.addHaarMeasure_addHaarMeasure _
-#align is_add_haar_measure_basis_add_haar AddHaarMeasure_basis_addHaar
+instance IsAddHaarMeasure_basis_addHaar (b : Basis ι ℝ E) : IsAddHaarMeasure b.addHaar := by
+  rw [Basis.addHaar]; exact Measure.isAddHaarMeasure_addHaarMeasure _
+#align is_add_haar_measure_basis_add_haar IsAddHaarMeasure_basis_addHaar
 
 theorem Basis.addHaar_self (b : Basis ι ℝ E) : b.addHaar (parallelepiped b) = 1 := by
   rw [Basis.addHaar]; exact addHaarMeasure_self