diff --git a/Mathlib/Algebra/Group/Pointwise/Set/Card.lean b/Mathlib/Algebra/Group/Pointwise/Set/Card.lean index 9472500e7fcc9..404fdd46e25ad 100644 --- a/Mathlib/Algebra/Group/Pointwise/Set/Card.lean +++ b/Mathlib/Algebra/Group/Pointwise/Set/Card.lean @@ -38,7 +38,7 @@ lemma natCard_mul_le : Nat.card (s * t) ≤ Nat.card s * Nat.card t := by end Mul section InvolutiveInv -variable [InvolutiveInv G] {s t : Set G} +variable [InvolutiveInv G] @[to_additive (attr := simp)] lemma _root_.Cardinal.mk_inv (s : Set G) : #↥(s⁻¹) = #s := by diff --git a/Mathlib/Algebra/GroupWithZero/Pointwise/Set/Card.lean b/Mathlib/Algebra/GroupWithZero/Pointwise/Set/Card.lean index 8466c8876f1c1..4e144b113a816 100644 --- a/Mathlib/Algebra/GroupWithZero/Pointwise/Set/Card.lean +++ b/Mathlib/Algebra/GroupWithZero/Pointwise/Set/Card.lean @@ -13,7 +13,7 @@ import Mathlib.SetTheory.Cardinal.Finite open scoped Cardinal Pointwise -variable {G G₀ M M₀ : Type*} +variable {G₀ M₀ : Type*} namespace Set variable [GroupWithZero G₀] [Zero M₀] [MulActionWithZero G₀ M₀] {a : G₀} diff --git a/Mathlib/Algebra/Homology/Additive.lean b/Mathlib/Algebra/Homology/Additive.lean index 5fbebb2c8beb9..1b14c45bf5b00 100644 --- a/Mathlib/Algebra/Homology/Additive.lean +++ b/Mathlib/Algebra/Homology/Additive.lean @@ -23,8 +23,8 @@ variable {ι : Type*} variable {V : Type u} [Category.{v} V] [Preadditive V] variable {W : Type*} [Category W] [Preadditive W] variable {W₁ W₂ : Type*} [Category W₁] [Category W₂] [HasZeroMorphisms W₁] [HasZeroMorphisms W₂] -variable {c : ComplexShape ι} {C D E : HomologicalComplex V c} -variable (f g : C ⟶ D) (h k : D ⟶ E) (i : ι) +variable {c : ComplexShape ι} {C D : HomologicalComplex V c} +variable (f : C ⟶ D) (i : ι) namespace HomologicalComplex diff --git a/Mathlib/Algebra/Quaternion.lean b/Mathlib/Algebra/Quaternion.lean index 69ce497aff36a..1ee91c3592cc2 100644 --- a/Mathlib/Algebra/Quaternion.lean +++ b/Mathlib/Algebra/Quaternion.lean @@ -93,7 +93,7 @@ theorem equivTuple_apply {R : Type*} (c₁ c₂ : R) (x : ℍ[R,c₁,c₂]) : @[simp] theorem mk.eta {R : Type*} {c₁ c₂} (a : ℍ[R,c₁,c₂]) : mk a.1 a.2 a.3 a.4 = a := rfl -variable {S T R : Type*} {c₁ c₂ : R} (r x y z : R) (a b c : ℍ[R,c₁,c₂]) +variable {S T R : Type*} {c₁ c₂ : R} (r x y : R) (a b : ℍ[R,c₁,c₂]) instance [Subsingleton R] : Subsingleton ℍ[R, c₁, c₂] := (equivTuple c₁ c₂).subsingleton instance [Nontrivial R] : Nontrivial ℍ[R, c₁, c₂] := (equivTuple c₁ c₂).surjective.nontrivial @@ -742,7 +742,7 @@ instance {R : Type*} [One R] [Neg R] [Nontrivial R] : Nontrivial ℍ[R] := namespace Quaternion -variable {S T R : Type*} [CommRing R] (r x y z : R) (a b c : ℍ[R]) +variable {S T R : Type*} [CommRing R] (r x y : R) (a b : ℍ[R]) export QuaternionAlgebra (re imI imJ imK) diff --git a/Mathlib/Algebra/TrivSqZeroExt.lean b/Mathlib/Algebra/TrivSqZeroExt.lean index c40ab975c18d7..cc4239ab85e25 100644 --- a/Mathlib/Algebra/TrivSqZeroExt.lean +++ b/Mathlib/Algebra/TrivSqZeroExt.lean @@ -870,10 +870,9 @@ section Algebra variable (S : Type*) (R R' : Type u) (M : Type v) variable [CommSemiring S] [Semiring R] [CommSemiring R'] [AddCommMonoid M] -variable [Algebra S R] [Algebra S R'] [Module S M] -variable [Module R M] [Module Rᵐᵒᵖ M] [SMulCommClass R Rᵐᵒᵖ M] +variable [Algebra S R] [Module S M] [Module R M] [Module Rᵐᵒᵖ M] [SMulCommClass R Rᵐᵒᵖ M] variable [IsScalarTower S R M] [IsScalarTower S Rᵐᵒᵖ M] -variable [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] [IsScalarTower S R' M] +variable [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] instance algebra' : Algebra S (tsze R M) := { (TrivSqZeroExt.inlHom R M).comp (algebraMap S R) with diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean index 51f9c3ccf41d9..070c60d31cc77 100644 --- a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean +++ b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean @@ -142,8 +142,7 @@ instance inf (P Q : MorphismProperty Scheme) [IsLocalAtTarget P] [IsLocalAtTarge fun h ↦ ⟨(iff_of_openCover' f 𝒰).mpr (fun i ↦ (h i).left), (iff_of_openCover' f 𝒰).mpr (fun i ↦ (h i).right)⟩⟩ -variable {P} [hP : IsLocalAtTarget P] -variable {X Y U V : Scheme.{u}} {f : X ⟶ Y} {g : U ⟶ Y} [IsOpenImmersion g] (𝒰 : Y.OpenCover) +variable {P} [hP : IsLocalAtTarget P] {X Y : Scheme.{u}} {f : X ⟶ Y} (𝒰 : Y.OpenCover) lemma of_isPullback {UX UY : Scheme.{u}} {iY : UY ⟶ Y} [IsOpenImmersion iY] {iX : UX ⟶ X} {f' : UX ⟶ UY} (h : IsPullback iX f' f iY) (H : P f) : P f' := by @@ -228,7 +227,7 @@ instance inf (P Q : MorphismProperty Scheme) [IsLocalAtSource P] [IsLocalAtSourc (iff_of_openCover' f 𝒰).mpr (fun i ↦ (h i).right)⟩⟩ variable {P} [IsLocalAtSource P] -variable {X Y U V : Scheme.{u}} {f : X ⟶ Y} {g : U ⟶ Y} [IsOpenImmersion g] (𝒰 : X.OpenCover) +variable {X Y : Scheme.{u}} {f : X ⟶ Y} (𝒰 : X.OpenCover) lemma comp {UX : Scheme.{u}} (H : P f) (i : UX ⟶ X) [IsOpenImmersion i] : P (i ≫ f) := diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Etale.lean b/Mathlib/AlgebraicGeometry/Morphisms/Etale.lean index 665513b4b09cb..35ee3280f7055 100644 --- a/Mathlib/AlgebraicGeometry/Morphisms/Etale.lean +++ b/Mathlib/AlgebraicGeometry/Morphisms/Etale.lean @@ -28,7 +28,7 @@ abbrev IsEtale {X Y : Scheme.{u}} (f : X ⟶ Y) := IsSmoothOfRelativeDimension 0 namespace IsEtale -variable {X Y : Scheme.{u}} (f : X ⟶ Y) +variable {X : Scheme.{u}} instance : IsStableUnderBaseChange @IsEtale := isSmoothOfRelativeDimension_isStableUnderBaseChange 0 diff --git a/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean b/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean index 880a1a62832f1..6cd62e8973f1b 100644 --- a/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean +++ b/Mathlib/AlgebraicGeometry/Morphisms/OpenImmersion.lean @@ -26,7 +26,7 @@ universe u namespace AlgebraicGeometry -variable {X Y Z : Scheme.{u}} (f : X ⟶ Y) (g : Y ⟶ Z) +variable {X Y : Scheme.{u}} theorem isOpenImmersion_iff_stalk {f : X ⟶ Y} : IsOpenImmersion f ↔ IsOpenEmbedding f.base ∧ ∀ x, IsIso (f.stalkMap x) := by diff --git a/Mathlib/AlgebraicGeometry/SpreadingOut.lean b/Mathlib/AlgebraicGeometry/SpreadingOut.lean index b5d7ef83b97b8..a327e1ae7ee02 100644 --- a/Mathlib/AlgebraicGeometry/SpreadingOut.lean +++ b/Mathlib/AlgebraicGeometry/SpreadingOut.lean @@ -49,8 +49,7 @@ open CategoryTheory namespace AlgebraicGeometry -variable {X Y S : Scheme.{u}} (f : X ⟶ Y) (sX : X ⟶ S) (sY : Y ⟶ S) (e : f ≫ sY = sX) -variable {R A : CommRingCat.{u}} +variable {X Y S : Scheme.{u}} (f : X ⟶ Y) (sX : X ⟶ S) (sY : Y ⟶ S) {R A : CommRingCat.{u}} /-- The germ map at `x` is injective if there exists some affine `U ∋ x` such that the map `Γ(X, U) ⟶ X_x` is injective -/ diff --git a/Mathlib/Analysis/Convex/Gauge.lean b/Mathlib/Analysis/Convex/Gauge.lean index 5ecb5e8b2c4cd..f9d037d23877a 100644 --- a/Mathlib/Analysis/Convex/Gauge.lean +++ b/Mathlib/Analysis/Convex/Gauge.lean @@ -41,7 +41,7 @@ open scoped Pointwise Topology NNReal noncomputable section -variable {𝕜 E F : Type*} +variable {𝕜 E : Type*} section AddCommGroup diff --git a/Mathlib/Analysis/Convex/Normed.lean b/Mathlib/Analysis/Convex/Normed.lean index fae3e58b55f18..9a305c1457de0 100644 --- a/Mathlib/Analysis/Convex/Normed.lean +++ b/Mathlib/Analysis/Convex/Normed.lean @@ -25,14 +25,14 @@ We prove the following facts: is bounded. -/ -variable {ι : Type*} {E P : Type*} +variable {E P : Type*} open AffineBasis Module Metric Set open scoped Convex Pointwise Topology section SeminormedAddCommGroup variable [SeminormedAddCommGroup E] [NormedSpace ℝ E] [PseudoMetricSpace P] [NormedAddTorsor E P] -variable {s t : Set E} +variable {s : Set E} /-- The norm on a real normed space is convex on any convex set. See also `Seminorm.convexOn` and `convexOn_univ_norm`. -/ diff --git a/Mathlib/Analysis/InnerProductSpace/Basic.lean b/Mathlib/Analysis/InnerProductSpace/Basic.lean index 2f715eb17ed19..6f06b27cb078c 100644 --- a/Mathlib/Analysis/InnerProductSpace/Basic.lean +++ b/Mathlib/Analysis/InnerProductSpace/Basic.lean @@ -1600,9 +1600,7 @@ end ContinuousLinearMap section -variable {ι : Type*} {ι' : Type*} {ι'' : Type*} -variable {E' : Type*} [SeminormedAddCommGroup E'] [InnerProductSpace 𝕜 E'] -variable {E'' : Type*} [SeminormedAddCommGroup E''] [InnerProductSpace 𝕜 E''] +variable {ι : Type*} {ι' : Type*} {E' : Type*} [SeminormedAddCommGroup E'] [InnerProductSpace 𝕜 E'] @[simp] theorem Orthonormal.equiv_refl {v : Basis ι 𝕜 E} (hv : Orthonormal 𝕜 v) : @@ -1683,7 +1681,7 @@ open scoped InnerProductSpace variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] variable [NormedAddCommGroup F] [InnerProductSpace ℝ F] -variable {ι : Type*} {ι' : Type*} {ι'' : Type*} +variable {ι : Type*} local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y @@ -2188,9 +2186,7 @@ local notation "IK" => @RCLike.I 𝕜 _ local postfix:90 "†" => starRingEnd _ -variable {ι : Type*} -variable {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)] - {V : ∀ i, G i →ₗᵢ[𝕜] E} (hV : OrthogonalFamily 𝕜 G V) [dec_V : ∀ (i) (x : G i), Decidable (x ≠ 0)] +variable {ι : Type*} {G : ι → Type*} /-- An orthogonal family forms an independent family of subspaces; that is, any collection of elements each from a different subspace in the family is linearly independent. In particular, the diff --git a/Mathlib/Analysis/Normed/Field/Basic.lean b/Mathlib/Analysis/Normed/Field/Basic.lean index eb3c22b61051f..00424d49f8973 100644 --- a/Mathlib/Analysis/Normed/Field/Basic.lean +++ b/Mathlib/Analysis/Normed/Field/Basic.lean @@ -955,7 +955,7 @@ theorem NormedAddCommGroup.tendsto_atTop' [Nonempty α] [Preorder α] [IsDirecte section RingHomIsometric -variable {R₁ : Type*} {R₂ : Type*} {R₃ : Type*} +variable {R₁ R₂ : Type*} /-- This class states that a ring homomorphism is isometric. This is a sufficient assumption for a continuous semilinear map to be bounded and this is the main use for this typeclass. -/ @@ -965,7 +965,7 @@ class RingHomIsometric [Semiring R₁] [Semiring R₂] [Norm R₁] [Norm R₂] ( attribute [simp] RingHomIsometric.is_iso -variable [SeminormedRing R₁] [SeminormedRing R₂] [SeminormedRing R₃] +variable [SeminormedRing R₁] instance RingHomIsometric.ids : RingHomIsometric (RingHom.id R₁) := ⟨rfl⟩ diff --git a/Mathlib/Analysis/Normed/Group/Basic.lean b/Mathlib/Analysis/Normed/Group/Basic.lean index 91cdbe19d79a5..dd3bf2a5b2797 100644 --- a/Mathlib/Analysis/Normed/Group/Basic.lean +++ b/Mathlib/Analysis/Normed/Group/Basic.lean @@ -44,7 +44,7 @@ normed group -/ -variable {𝓕 𝕜 α ι κ E F G : Type*} +variable {𝓕 α ι κ E F G : Type*} open Filter Function Metric Bornology @@ -337,7 +337,7 @@ abbrev GroupNorm.toNormedCommGroup [CommGroup E] (f : GroupNorm E) : NormedCommG section SeminormedGroup variable [SeminormedGroup E] [SeminormedGroup F] [SeminormedGroup G] {s : Set E} - {a a₁ a₂ b b₁ b₂ c : E} {r r₁ r₂ : ℝ} + {a a₁ a₂ b c : E} {r r₁ r₂ : ℝ} @[to_additive] theorem dist_eq_norm_div (a b : E) : dist a b = ‖a / b‖ := @@ -1024,7 +1024,7 @@ end Induced section SeminormedCommGroup -variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a a₁ a₂ b b₁ b₂ : E} {r r₁ r₂ : ℝ} +variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a b : E} {r : ℝ} @[to_additive] theorem dist_inv (x y : E) : dist x⁻¹ y = dist x y⁻¹ := by @@ -1290,7 +1290,7 @@ end SeminormedCommGroup section NormedGroup -variable [NormedGroup E] [NormedGroup F] {a b : E} +variable [NormedGroup E] {a b : E} @[to_additive (attr := simp) norm_eq_zero] theorem norm_eq_zero'' : ‖a‖ = 0 ↔ a = 1 := diff --git a/Mathlib/Analysis/Normed/Group/Bounded.lean b/Mathlib/Analysis/Normed/Group/Bounded.lean index bd28a0b52f340..dcebdaec8bfb2 100644 --- a/Mathlib/Analysis/Normed/Group/Bounded.lean +++ b/Mathlib/Analysis/Normed/Group/Bounded.lean @@ -21,11 +21,10 @@ normed group open Filter Metric Bornology open scoped Pointwise Topology -variable {α ι E F G : Type*} +variable {α E F G : Type*} section SeminormedGroup variable [SeminormedGroup E] [SeminormedGroup F] [SeminormedGroup G] {s : Set E} - {a a₁ a₂ b b₁ b₂ : E} {r r₁ r₂ : ℝ} @[to_additive (attr := simp) comap_norm_atTop] lemma comap_norm_atTop' : comap norm atTop = cobounded E := by diff --git a/Mathlib/Analysis/Normed/Group/Uniform.lean b/Mathlib/Analysis/Normed/Group/Uniform.lean index 8f4a7f9f06b4e..73b33458e9210 100644 --- a/Mathlib/Analysis/Normed/Group/Uniform.lean +++ b/Mathlib/Analysis/Normed/Group/Uniform.lean @@ -15,13 +15,13 @@ This file proves lipschitzness of normed group operations and shows that normed groups. -/ -variable {𝓕 α E F : Type*} +variable {𝓕 E F : Type*} open Filter Function Metric Bornology open scoped ENNReal NNReal Uniformity Pointwise Topology section SeminormedGroup -variable [SeminormedGroup E] [SeminormedGroup F] {s : Set E} {a a₁ a₂ b b₁ b₂ : E} {r r₁ r₂ : ℝ} +variable [SeminormedGroup E] [SeminormedGroup F] {s : Set E} {a b : E} {r : ℝ} @[to_additive] instance NormedGroup.to_isometricSMul_right : IsometricSMul Eᵐᵒᵖ E := @@ -177,7 +177,7 @@ end SeminormedGroup section SeminormedCommGroup -variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a a₁ a₂ b b₁ b₂ : E} {r r₁ r₂ : ℝ} +variable [SeminormedCommGroup E] [SeminormedCommGroup F] {a₁ a₂ b₁ b₂ : E} {r₁ r₂ : ℝ} @[to_additive] instance NormedGroup.to_isometricSMul_left : IsometricSMul E E := @@ -239,7 +239,7 @@ theorem edist_mul_mul_le (a₁ a₂ b₁ b₂ : E) : section PseudoEMetricSpace variable {α E : Type*} [SeminormedCommGroup E] [PseudoEMetricSpace α] {K Kf Kg : ℝ≥0} - {f g : α → E} {s : Set α} {x : α} + {f g : α → E} {s : Set α} @[to_additive (attr := simp)] lemma lipschitzWith_inv_iff : LipschitzWith K f⁻¹ ↔ LipschitzWith K f := by simp [LipschitzWith] diff --git a/Mathlib/Analysis/Normed/Module/FiniteDimension.lean b/Mathlib/Analysis/Normed/Module/FiniteDimension.lean index 303247548cea2..789c690f2042f 100644 --- a/Mathlib/Analysis/Normed/Module/FiniteDimension.lean +++ b/Mathlib/Analysis/Normed/Module/FiniteDimension.lean @@ -54,8 +54,7 @@ namespace LinearIsometry open LinearMap -variable {R : Type*} [Semiring R] -variable {F E₁ : Type*} [SeminormedAddCommGroup F] [NormedAddCommGroup E₁] [Module R E₁] +variable {F E₁ : Type*} [SeminormedAddCommGroup F] [NormedAddCommGroup E₁] variable {R₁ : Type*} [Field R₁] [Module R₁ E₁] [Module R₁ F] [FiniteDimensional R₁ E₁] [FiniteDimensional R₁ F] @@ -110,9 +109,7 @@ end AffineIsometry section CompleteField variable {𝕜 : Type u} [NontriviallyNormedField 𝕜] {E : Type v} [NormedAddCommGroup E] - [NormedSpace 𝕜 E] {F : Type w} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {F' : Type x} - [AddCommGroup F'] [Module 𝕜 F'] [TopologicalSpace F'] [TopologicalAddGroup F'] - [ContinuousSMul 𝕜 F'] [CompleteSpace 𝕜] + [NormedSpace 𝕜 E] {F : Type w} [NormedAddCommGroup F] [NormedSpace 𝕜 F] [CompleteSpace 𝕜] section Affine diff --git a/Mathlib/CategoryTheory/Adjunction/Evaluation.lean b/Mathlib/CategoryTheory/Adjunction/Evaluation.lean index d11a3d4ac62c1..ffb59cad14a86 100644 --- a/Mathlib/CategoryTheory/Adjunction/Evaluation.lean +++ b/Mathlib/CategoryTheory/Adjunction/Evaluation.lean @@ -22,7 +22,6 @@ open CategoryTheory.Limits universe v₁ v₂ v₃ u₁ u₂ u₃ variable {C : Type u₁} [Category.{v₁} C] (D : Type u₂) [Category.{v₂} D] - (E : Type u₃) [Category.{v₃} E] noncomputable section diff --git a/Mathlib/CategoryTheory/GradedObject.lean b/Mathlib/CategoryTheory/GradedObject.lean index b6e2df434c2b9..2bc160aeba95d 100644 --- a/Mathlib/CategoryTheory/GradedObject.lean +++ b/Mathlib/CategoryTheory/GradedObject.lean @@ -316,7 +316,7 @@ lemma hasMap_of_iso (e : X ≅ Y) (p: I → J) [HasMap X p] : HasMap Y p := fun exact hasColimitOfIso α.symm section -variable [X.HasMap p] [Y.HasMap p] [Z.HasMap p] +variable [X.HasMap p] [Y.HasMap p] /-- Given `X : GradedObject I C` and `p : I → J`, `X.mapObj p` is the graded object by `J` which in degree `j` consists of the coproduct of the `X i` such that `p i = j`. -/ diff --git a/Mathlib/CategoryTheory/GuitartExact/Basic.lean b/Mathlib/CategoryTheory/GuitartExact/Basic.lean index cb64500850d99..b697c1ee0f1a1 100644 --- a/Mathlib/CategoryTheory/GuitartExact/Basic.lean +++ b/Mathlib/CategoryTheory/GuitartExact/Basic.lean @@ -128,7 +128,6 @@ abbrev CostructuredArrowDownwards.mk (comm : R.map a ≫ w.app X₁ ≫ B.map b CostructuredArrow.mk (Y := StructuredArrow.mk a) (StructuredArrow.homMk b (by simpa using comm)) -variable (comm : R.map a ≫ w.app X₁ ≫ B.map b = g) variable {w g} lemma StructuredArrowRightwards.mk_surjective diff --git a/Mathlib/CategoryTheory/Sites/NonabelianCohomology/H1.lean b/Mathlib/CategoryTheory/Sites/NonabelianCohomology/H1.lean index 44a948a9222b1..b15c8b4f9117f 100644 --- a/Mathlib/CategoryTheory/Sites/NonabelianCohomology/H1.lean +++ b/Mathlib/CategoryTheory/Sites/NonabelianCohomology/H1.lean @@ -48,7 +48,7 @@ variable {C : Type u} [Category.{v} C] namespace PresheafOfGroups -variable (G : Cᵒᵖ ⥤ Grp.{w}) {X : C} {I : Type w'} (U : I → C) +variable (G : Cᵒᵖ ⥤ Grp.{w}) {I : Type w'} (U : I → C) /-- A zero cochain consists of a family of sections. -/ def ZeroCochain := ∀ (i : I), G.obj (Opposite.op (U i)) diff --git a/Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean b/Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean index 6d675a7865092..2924a54b4d530 100644 --- a/Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean +++ b/Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean @@ -34,8 +34,7 @@ open Fintype (card) namespace SimpleGraph -variable {α β 𝕜 : Type*} [LinearOrderedField 𝕜] {G H : SimpleGraph α} {ε δ : 𝕜} {n : ℕ} - {s : Finset α} +variable {α β 𝕜 : Type*} [LinearOrderedField 𝕜] {G H : SimpleGraph α} {ε δ : 𝕜} section LocallyLinear diff --git a/Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean b/Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean index bff996c3fa38c..3de98cd5194b3 100644 --- a/Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean +++ b/Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean @@ -23,7 +23,7 @@ attribute [-instance] decidableEq_of_subsingleton open Finset Fintype -variable {α : Type*} (G G' : SimpleGraph α) [DecidableRel G.Adj] {ε : ℝ} {s t u : Finset α} +variable {α : Type*} (G : SimpleGraph α) [DecidableRel G.Adj] {ε : ℝ} {s t u : Finset α} namespace SimpleGraph @@ -146,7 +146,7 @@ private lemma triple_eq_triple_of_mem (hst : Disjoint s t) (hsu : Disjoint s u) · rintro rfl solve_by_elim -variable [Fintype α] {P : Finpartition (univ : Finset α)} +variable [Fintype α] /-- The **Triangle Counting Lemma**. If `G` is a graph and `s`, `t`, `u` are disjoint sets of vertices such that each pair is `ε`-uniform and `2 * ε`-dense, then `G` contains at least diff --git a/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean b/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean index 3135218de5e3d..c911166bc53ac 100644 --- a/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean +++ b/Mathlib/Combinatorics/SimpleGraph/Triangle/Tripartite.lean @@ -38,7 +38,7 @@ This construction shows up unrelatedly twice in the theory of Roth numbers: open Finset Function Sum3 variable {α β γ 𝕜 : Type*} [LinearOrderedField 𝕜] {t : Finset (α × β × γ)} {a a' : α} {b b' : β} - {c c' : γ} {x : α × β × γ} {ε : 𝕜} + {c c' : γ} {x : α × β × γ} namespace SimpleGraph namespace TripartiteFromTriangles diff --git a/Mathlib/Data/Real/Sqrt.lean b/Mathlib/Data/Real/Sqrt.lean index b43bd46488f69..5b1193b70b404 100644 --- a/Mathlib/Data/Real/Sqrt.lean +++ b/Mathlib/Data/Real/Sqrt.lean @@ -311,8 +311,6 @@ end Mathlib.Meta.Positivity namespace Real -variable {x y : ℝ} - @[simp] theorem sqrt_mul {x : ℝ} (hx : 0 ≤ x) (y : ℝ) : √(x * y) = √x * √y := by simp_rw [Real.sqrt, ← NNReal.coe_mul, NNReal.coe_inj, Real.toNNReal_mul hx, NNReal.sqrt_mul] diff --git a/Mathlib/MeasureTheory/Constructions/Pi.lean b/Mathlib/MeasureTheory/Constructions/Pi.lean index aafd0f1b3c5ef..670e4e5bf0347 100644 --- a/Mathlib/MeasureTheory/Constructions/Pi.lean +++ b/Mathlib/MeasureTheory/Constructions/Pi.lean @@ -80,7 +80,7 @@ theorem isPiSystem_pi [∀ i, MeasurableSpace (α i)] : section Finite -variable [Finite ι] [Finite ι'] +variable [Finite ι] /-- Boxes of countably spanning sets are countably spanning. -/ theorem IsCountablySpanning.pi {C : ∀ i, Set (Set (α i))} (hC : ∀ i, IsCountablySpanning (C i)) : diff --git a/Mathlib/MeasureTheory/Group/Action.lean b/Mathlib/MeasureTheory/Group/Action.lean index 0cb212b5273b1..cad802e003d1f 100644 --- a/Mathlib/MeasureTheory/Group/Action.lean +++ b/Mathlib/MeasureTheory/Group/Action.lean @@ -28,7 +28,7 @@ namespace MeasureTheory universe u v w -variable {G : Type u} {M : Type v} {α : Type w} {s : Set α} +variable {G : Type u} {M : Type v} {α : Type w} namespace SMulInvariantMeasure @@ -198,7 +198,7 @@ instance smulInvariantMeasure_map_smul [SMul M α] [SMul N α] [SMulCommClass N end SMulHomClass -variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] (c : G) (μ : Measure α) +variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] (μ : Measure α) variable [MeasurableSpace G] [MeasurableSMul G α] in /-- Equivalent definitions of a measure invariant under a multiplicative action of a group. diff --git a/Mathlib/MeasureTheory/Group/LIntegral.lean b/Mathlib/MeasureTheory/Group/LIntegral.lean index e0344acdeed93..74c8453b516af 100644 --- a/Mathlib/MeasureTheory/Group/LIntegral.lean +++ b/Mathlib/MeasureTheory/Group/LIntegral.lean @@ -20,7 +20,7 @@ open Measure TopologicalSpace open scoped ENNReal -variable {G : Type*} [MeasurableSpace G] {μ : Measure G} {g : G} +variable {G : Type*} [MeasurableSpace G] {μ : Measure G} section MeasurableMul diff --git a/Mathlib/MeasureTheory/Integral/Marginal.lean b/Mathlib/MeasureTheory/Integral/Marginal.lean index 76fcaa682df92..4e19390aa37fb 100644 --- a/Mathlib/MeasureTheory/Integral/Marginal.lean +++ b/Mathlib/MeasureTheory/Integral/Marginal.lean @@ -66,7 +66,7 @@ section LMarginal variable {δ δ' : Type*} {π : δ → Type*} [∀ x, MeasurableSpace (π x)] variable {μ : ∀ i, Measure (π i)} [DecidableEq δ] -variable {s t : Finset δ} {f g : (∀ i, π i) → ℝ≥0∞} {x y : ∀ i, π i} {i : δ} +variable {s t : Finset δ} {f : (∀ i, π i) → ℝ≥0∞} {x : ∀ i, π i} /-- Integrate `f(x₁,…,xₙ)` over all variables `xᵢ` where `i ∈ s`. Return a function in the remaining variables (it will be constant in the `xᵢ` for `i ∈ s`). diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean b/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean index 4d2eb7fd31ab1..678a6983571d0 100644 --- a/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean +++ b/Mathlib/MeasureTheory/MeasurableSpace/Basic.lean @@ -55,7 +55,7 @@ open Set Encodable Function Equiv Filter MeasureTheory universe uι -variable {α β γ δ δ' : Type*} {ι : Sort uι} {s t u : Set α} +variable {α β γ δ δ' : Type*} {ι : Sort uι} {s : Set α} namespace MeasurableSpace @@ -225,7 +225,7 @@ variable {f g : α → β} section TypeclassMeasurableSpace -variable [MeasurableSpace α] [MeasurableSpace β] [MeasurableSpace γ] +variable [MeasurableSpace α] [MeasurableSpace β] @[nontriviality, measurability] theorem Subsingleton.measurable [Subsingleton α] : Measurable f := fun _ _ => diff --git a/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean b/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean index e9f2db14bfc25..9dec6c3e39e9b 100644 --- a/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean +++ b/Mathlib/MeasureTheory/MeasurableSpace/Prod.lean @@ -18,7 +18,7 @@ noncomputable section open Set MeasurableSpace -variable {α β γ : Type*} [MeasurableSpace α] [MeasurableSpace β] [MeasurableSpace γ] +variable {α β : Type*} [MeasurableSpace α] [MeasurableSpace β] /-- The product of generated σ-algebras is the one generated by rectangles, if both generating sets are countably spanning. -/ diff --git a/Mathlib/MeasureTheory/Measure/Regular.lean b/Mathlib/MeasureTheory/Measure/Regular.lean index ed27aa6936522..91b924e0a4f30 100644 --- a/Mathlib/MeasureTheory/Measure/Regular.lean +++ b/Mathlib/MeasureTheory/Measure/Regular.lean @@ -446,7 +446,7 @@ protected theorem FiniteSpanningSetsIn.outerRegular namespace InnerRegularWRT -variable {p q : Set α → Prop} {U s : Set α} {ε r : ℝ≥0∞} +variable {p : Set α → Prop} /-- If the restrictions of a measure to a monotone sequence of sets covering the space are inner regular for some property `p` and all measurable sets, then the measure itself is @@ -637,7 +637,7 @@ end InnerRegularWRT namespace InnerRegular -variable {U : Set α} {ε : ℝ≥0∞} [TopologicalSpace α] +variable [TopologicalSpace α] /-- The measure of a measurable set is the supremum of the measures of compact sets it contains. -/ theorem _root_.MeasurableSet.measure_eq_iSup_isCompact ⦃U : Set α⦄ (hU : MeasurableSet U) diff --git a/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean b/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean index af6dc235b4928..82a5c54c0a72c 100644 --- a/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean +++ b/Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean @@ -636,8 +636,7 @@ end section mapAway variable [AddCommMonoid ι] [DecidableEq ι] [GradedAlgebra 𝒜] -variable {d e : ι} {f : A} (hf : f ∈ 𝒜 d) {g : A} (hg : g ∈ 𝒜 e) -variable {x : A} (hx : x = f * g) +variable {e : ι} {f : A} {g : A} (hg : g ∈ 𝒜 e) {x : A} (hx : x = f * g) variable (𝒜) diff --git a/Mathlib/RingTheory/Localization/AtPrime.lean b/Mathlib/RingTheory/Localization/AtPrime.lean index 65cccdc214ca9..76d9a9d2cb2e8 100644 --- a/Mathlib/RingTheory/Localization/AtPrime.lean +++ b/Mathlib/RingTheory/Localization/AtPrime.lean @@ -31,7 +31,7 @@ commutative ring, field of fractions -/ -variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemiring S] +variable {R : Type*} [CommSemiring R] (S : Type*) [CommSemiring S] variable [Algebra R S] {P : Type*} [CommSemiring P] section AtPrime diff --git a/Mathlib/RingTheory/Localization/Integral.lean b/Mathlib/RingTheory/Localization/Integral.lean index 07c55c2708e4b..ad327225f2383 100644 --- a/Mathlib/RingTheory/Localization/Integral.lean +++ b/Mathlib/RingTheory/Localization/Integral.lean @@ -25,7 +25,7 @@ commutative ring, field of fractions variable {R : Type*} [CommRing R] (M : Submonoid R) {S : Type*} [CommRing S] -variable [Algebra R S] {P : Type*} [CommRing P] +variable [Algebra R S] open Polynomial diff --git a/Mathlib/RingTheory/Localization/LocalizationLocalization.lean b/Mathlib/RingTheory/Localization/LocalizationLocalization.lean index 62db6f2a12761..0637b7cd2c470 100644 --- a/Mathlib/RingTheory/Localization/LocalizationLocalization.lean +++ b/Mathlib/RingTheory/Localization/LocalizationLocalization.lean @@ -27,8 +27,7 @@ namespace IsLocalization section LocalizationLocalization -variable {R : Type*} [CommSemiring R] (M : Submonoid R) {S : Type*} [CommSemiring S] -variable [Algebra R S] {P : Type*} [CommSemiring P] +variable {R : Type*} [CommSemiring R] (M : Submonoid R) {S : Type*} [CommSemiring S] [Algebra R S] variable (N : Submonoid S) (T : Type*) [CommSemiring T] [Algebra R T] @@ -251,7 +250,7 @@ end IsLocalization namespace IsFractionRing -variable {R : Type*} [CommRing R] (M : Submonoid R) {S : Type*} [CommRing S] +variable {R : Type*} [CommRing R] (M : Submonoid R) open IsLocalization diff --git a/Mathlib/RingTheory/TensorProduct/Free.lean b/Mathlib/RingTheory/TensorProduct/Free.lean index 1f644e47cf568..a857cfdf874c6 100644 --- a/Mathlib/RingTheory/TensorProduct/Free.lean +++ b/Mathlib/RingTheory/TensorProduct/Free.lean @@ -30,7 +30,7 @@ namespace Algebra namespace TensorProduct -variable {R S A : Type*} +variable {R A : Type*} section Basis diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain/Nat.lean b/Mathlib/RingTheory/UniqueFactorizationDomain/Nat.lean index 680aa8f4249fe..4c69bfb655b75 100644 --- a/Mathlib/RingTheory/UniqueFactorizationDomain/Nat.lean +++ b/Mathlib/RingTheory/UniqueFactorizationDomain/Nat.lean @@ -15,8 +15,6 @@ import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors * `Nat.instUniqueFactorizationMonoid`: the natural numbers have unique factorization -/ -variable {α : Type*} - namespace Nat instance instWfDvdMonoid : WfDvdMonoid ℕ where diff --git a/Mathlib/Testing/Plausible/Functions.lean b/Mathlib/Testing/Plausible/Functions.lean index 9a83323198f47..a9bdf24d8ccb4 100644 --- a/Mathlib/Testing/Plausible/Functions.lean +++ b/Mathlib/Testing/Plausible/Functions.lean @@ -40,9 +40,9 @@ their defining property is invariant through shrinking. Injective functions are an example of how complicated it can get. -/ -universe u v w +universe u v -variable {α : Type u} {β : Type v} {γ : Sort w} +variable {α : Type u} {β : Type v} namespace Plausible diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean index 74529c1335d72..ba49c204bab72 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean @@ -21,12 +21,12 @@ noncomputable section open Filter Finset Function Topology -variable {α β γ δ : Type*} +variable {α β γ : Type*} section HasProd variable [CommMonoid α] [TopologicalSpace α] -variable {f g : β → α} {a b : α} {s : Finset β} +variable {f g : β → α} {a b : α} /-- Constant one function has product `1` -/ @[to_additive "Constant zero function has sum `0`"] @@ -355,7 +355,7 @@ end HasProd section tprod -variable [CommMonoid α] [TopologicalSpace α] {f g : β → α} {a a₁ a₂ : α} +variable [CommMonoid α] [TopologicalSpace α] {f g : β → α} @[to_additive] theorem tprod_congr_set_coe (f : β → α) {s t : Set β} (h : s = t) : diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean b/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean index 8b1f1a092440e..4386fe90f6bd1 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean @@ -20,7 +20,7 @@ open Filter Finset Function open scoped Topology -variable {α β γ δ : Type*} +variable {α β γ : Type*} /-! ## Product, Sigma and Pi types -/ diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean b/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean index 2bf685cd201e1..cc83507487809 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Defs.lean @@ -111,7 +111,7 @@ notation3 "∏' "(...)", "r:67:(scoped f => tprod f) => r @[inherit_doc tsum] notation3 "∑' "(...)", "r:67:(scoped f => tsum f) => r -variable {f g : β → α} {a b : α} {s : Finset β} +variable {f : β → α} {a : α} {s : Finset β} @[to_additive] theorem HasProd.multipliable (h : HasProd f a) : Multipliable f := diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Group.lean b/Mathlib/Topology/Algebra/InfiniteSum/Group.lean index 4c5353916aae3..937a415544928 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Group.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Group.lean @@ -20,7 +20,7 @@ open Filter Finset Function open scoped Topology -variable {α β γ δ : Type*} +variable {α β γ : Type*} section TopologicalGroup @@ -197,7 +197,7 @@ theorem multipliable_iff_cauchySeq_finset [CompleteSpace α] {f : β → α} : Multipliable f ↔ CauchySeq fun s : Finset β ↦ ∏ b ∈ s, f b := by classical exact cauchy_map_iff_exists_tendsto.symm -variable [UniformGroup α] {f g : β → α} {a a₁ a₂ : α} +variable [UniformGroup α] {f g : β → α} @[to_additive] theorem cauchySeq_finset_iff_prod_vanishing : diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean b/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean index ea55550f54743..aa0cdf8f9a57d 100644 --- a/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean +++ b/Mathlib/Topology/Algebra/InfiniteSum/Ring.lean @@ -19,12 +19,12 @@ This file provides lemmas about the interaction between infinite sums and multip open Filter Finset Function -variable {ι κ R α : Type*} +variable {ι κ α : Type*} section NonUnitalNonAssocSemiring -variable [NonUnitalNonAssocSemiring α] [TopologicalSpace α] [TopologicalSemiring α] {f g : ι → α} - {a a₁ a₂ : α} +variable [NonUnitalNonAssocSemiring α] [TopologicalSpace α] [TopologicalSemiring α] {f : ι → α} + {a₁ : α} theorem HasSum.mul_left (a₂) (h : HasSum f a₁) : HasSum (fun i ↦ a₂ * f i) (a₂ * a₁) := by simpa only using h.map (AddMonoidHom.mulLeft a₂) (continuous_const.mul continuous_id) @@ -63,8 +63,7 @@ end NonUnitalNonAssocSemiring section DivisionSemiring -variable [DivisionSemiring α] [TopologicalSpace α] [TopologicalSemiring α] {f g : ι → α} - {a a₁ a₂ : α} +variable [DivisionSemiring α] [TopologicalSpace α] [TopologicalSemiring α] {f : ι → α} {a a₁ a₂ : α} theorem HasSum.div_const (h : HasSum f a) (b : α) : HasSum (fun i ↦ f i / b) (a / b) := by simp only [div_eq_mul_inv, h.mul_right b⁻¹] diff --git a/Mathlib/Topology/ContinuousMap/Ordered.lean b/Mathlib/Topology/ContinuousMap/Ordered.lean index 5ef9876bb5f8c..7677b1c20ea56 100644 --- a/Mathlib/Topology/ContinuousMap/Ordered.lean +++ b/Mathlib/Topology/ContinuousMap/Ordered.lean @@ -13,8 +13,7 @@ import Mathlib.Topology.ContinuousMap.Defs -/ -variable {α : Type*} {β : Type*} {γ : Type*} -variable [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ] +variable {α β : Type*} [TopologicalSpace α] [TopologicalSpace β] namespace ContinuousMap diff --git a/Mathlib/Topology/Instances/ENNReal.lean b/Mathlib/Topology/Instances/ENNReal.lean index 94b73607b7f71..029ada7f6a78a 100644 --- a/Mathlib/Topology/Instances/ENNReal.lean +++ b/Mathlib/Topology/Instances/ENNReal.lean @@ -25,7 +25,7 @@ variable {α : Type*} {β : Type*} {γ : Type*} namespace ENNReal -variable {a b c d : ℝ≥0∞} {r p q : ℝ≥0} {x y z : ℝ≥0∞} {ε ε₁ ε₂ : ℝ≥0∞} {s : Set ℝ≥0∞} +variable {a b : ℝ≥0∞} {r : ℝ≥0} {x : ℝ≥0∞} {ε : ℝ≥0∞} section TopologicalSpace diff --git a/Mathlib/Topology/MetricSpace/Dilation.lean b/Mathlib/Topology/MetricSpace/Dilation.lean index 201c0e06799e3..6ab93147d696b 100644 --- a/Mathlib/Topology/MetricSpace/Dilation.lean +++ b/Mathlib/Topology/MetricSpace/Dilation.lean @@ -74,7 +74,7 @@ end Defs namespace Dilation -variable {α : Type*} {β : Type*} {γ : Type*} {F : Type*} {G : Type*} +variable {α : Type*} {β : Type*} {γ : Type*} {F : Type*} section Setup @@ -229,8 +229,8 @@ end Setup section PseudoEmetricDilation variable [PseudoEMetricSpace α] [PseudoEMetricSpace β] [PseudoEMetricSpace γ] -variable [FunLike F α β] [DilationClass F α β] [FunLike G β γ] [DilationClass G β γ] -variable (f : F) (g : G) {x y z : α} {s : Set α} +variable [FunLike F α β] [DilationClass F α β] +variable (f : F) /-- Every isometry is a dilation of ratio `1`. -/ @[simps] diff --git a/Mathlib/Topology/MetricSpace/Isometry.lean b/Mathlib/Topology/MetricSpace/Isometry.lean index 5e434b37434df..a987f5c09f284 100644 --- a/Mathlib/Topology/MetricSpace/Isometry.lean +++ b/Mathlib/Topology/MetricSpace/Isometry.lean @@ -62,7 +62,7 @@ namespace Isometry section PseudoEmetricIsometry variable [PseudoEMetricSpace α] [PseudoEMetricSpace β] [PseudoEMetricSpace γ] -variable {f : α → β} {x y z : α} {s : Set α} +variable {f : α → β} {x : α} /-- An isometry preserves edistances. -/ theorem edist_eq (hf : Isometry f) (x y : α) : edist (f x) (f y) = edist x y := diff --git a/Mathlib/Topology/MetricSpace/Pseudo/Real.lean b/Mathlib/Topology/MetricSpace/Pseudo/Real.lean index baa4f534f75cc..6183ec868a947 100644 --- a/Mathlib/Topology/MetricSpace/Pseudo/Real.lean +++ b/Mathlib/Topology/MetricSpace/Pseudo/Real.lean @@ -15,7 +15,7 @@ open scoped NNReal Topology namespace Real -variable {ι α : Type*} [PseudoMetricSpace α] +variable {ι : Type*} lemma dist_left_le_of_mem_uIcc {x y z : ℝ} (h : y ∈ uIcc x z) : dist x y ≤ dist x z := by simpa only [dist_comm x] using abs_sub_left_of_mem_uIcc h @@ -35,7 +35,7 @@ lemma dist_le_of_mem_Icc {x y x' y' : ℝ} (hx : x ∈ Icc x' y') (hy : y ∈ Ic lemma dist_le_of_mem_Icc_01 {x y : ℝ} (hx : x ∈ Icc (0 : ℝ) 1) (hy : y ∈ Icc (0 : ℝ) 1) : dist x y ≤ 1 := by simpa only [sub_zero] using Real.dist_le_of_mem_Icc hx hy -variable {π : ι → Type*} [Fintype ι] [∀ i, PseudoMetricSpace (π i)] {x y x' y' : ι → ℝ} +variable [Fintype ι] {x y x' y' : ι → ℝ} lemma dist_le_of_mem_pi_Icc (hx : x ∈ Icc x' y') (hy : y ∈ Icc x' y') : dist x y ≤ dist x' y' := by refine (dist_pi_le_iff dist_nonneg).2 fun b => diff --git a/Mathlib/Topology/Order/ExtrClosure.lean b/Mathlib/Topology/Order/ExtrClosure.lean index d1b2049789057..31b06abf781bd 100644 --- a/Mathlib/Topology/Order/ExtrClosure.lean +++ b/Mathlib/Topology/Order/ExtrClosure.lean @@ -20,7 +20,7 @@ open Filter Set open Topology variable {X Y : Type*} [TopologicalSpace X] [TopologicalSpace Y] [Preorder Y] - [OrderClosedTopology Y] {f g : X → Y} {s : Set X} {a : X} + [OrderClosedTopology Y] {f : X → Y} {s : Set X} {a : X} protected theorem IsMaxOn.closure (h : IsMaxOn f s a) (hc : ContinuousOn f (closure s)) : IsMaxOn f (closure s) a := fun x hx => diff --git a/Mathlib/Topology/Order/MonotoneConvergence.lean b/Mathlib/Topology/Order/MonotoneConvergence.lean index bad7ee58b291e..7936b81bae9f3 100644 --- a/Mathlib/Topology/Order/MonotoneConvergence.lean +++ b/Mathlib/Topology/Order/MonotoneConvergence.lean @@ -107,7 +107,7 @@ end IsGLB section CiSup -variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α} +variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) : Tendsto f atTop (𝓝 (⨆ i, f i)) := by @@ -121,7 +121,7 @@ end CiSup section CiInf -variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α} +variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) : Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual using 1 @@ -133,7 +133,7 @@ end CiInf section iSup -variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α} +variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} theorem tendsto_atTop_iSup (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) := tendsto_atTop_ciSup h_mono (OrderTop.bddAbove _) @@ -145,7 +145,7 @@ end iSup section iInf -variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α} +variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} theorem tendsto_atBot_iInf (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) := tendsto_atBot_ciInf h_mono (OrderBot.bddBelow _) diff --git a/Mathlib/Topology/Order/T5.lean b/Mathlib/Topology/Order/T5.lean index 39e0d08dc9b0a..597085db3f109 100644 --- a/Mathlib/Topology/Order/T5.lean +++ b/Mathlib/Topology/Order/T5.lean @@ -16,8 +16,7 @@ topological space. open Filter Set Function OrderDual Topology Interval -variable {X : Type*} [LinearOrder X] [TopologicalSpace X] [OrderTopology X] {a b c : X} - {s t : Set X} +variable {X : Type*} [LinearOrder X] [TopologicalSpace X] [OrderTopology X] {a : X} {s t : Set X} namespace Set diff --git a/Mathlib/Topology/ShrinkingLemma.lean b/Mathlib/Topology/ShrinkingLemma.lean index 8f03eeab6a068..65f6b72889730 100644 --- a/Mathlib/Topology/ShrinkingLemma.lean +++ b/Mathlib/Topology/ShrinkingLemma.lean @@ -206,7 +206,7 @@ section NormalSpace open ShrinkingLemma -variable {u : ι → Set X} {s : Set X} {p : Set X → Prop} [NormalSpace X] +variable {u : ι → Set X} {s : Set X} [NormalSpace X] /-- **Shrinking lemma**. A point-finite open cover of a closed subset of a normal space can be "shrunk" to a new open cover so that the closure of each new open set is contained in the diff --git a/Mathlib/Topology/UniformSpace/OfCompactT2.lean b/Mathlib/Topology/UniformSpace/OfCompactT2.lean index 5eaf71a852f4f..c9d49e9474570 100644 --- a/Mathlib/Topology/UniformSpace/OfCompactT2.lean +++ b/Mathlib/Topology/UniformSpace/OfCompactT2.lean @@ -26,7 +26,7 @@ uniform space, uniform continuity, compact space open Uniformity Topology Filter UniformSpace Set -variable {α β γ : Type*} [UniformSpace α] [UniformSpace β] +variable {γ : Type*} /-! ### Uniformity on compact spaces