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Ruben-VandeVeldeRuben-VandeVelde
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chore: tidy various files (#13056)
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‎Mathlib/Algebra/Exact.lean‎

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@@ -10,13 +10,10 @@ import Mathlib.Algebra.Module.Submodule.Range
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/-! # Exactness of a pair
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* For two maps `f : M → N` and `g : N → P`, with `Zero P`,
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`Function.AddExact f g` says that `Set.range f = Set.preimage {0}
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* For two maps `f : M → N` and `g : N → P`, with `One P`,
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`Function.Exact f g` says that `Set.range f = Set.preimage {1}
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`Function.Exact f g` says that `Set.range f = Set.preimage g {0}`
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* For linear maps `f : M →ₗ[R] N` and `g : N →ₗ[R] P`,
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`Exact f g` says that `range f = ker g``
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`Exact f g` says that `range f = ker g`
2017
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## TODO :
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‎Mathlib/Algebra/Module/Injective.lean‎

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@@ -454,7 +454,7 @@ theorem extension_property_addMonoidHom (h : Module.Baer ℤ Q)
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/-- **Baer's criterion** for injective module : a Baer module is an injective module, i.e. if every
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linear map from an ideal can be extended, then the module is injective. -/
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protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q where
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out := fun X Y _ _ _ _ i hi f ↦ by
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out X Y _ _ _ _ i hi f := by
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obtain ⟨h, H⟩ := Module.Baer.extension_property h i hi f
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exact ⟨h, DFunLike.congr_fun H⟩
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set_option linter.uppercaseLean3 false in
@@ -466,7 +466,7 @@ protected theorem of_injective [Small.{v} R] (inj : Module.Injective R Q) : Modu
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let eR := Shrink.linearEquiv R R
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obtain ⟨g', hg'⟩ := Module.Injective.out (eR.symm.toLinearMap ∘ₗ I.subtype ∘ₗ eI.toLinearMap)
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(eR.symm.injective.comp <| Subtype.val_injective.comp eI.injective) (g ∘ₗ eI.toLinearMap)
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exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa [eI,eR] using hg' (equivShrink I ⟨x, mx⟩)⟩
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exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa [eI, eR] using hg' (equivShrink I ⟨x, mx⟩)⟩
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protected theorem iff_injective [Small.{v} R] : Module.Baer R Q ↔ Module.Injective R Q :=
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⟨Module.Baer.injective, Module.Baer.of_injective⟩

‎Mathlib/Algebra/Order/Hom/Monoid.lean‎

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@@ -47,7 +47,7 @@ This file used to define typeclasses for order-preserving (additive) monoid homo
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`OrderAddMonoidHomClass`, `OrderMonoidHomClass`, and `OrderMonoidWithZeroHomClass`.
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In #10544 we migrated from these typeclasses
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to assumptions like `[FunLike F M N] [MonoidHomClass F M N] [OrderHomClass F M N ]`,
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to assumptions like `[FunLike F M N] [MonoidHomClass F M N] [OrderHomClass F M N]`,
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making some definitions and lemmas irrelevant.
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## Tags

‎Mathlib/Algebra/Polynomial/Div.lean‎

Lines changed: 7 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -559,8 +559,8 @@ theorem rootMultiplicity_C (r a : R) : rootMultiplicity a (C r) = 0 := by
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split_ifs with hr
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· rfl
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have h : natDegree (C r) < natDegree (X - C a) := by simp
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simp_rw [multiplicity.multiplicity_eq_zero.mpr ((monic_X_sub_C a).not_dvd_of_natDegree_lt hr h)]
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rfl
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simp_rw [multiplicity.multiplicity_eq_zero.mpr ((monic_X_sub_C a).not_dvd_of_natDegree_lt hr h),
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PartENat.get_zero]
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set_option linter.uppercaseLean3 false in
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#align polynomial.root_multiplicity_C Polynomial.rootMultiplicity_C
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@@ -614,12 +614,13 @@ set_option linter.uppercaseLean3 false in
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#align polynomial.mod_by_monic_X_sub_C_eq_C_eval Polynomial.modByMonic_X_sub_C_eq_C_eval
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theorem mul_divByMonic_eq_iff_isRoot : (X - C a) * (p /ₘ (X - C a)) = p ↔ IsRoot p a :=
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⟨fun h => by
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rw [← h, IsRoot.def, eval_mul, eval_sub, eval_X, eval_C, sub_self, zero_mul],
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fun h : p.eval a = 0 => by
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conv_rhs =>
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.trans
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⟨fun h => by rw [← h, eval_mul, eval_sub, eval_X, eval_C, sub_self, zero_mul],
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fun h => by
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conv_rhs =>
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rw [← modByMonic_add_div p (monic_X_sub_C a)]
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rw [modByMonic_X_sub_C_eq_C_eval, h, C_0, zero_add]⟩
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IsRoot.def.symm
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#align polynomial.mul_div_by_monic_eq_iff_is_root Polynomial.mul_divByMonic_eq_iff_isRoot
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theorem dvd_iff_isRoot : X - C a ∣ p ↔ IsRoot p a :=

‎Mathlib/Analysis/BoxIntegral/Partition/Basic.lean‎

Lines changed: 4 additions & 7 deletions
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@@ -142,10 +142,8 @@ instance partialOrder : PartialOrder (Prepartition I) where
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fun π₁ π₂ h₁ h₂ => injective_boxes (Subset.antisymm (this h₁ h₂) (this h₂ h₁))
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intro π₁ π₂ h₁ h₂ J hJ
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rcases h₁ hJ with ⟨J', hJ', hle⟩; rcases h₂ hJ' with ⟨J'', hJ'', hle'⟩
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obtain rfl : J = J''
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· exact π₁.eq_of_le hJ hJ'' (hle.trans hle')
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obtain rfl : J' = J
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· exact le_antisymm ‹_› ‹_›
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obtain rfl : J = J'' := π₁.eq_of_le hJ hJ'' (hle.trans hle')
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obtain rfl : J' = J := le_antisymm ‹_› ‹_›
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assumption
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instance : OrderTop (Prepartition I) where
@@ -539,9 +537,8 @@ theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
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exact WithBot.coe_le_coe.2 (le_of_mem _ h₁)
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· simp only [iUnion_restrict, iUnion_biUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_iUnion]
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rintro x ⟨hxJ, J₁, h₁, hx⟩
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obtain rfl : J = J₁
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· exact π.eq_of_mem_of_mem hJ h₁ hxJ (iUnion_subset _ hx)
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· exact hx
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obtain rfl : J = J₁ := π.eq_of_mem_of_mem hJ h₁ hxJ (iUnion_subset _ hx)
541+
exact hx
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#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
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theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :

‎Mathlib/CategoryTheory/EffectiveEpi/Enough.lean‎

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@@ -62,9 +62,9 @@ instance (X : D) : EffectiveEpi (F.effectiveEpiOver X) :=
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/-- An effective presentation of an object with respect to an equivalence of categories. -/
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def equivalenceEffectivePresentation (e : C ≌ D) (X : D) :
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EffectivePresentation e.functor X where
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p := e.inverse.obj X
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f := e.counit.app _
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effectiveEpi := inferInstance
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p := e.inverse.obj X
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f := e.counit.app _
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effectiveEpi := inferInstance
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instance [IsEquivalence F] : EffectivelyEnough F where
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presentation X := ⟨equivalenceEffectivePresentation F.asEquivalence X⟩

‎Mathlib/CategoryTheory/Sites/Coherent/Equivalence.lean‎

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@@ -64,8 +64,9 @@ The coherent sheaf condition on an essentially small site can be checked after p
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the equivalence with a small category.
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-/
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theorem precoherent_isSheaf_iff_of_essentiallySmall [EssentiallySmall C] (F : Cᵒᵖ ⥤ A) :
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IsSheaf (coherentTopology C) F ↔ IsSheaf (coherentTopology (SmallModel C))
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((equivSmallModel C).inverse.op ⋙ F) := precoherent_isSheaf_iff _ _ _
67+
IsSheaf (coherentTopology C) F ↔
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IsSheaf (coherentTopology (SmallModel C)) ((equivSmallModel C).inverse.op ⋙ F) :=
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precoherent_isSheaf_iff _ _ _
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end Coherent
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‎Mathlib/Data/Finset/Sigma.lean‎

Lines changed: 2 additions & 2 deletions
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@@ -110,8 +110,8 @@ theorem inf_sigma [SemilatticeInf β] [OrderTop β] :
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#align finset.inf_sigma Finset.inf_sigma
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theorem _root_.biSup_finsetSigma [CompleteLattice β] (s : Finset ι) (t : ∀ i, Finset (α i))
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(f : Sigma α → β) : ⨆ ij ∈ s.sigma t, f ij = ⨆ (i ∈ s) (j ∈ t i), f ⟨i, j⟩ :=
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by simp_rw [← Finset.iSup_coe, Finset.coe_sigma, biSup_sigma]
113+
(f : Sigma α → β) : ⨆ ij ∈ s.sigma t, f ij = ⨆ (i ∈ s) (j ∈ t i), f ⟨i, j⟩ := by
114+
simp_rw [← Finset.iSup_coe, Finset.coe_sigma, biSup_sigma]
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theorem _root_.biSup_finsetSigma' [CompleteLattice β] (s : Finset ι) (t : ∀ i, Finset (α i))
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(f : ∀ i, α i → β) : ⨆ (i ∈ s) (j ∈ t i), f i j = ⨆ ij ∈ s.sigma t, f ij.fst ij.snd :=

‎Mathlib/Data/Nat/Interval.lean‎

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@@ -118,11 +118,9 @@ theorem card_Ioo : (Ioo a b).card = b - a - 1 :=
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@[simp]
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theorem card_uIcc : (uIcc a b).card = (b - a : ℤ).natAbs + 1 := by
121-
refine' (card_Icc _ _).trans (Int.ofNat.inj _)
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change ((↑) : ℕ → ℤ) _ = _
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refine (card_Icc _ _).trans (Int.natCast_inj.mp ?_)
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rw [sup_eq_max, inf_eq_min, Int.ofNat_sub]
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· change _ = ↑(Int.natAbs (b - a) + 1)
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omega
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· omega
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· exact min_le_max.trans le_self_add
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#align nat.card_uIcc Nat.card_uIcc
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‎Mathlib/Data/Real/ConjExponents.lean‎

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@@ -197,8 +197,8 @@ lemma mul_eq_add : p * q = p + q := by
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@[symm]
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protected lemma symm : q.IsConjExponent p where
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one_lt := by
200-
rw [h.conj_eq]
201-
exact (one_lt_div h.sub_one_pos).mpr (tsub_lt_self h.pos zero_lt_one)
200+
rw [h.conj_eq]
201+
exact (one_lt_div h.sub_one_pos).mpr (tsub_lt_self h.pos zero_lt_one)
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inv_add_inv_conj := by simpa [add_comm] using h.inv_add_inv_conj
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lemma div_conj_eq_sub_one : p / q = p - 1 := by field_simp [h.symm.ne_zero]; rw [h.sub_one_mul_conj]

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