diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean index 8947d5009b26c..1814b8a618f4d 100644 --- a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean +++ b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean @@ -594,8 +594,7 @@ theorem continuousWithinAt_arg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re < 0) ( lift z to ℝ using him simpa using hre.ne · rw [arg, if_neg hre.not_le, if_pos him.ge] -#align complex.continuous_within_at_arg_of_re_neg_of_im_zero -Complex.continuousWithinAt_arg_of_re_neg_of_im_zero +#align complex.continuous_within_at_arg_of_re_neg_of_im_zero Complex.continuousWithinAt_arg_of_re_neg_of_im_zero theorem tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re < 0) (him : z.im = 0) : Tendsto arg (𝓝[{ z : ℂ | 0 ≤ z.im }] z) (𝓝 π) := by diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean index 113099aa641cf..c404048ee2665 100644 --- a/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean +++ b/Mathlib/Analysis/SpecialFunctions/Complex/Log.lean @@ -190,8 +190,7 @@ theorem tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero {z : ℂ} (hre : z.re · simp [sub_eq_add_neg] · lift z to ℝ using him simpa using hre.ne -#align complex.tendsto_log_nhds_within_im_neg_of_re_neg_of_im_zero -Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero +#align complex.tendsto_log_nhds_within_im_neg_of_re_neg_of_im_zero Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero theorem continuousWithinAt_log_of_re_neg_of_im_zero {z : ℂ} (hre : z.re < 0) (him : z.im = 0) : ContinuousWithinAt log { z : ℂ | 0 ≤ z.im } z := by @@ -210,8 +209,7 @@ theorem tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero {z : ℂ} (hre : z (him : z.im = 0) : Tendsto log (𝓝[{ z : ℂ | 0 ≤ z.im }] z) (𝓝 <| Real.log (abs z) + π * I) := by simpa only [log, arg_eq_pi_iff.2 ⟨hre, him⟩] using (continuousWithinAt_log_of_re_neg_of_im_zero hre him).tendsto -#align complex.tendsto_log_nhds_within_im_nonneg_of_re_neg_of_im_zero -Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero +#align complex.tendsto_log_nhds_within_im_nonneg_of_re_neg_of_im_zero Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero @[simp] theorem map_exp_comap_re_atBot : map exp (comap re atBot) = 𝓝[≠] 0 := by diff --git a/Mathlib/CategoryTheory/Endofunctor/Algebra.lean b/Mathlib/CategoryTheory/Endofunctor/Algebra.lean index 498379f10d031..fc07d595893be 100644 --- a/Mathlib/CategoryTheory/Endofunctor/Algebra.lean +++ b/Mathlib/CategoryTheory/Endofunctor/Algebra.lean @@ -116,8 +116,7 @@ variable (f : A₀ ⟶ A₁) (g : A₁ ⟶ A₂) @[simp] theorem comp_eq_comp : Algebra.Hom.comp f g = f ≫ g := rfl -#align category_theory.endofunctor.algebra.comp_eq_comp - CategoryTheory.Endofunctor.Algebra.comp_eq_comp +#align category_theory.endofunctor.algebra.comp_eq_comp CategoryTheory.Endofunctor.Algebra.comp_eq_comp @[simp] theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 := diff --git a/Mathlib/Data/Finset/Basic.lean b/Mathlib/Data/Finset/Basic.lean index 90cf78fcafb6b..1d3cc53e2d457 100644 --- a/Mathlib/Data/Finset/Basic.lean +++ b/Mathlib/Data/Finset/Basic.lean @@ -810,8 +810,7 @@ theorem eq_singleton_or_nontrivial (ha : a ∈ s) : s = {a} ∨ (s : Set α).Non theorem Nonempty.exists_eq_singleton_or_nontrivial : s.Nonempty → (∃ a, s = {a}) ∨ (s : Set α).Nontrivial := fun ⟨a, ha⟩ => (eq_singleton_or_nontrivial ha).imp_left <| Exists.intro a -#align finset.nonempty.exists_eq_singleton_or_nontrivial - Finset.Nonempty.exists_eq_singleton_or_nontrivial +#align finset.nonempty.exists_eq_singleton_or_nontrivial Finset.Nonempty.exists_eq_singleton_or_nontrivial instance [Nonempty α] : Nontrivial (Finset α) := ‹Nonempty α›.elim fun a => ⟨⟨{a}, ∅, singleton_ne_empty _⟩⟩ diff --git a/Mathlib/Data/Set/Ncard.lean b/Mathlib/Data/Set/Ncard.lean index 14207b073cc98..54491627d215b 100644 --- a/Mathlib/Data/Set/Ncard.lean +++ b/Mathlib/Data/Set/Ncard.lean @@ -542,8 +542,7 @@ theorem ncard_eq_ncard_iff_ncard_diff_eq_ncard_diff (hs : s.Finite := by toFinit (ht : t.Finite := by toFinite_tac) : s.ncard = t.ncard ↔ (s \ t).ncard = (t \ s).ncard := by rw [← ncard_inter_add_ncard_diff_eq_ncard s t hs, ← ncard_inter_add_ncard_diff_eq_ncard t s ht, inter_comm, add_right_inj] -#align set.ncard_eq_ncard_iff_ncard_diff_eq_ncard_diff - Set.ncard_eq_ncard_iff_ncard_diff_eq_ncard_diff +#align set.ncard_eq_ncard_iff_ncard_diff_eq_ncard_diff Set.ncard_eq_ncard_iff_ncard_diff_eq_ncard_diff theorem ncard_le_ncard_iff_ncard_diff_le_ncard_diff (hs : s.Finite := by toFinite_tac) (ht : t.Finite := by toFinite_tac) : s.ncard ≤ t.ncard ↔ (s \ t).ncard ≤ (t \ s).ncard := by @@ -556,8 +555,7 @@ theorem ncard_lt_ncard_iff_ncard_diff_lt_ncard_diff (hs : s.Finite := by toFinit (ht : t.Finite := by toFinite_tac) : s.ncard < t.ncard ↔ (s \ t).ncard < (t \ s).ncard := by rw [← ncard_inter_add_ncard_diff_eq_ncard s t hs, ← ncard_inter_add_ncard_diff_eq_ncard t s ht, inter_comm, add_lt_add_iff_left] -#align set.ncard_lt_ncard_iff_ncard_diff_lt_ncard_diff - Set.ncard_lt_ncard_iff_ncard_diff_lt_ncard_diff +#align set.ncard_lt_ncard_iff_ncard_diff_lt_ncard_diff Set.ncard_lt_ncard_iff_ncard_diff_lt_ncard_diff theorem ncard_add_ncard_compl (s : Set α) (hs : s.Finite := by toFinite_tac) (hsc : sᶜ.Finite := by toFinite_tac) : s.ncard + sᶜ.ncard = Nat.card α := by diff --git a/Mathlib/GroupTheory/SchurZassenhaus.lean b/Mathlib/GroupTheory/SchurZassenhaus.lean index 6ae005400b446..21957caa7a0f4 100644 --- a/Mathlib/GroupTheory/SchurZassenhaus.lean +++ b/Mathlib/GroupTheory/SchurZassenhaus.lean @@ -286,8 +286,7 @@ private theorem exists_right_complement'_of_coprime_aux' [Fintype G] (hG : Finty theorem exists_right_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' N H := exists_right_complement'_of_coprime_aux' rfl hN -#align subgroup.exists_right_complement'_of_coprime_of_fintype - Subgroup.exists_right_complement'_of_coprime_of_fintype +#align subgroup.exists_right_complement'_of_coprime_of_fintype Subgroup.exists_right_complement'_of_coprime_of_fintype /-- **Schur-Zassenhaus** for normal subgroups: If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a @@ -318,8 +317,7 @@ theorem exists_right_complement'_of_coprime {N : Subgroup G} [N.Normal] theorem exists_left_complement'_of_coprime_of_fintype [Fintype G] {N : Subgroup G} [N.Normal] (hN : Nat.coprime (Fintype.card N) N.index) : ∃ H : Subgroup G, IsComplement' H N := Exists.imp (fun _ => IsComplement'.symm) (exists_right_complement'_of_coprime_of_fintype hN) -#align subgroup.exists_left_complement'_of_coprime_of_fintype - Subgroup.exists_left_complement'_of_coprime_of_fintype +#align subgroup.exists_left_complement'_of_coprime_of_fintype Subgroup.exists_left_complement'_of_coprime_of_fintype /-- **Schur-Zassenhaus** for normal subgroups: If `H : Subgroup G` is normal, and has order coprime to its index, then there exists a diff --git a/Mathlib/GroupTheory/Transfer.lean b/Mathlib/GroupTheory/Transfer.lean index adba0a7ee8837..d60a504a9377f 100644 --- a/Mathlib/GroupTheory/Transfer.lean +++ b/Mathlib/GroupTheory/Transfer.lean @@ -144,8 +144,7 @@ theorem transfer_eq_prod_quotient_orbitRel_zpowers_quot [FiniteIndex H] (g : G) · intro k hk simp only [if_neg hk, inv_mul_self] exact map_one ϕ -#align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot - MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot +#align monoid_hom.transfer_eq_prod_quotient_orbit_rel_zpowers_quot MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot /-- Auxiliary lemma in order to state `transfer_eq_pow`. -/ theorem transfer_eq_pow_aux (g : G) diff --git a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean index 90c66bbc7c404..0ee41a10e2927 100644 --- a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean +++ b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean @@ -1836,8 +1836,7 @@ theorem _root_.StronglyMeasurable.apply_continuousLinearMap {_m : MeasurableSpac theorem apply_continuousLinearMap {φ : α → F →L[𝕜] E} (hφ : AEStronglyMeasurable φ μ) (v : F) : AEStronglyMeasurable (fun a => φ a v) μ := (ContinuousLinearMap.apply 𝕜 E v).continuous.comp_aestronglyMeasurable hφ -#align measure_theory.ae_strongly_measurable.apply_continuous_linear_map -MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap +#align measure_theory.ae_strongly_measurable.apply_continuous_linear_map MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap theorem _root_.ContinuousLinearMap.aestronglyMeasurable_comp₂ (L : E →L[𝕜] F →L[𝕜] G) {f : α → E} {g : α → F} (hf : AEStronglyMeasurable f μ) (hg : AEStronglyMeasurable g μ) : @@ -1896,8 +1895,7 @@ protected noncomputable def mk (f : α → β) (hf : AEFinStronglyMeasurable f theorem finStronglyMeasurable_mk (hf : AEFinStronglyMeasurable f μ) : FinStronglyMeasurable (hf.mk f) μ := hf.choose_spec.1 -#align measure_theory.ae_fin_strongly_measurable.fin_strongly_measurable_mk -MeasureTheory.AEFinStronglyMeasurable.finStronglyMeasurable_mk +#align measure_theory.ae_fin_strongly_measurable.fin_strongly_measurable_mk MeasureTheory.AEFinStronglyMeasurable.finStronglyMeasurable_mk theorem ae_eq_mk (hf : AEFinStronglyMeasurable f μ) : f =ᵐ[μ] hf.mk f := hf.choose_spec.2 diff --git a/Mathlib/RingTheory/IntegralClosure.lean b/Mathlib/RingTheory/IntegralClosure.lean index 578093a8951d7..18a6faa950b70 100644 --- a/Mathlib/RingTheory/IntegralClosure.lean +++ b/Mathlib/RingTheory/IntegralClosure.lean @@ -720,8 +720,7 @@ theorem normalizeScaleRoots_coeff_mul_leadingCoeff_pow (i : ℕ) (hp : 1 ≤ nat apply Nat.le_pred_of_lt rw [lt_iff_le_and_ne] exact ⟨le_natDegree_of_ne_zero h₁, h₂⟩ -#align normalize_scale_roots_coeff_mul_leading_coeff_pow - normalizeScaleRoots_coeff_mul_leadingCoeff_pow +#align normalize_scale_roots_coeff_mul_leading_coeff_pow normalizeScaleRoots_coeff_mul_leadingCoeff_pow theorem leadingCoeff_smul_normalizeScaleRoots (p : R[X]) : p.leadingCoeff • normalizeScaleRoots p = scaleRoots p p.leadingCoeff := by diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain.lean b/Mathlib/RingTheory/UniqueFactorizationDomain.lean index d38481b7a0b45..353d41a21dada 100644 --- a/Mathlib/RingTheory/UniqueFactorizationDomain.lean +++ b/Mathlib/RingTheory/UniqueFactorizationDomain.lean @@ -986,8 +986,7 @@ theorem multiplicity_eq_count_normalizedFactors [DecidableEq R] {a b : R} (ha : le_multiplicity_iff_replicate_le_normalizedFactors ha hb, ← le_count_iff_replicate_le] simp rw [le_multiplicity_iff_replicate_le_normalizedFactors ha hb, ← le_count_iff_replicate_le] -#align unique_factorization_monoid.multiplicity_eq_count_normalized_factors - UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors +#align unique_factorization_monoid.multiplicity_eq_count_normalized_factors UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors /-- The number of times an irreducible factor `p` appears in `normalizedFactors x` is defined by diff --git a/Mathlib/Topology/Connected.lean b/Mathlib/Topology/Connected.lean index a6c194b7ee709..c998cae168f39 100644 --- a/Mathlib/Topology/Connected.lean +++ b/Mathlib/Topology/Connected.lean @@ -1146,8 +1146,7 @@ theorem locallyConnectedSpace_iff_open_connected_subsets : · exact fun h => ⟨fun U => ⟨fun hU => let ⟨V, hVU, hV⟩ := h U hU ⟨V, hV, hVU⟩, fun ⟨V, ⟨hV, hxV, _⟩, hVU⟩ => mem_nhds_iff.mpr ⟨V, hVU, hV, hxV⟩⟩⟩ -#align locally_connected_space_iff_open_connected_subsets - locallyConnectedSpace_iff_open_connected_subsets +#align locally_connected_space_iff_open_connected_subsets locallyConnectedSpace_iff_open_connected_subsets /-- A space with discrete topology is a locally connected space. -/ instance (priority := 100) DiscreteTopology.toLocallyConnectedSpace (α) [TopologicalSpace α] @@ -1196,8 +1195,7 @@ theorem locallyConnectedSpace_iff_connectedComponentIn_open : (connectedComponentIn_subset _ _).trans interior_subset, h _ isOpen_interior x _, mem_connectedComponentIn _, isConnected_connectedComponentIn_iff.mpr _⟩ <;> exact mem_interior_iff_mem_nhds.mpr hU -#align locally_connected_space_iff_connected_component_in_open - locallyConnectedSpace_iff_connectedComponentIn_open +#align locally_connected_space_iff_connected_component_in_open locallyConnectedSpace_iff_connectedComponentIn_open theorem locallyConnectedSpace_iff_connected_subsets : LocallyConnectedSpace α ↔ ∀ (x : α), ∀ U ∈ 𝓝 x, ∃ V ∈ 𝓝 x, IsPreconnected V ∧ V ⊆ U := by @@ -1348,14 +1346,12 @@ theorem Continuous.image_connectedComponent_eq_singleton {β : Type _} [Topologi f '' connectedComponent a = {f a} := (Set.subsingleton_iff_singleton <| mem_image_of_mem f mem_connectedComponent).mp (isPreconnected_connectedComponent.image f h.continuousOn).subsingleton -#align continuous.image_connected_component_eq_singleton - Continuous.image_connectedComponent_eq_singleton +#align continuous.image_connected_component_eq_singleton Continuous.image_connectedComponent_eq_singleton theorem isTotallyDisconnected_of_totallyDisconnectedSpace [TotallyDisconnectedSpace α] (s : Set α) : IsTotallyDisconnected s := fun t _ ht => TotallyDisconnectedSpace.isTotallyDisconnected_univ _ t.subset_univ ht -#align is_totally_disconnected_of_totally_disconnected_space - isTotallyDisconnected_of_totallyDisconnectedSpace +#align is_totally_disconnected_of_totally_disconnected_space isTotallyDisconnected_of_totallyDisconnectedSpace theorem isTotallyDisconnected_of_image [TopologicalSpace β] {f : α → β} (hf : ContinuousOn f s) (hf' : Injective f) (h : IsTotallyDisconnected (f '' s)) : IsTotallyDisconnected s :=