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chore: fix align linebreaks (#5683)
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The result of running
```
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;
```
Hopefully for the last time...




Co-authored-by: Moritz Firsching <firsching@google.com>
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mo271 and mo271 committed Jul 3, 2023
1 parent 15cdb8e commit 2a70296
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Showing 11 changed files with 18 additions and 36 deletions.
3 changes: 1 addition & 2 deletions Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
Expand Up @@ -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
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6 changes: 2 additions & 4 deletions Mathlib/Analysis/SpecialFunctions/Complex/Log.lean
Expand Up @@ -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
Expand All @@ -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
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3 changes: 1 addition & 2 deletions Mathlib/CategoryTheory/Endofunctor/Algebra.lean
Expand Up @@ -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 :=
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3 changes: 1 addition & 2 deletions Mathlib/Data/Finset/Basic.lean
Expand Up @@ -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 _⟩⟩
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6 changes: 2 additions & 4 deletions Mathlib/Data/Set/Ncard.lean
Expand Up @@ -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
Expand All @@ -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
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6 changes: 2 additions & 4 deletions Mathlib/GroupTheory/SchurZassenhaus.lean
Expand Up @@ -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
Expand Down Expand Up @@ -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
Expand Down
3 changes: 1 addition & 2 deletions Mathlib/GroupTheory/Transfer.lean
Expand Up @@ -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)
Expand Down
6 changes: 2 additions & 4 deletions Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
Expand Up @@ -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) :
Expand Down Expand Up @@ -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
Expand Down
3 changes: 1 addition & 2 deletions Mathlib/RingTheory/IntegralClosure.lean
Expand Up @@ -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
Expand Down
3 changes: 1 addition & 2 deletions Mathlib/RingTheory/UniqueFactorizationDomain.lean
Expand Up @@ -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
Expand Down
12 changes: 4 additions & 8 deletions Mathlib/Topology/Connected.lean
Expand Up @@ -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]
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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 :=
Expand Down

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