file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Topology/Covering.lean | IsEvenlyCovered.mem_toTrivialization_baseSet | [] | [
52,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_add_aleph | [
{
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"tactic": "rw [Cardinal.add_eq_max (aleph0_le_aleph o₁), max_aleph_eq]"
}
] | [
853,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.le_rpow_one_div_iff | [
{
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"tactic": "nth_rw 1 [← rpow_one x]"
},
{
"state_after": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ (z * z⁻¹) ≤ y ^ (1 / z) ↔ x ^ z ≤ y",... | [
584,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
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Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_cofinite_zero_of_summable | [
{
"state_after": "α : Type u_1\nf : α → ℝ≥0\nhf : Summable fun a => ↑(f a)\n⊢ Tendsto (fun a => ↑(f a)) cofinite (𝓝 ↑0)",
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"tactic": "simp only [← summable_coe, ← tendsto_coe] at hf ⊢"
},
{
"state_after": ... | [
238,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderiv_const | [
{
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1094,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.neg | [
{
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1025,
54
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1024,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.prod_le_iff | [
{
"state_after": "case mp\nM : Type u_1\nN : Type u_2\nP : Type ?u.111775\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.111796\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\ns : Submonoid M\nt : Submonoid N\nu : Submonoid (M × N)\n⊢ prod s t ≤ u → ... | [
994,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
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Mathlib/Combinatorics/Composition.lean | Composition.one_le_blocks | [] | [
180,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_seq_iff | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
137,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt | [] | [
696,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
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Mathlib/Analysis/Convex/Slope.lean | StrictConcaveOn.slope_anti_adjacent | [
{
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"state... | [
101,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.evaln_sound | [
{
"state_after": "no goals",
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},
{
"state_after": "case zero.intro\nk : ℕ\nc : Code\nn✝ x✝ : ℕ\nh✝ : x✝ ∈ evaln (k + 1) c n✝\nn x : ℕ\nleft✝ : n ≤ k\nh : pure 0 = some x\n⊢ x ∈ pure 0 n\n\nc... | [
857,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge | [] | [
390,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizerComparison_map_desc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nX Y : C\nf g : X ⟶ Y\nD : Type u₂\ninst✝² : Category D\nG : C ⥤ D\ninst✝¹ : HasCoequalizer f g\ninst✝ : HasCoequalizer (G.map f) (G.map g)\nZ : C\nh : Y ⟶ Z\nw : f ≫ h = g ≫ h\n⊢ G.map f ≫ G.map h = G.map g ≫ G.map h",
"tacti... | [
1158,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.continuous_of_continuous_comp | [
{
"state_after": "𝕜 : Type ?u.514785\n𝕜₂ : Type ?u.514788\n𝕝 : Type u_5\n𝕝₂ : Type u_1\nE : Type u_4\nF : Type u_2\nG : Type ?u.514803\nι : Type ?u.514806\nι' : Type u_3\ninst✝¹⁷ : NontriviallyNormedField 𝕜\ninst✝¹⁶ : AddCommGroup E\ninst✝¹⁵ : Module 𝕜 E\ninst✝¹⁴ : NormedField 𝕝\ninst✝¹³ : Module 𝕝 E\ni... | [
616,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_submonoid | [] | [
341,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
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Mathlib/RingTheory/Subring/Pointwise.lean | Subring.smul_mem_pointwise_smul | [] | [
78,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.iSup_restrict_spanningSets | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.731158\nγ : Type ?u.731161\nδ : Type ?u.731164\nι : Type ?u.731167\nR : Type ?u.731170\nR' : Type ?u.731173\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set... | [
3537,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3532,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.zero_smul_set_subset | [] | [
815,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
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Mathlib/Data/Multiset/Functor.lean | Multiset.map_comp_coe | [
{
"state_after": "case h\nF : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommApplicative F\nα' β' : Type u\nf : α' → F β'\nα β : Type u_1\nh : α → β\nx✝ : List α\n⊢ (Functor.map h ∘ Coe.coe) x✝ = (Coe.coe ∘ Functor.map h) x✝",
"state_before": "F : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommA... | [
100,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.flatten_equiv | [
{
"state_after": "case h1\nα : Type u\nβ : Type v\nγ : Type w\nc : Computation (WSeq α)\ns : WSeq α\nh : s ∈ c\n⊢ flatten (Computation.pure s) ~ʷ s\n\ncase h2\nα : Type u\nβ : Type v\nγ : Type w\nc : Computation (WSeq α)\ns : WSeq α\nh : s ∈ c\n⊢ ∀ (s_1 : Computation (WSeq α)), flatten s_1 ~ʷ s → flatten (Compu... | [
1153,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
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Mathlib/AlgebraicTopology/ExtraDegeneracy.lean | CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_base | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\nf : Arrow C\ninst✝ : ∀ (n : ℕ), HasWidePullback f.right (fun x => f.left) fun x => f.hom\nS : SplitEpi f.hom\nn : ℕ\n⊢ (s f S n ≫ WidePullback.base fun x => f.hom) = WidePullback.base fun x => f.hom",
"tactic": "apply WideP... | [
302,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.one_rmatch_iff | [
{
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"tactic": "induction x <;> simp [rmatch, matchEpsilon, *]"
}
] | [
224,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_div | [
{
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"tactic": "rw [division_def, sqrt_mul hx, sqrt_inv, division_def]"
}
] | [
411,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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Mathlib/Topology/Basic.lean | topologicalSpace_eq | [] | [
115,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | quotient_norm_neg | [
{
"state_after": "M : Type u_1\nN : Type ?u.81421\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nx : M ⧸ S\n⊢ sInf (norm '' {m | ↑m = -x}) = sInf (norm '' {m | ↑m = x})",
"state_before": "M : Type u_1\nN : Type ?u.81421\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : Se... | [
146,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | Odd.zpow_pos_iff | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : LinearOrderedField α\na b c d : α\nn k : ℤ\nhk : n = 2 * k + 1\n⊢ 0 < a ^ n ↔ 0 < a",
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"tactic": "cases' hn with k hk"
},
{
"state... | [
202,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.singularPart_add | [
{
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"state_before": "α... | [
299,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_source_mem_nhds | [
{
"state_after": "no goals",
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819,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_one_div_of_neg | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\nha : a < 0\nhb : b < 0\n⊢ (∫ (x : ℝ) in a..b, 1 / x) = Real.log (b / a)",
"tactic": "simp only [one_div, integral_inv_of_neg ha hb]"
}
] | [
452,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.continuousAt_coe | [
{
"state_after": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nY : Type u_1\ninst✝ : TopologicalSpace Y\nf : OnePoint X → Y\nx : X\n⊢ Tendsto (f ∘ some) (𝓝 x) (𝓝 (f ↑x)) ↔ Tendsto (f ∘ some) (𝓝 x) (𝓝 ((f ∘ some) x))",
"state_before": "X : Type u_2\ninst✝¹ : TopologicalSpac... | [
386,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Order/Heyting/Basic.lean | le_compl_compl | [] | [
899,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_conjTranspose | [
{
"state_after": "no goals",
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160,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumArrowEquivProdArrow_apply_snd | [] | [
886,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
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Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhds | [] | [
345,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.symm_injective | [
{
"state_after": "no goals",
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"tactic": "rw [← e.symm_symm, h, e'.symm_symm]"
}
] | [
885,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_sub_le | [
{
"state_after": "no goals",
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877,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.neg_quot | [
{
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... | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_zero | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Convex.toCone_isLeast | [
{
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"state_before": "𝕜 : T... | [
680,
30
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677,
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Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_one | [] | [
736,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
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Mathlib/Order/LiminfLimsup.lean | Filter.sdiff_liminf | [
{
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1044,
82
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1042,
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_sdiff_sub | [
{
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540,
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536,
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Mathlib/Algebra/Order/Floor.lean | Nat.one_le_floor_iff | [
{
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}
] | [
206,
54
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205,
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Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv | [
{
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] | [
45,
80
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.subsingleton_or_norm_symm_pos | [
{
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1976,
26
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1970,
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_one | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.le_TFAE | [
{
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"state_before": "ι : Type... | [
164,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.fork_π_app_zero | [] | [
776,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
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Mathlib/Topology/Algebra/Order/LeftRight.lean | continuousWithinAt_Iio_iff_Iic | [] | [
44,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
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Mathlib/Order/MinMax.lean | min_lt_min | [] | [
223,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.blsub_lt_ord_lift_of_isRegular | [
{
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"tactic": "rwa [hc.cof_eq]"
}
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41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
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Mathlib/Deprecated/Group.lean | IsGroupHom.to_isMonoidHom | [] | [
288,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Topology/Sequences.lean | UniformSpace.compactSpace_iff_seqCompactSpace | [
{
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"tactic": "simp only [← isCompact_univ_iff, seqCompactSpace_iff, UniformSpace.isCompact_iff_isSeqCompact]"
}
] | [
399,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/Topology/Category/CompHaus/EffectiveEpi.lean | CompHaus.effectiveEpiFamily_tfae | [
{
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225,
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194,
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Mathlib/Logic/Basic.lean | forall_true_iff' | [] | [
719,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_smul_le | [
{
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21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.nat_cast_fst | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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Mathlib/Topology/Order/Basic.lean | interior_Ioo | [] | [
321,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.nonUniforms_mono | [] | [
217,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.one_lt_coe | [] | [
77,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_mul_assoc | [] | [
420,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
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Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Coalgebra.id_eq_id | [] | [
329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/CategoryTheory/Abelian/Homology.lean | homology.hom_to_ext | [
{
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187,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.le_iInf_add_iInf | [
{
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"state_before": "ι : Sort u_1\nι' : Sort u_2\ninst✝¹ : Nonempty ι\ninst✝ : Nonempty ι'\nf : ι ... | [
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29
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520,
1
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.gOne_def | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Topology/Instances/Rat.lean | Nat.closedEmbedding_coe_rat | [
{
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"state_before": "⊢ Pairwise fun x y => 1 ≤ dist ↑x ↑y",
"tactic": "simpa using Nat.pairwise_one_le_dist"
}
] | [
71,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_image_image | [] | [
2053,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2052,
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_iSup_right | [
{
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374,
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372,
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Mathlib/Algebra/Order/Pointwise.lean | csSup_div | [
{
"state_after": "no goals",
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165,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Topology/Algebra/UniformGroup.lean | CauchySeq.const_mul | [] | [
456,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.coeFn_compLp' | [] | [
955,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.le_def | [] | [
657,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_eq_zero_iff | [
{
"state_after": "α : Type ?u.357763\nβ : Type ?u.357766\nγ : Type ?u.357769\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\n⊢ IsEmpty (Quotient.out o).α ↔ o = 0",
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30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
1
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Colorable.cliqueFree | [
{
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"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn m : ℕ\nhc : Colorable G n\nhm : n < m\n⊢ CliqueFree G m",
"tactic": "by_c... | [
452,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
11
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_tensor_id | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\ninst✝² : MonoidalCategory C\nX Y : C\ninst✝¹ : HasRightDual X\ninst✝ : HasRightDual Y\nf : X ⟶ Y\n⊢ (𝟙 Yᘁ ⊗ η_ X Xᘁ ≫ (f ⊗ 𝟙 Xᘁ)) ≫ (α_ Yᘁ Y Xᘁ).inv ≫ (ε_ Y Yᘁ ⊗ 𝟙 Xᘁ) ≫ (λ_ Xᘁ).hom =\n (ρ_ Yᘁ).hom ≫ (ρ_ Yᘁ).inv ≫ (𝟙 Yᘁ ⊗ η_ X Xᘁ) ≫ (𝟙 Yᘁ ⊗ f ⊗ 𝟙 Xᘁ) ... | [
486,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.continuous_mass | [
{
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"state_befo... | [
484,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.le_prod_nonempty_of_submultiplicative_on_pred | [
{
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49,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
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] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_normalize_iff | [
{
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"tactic": "simp"
}
] | [
259,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_eq_range | [] | [
432,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
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Mathlib/Data/Int/Interval.lean | Int.Ioc_eq_finset_map | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/Data/Vector/Mem.lean | Vector.mem_iff_get | [
{
"state_after": "α : Type u_1\nβ : Type ?u.160\nn : ℕ\na a' : α\nv : Vector α n\n⊢ (∃ i h, List.get (toList v) { val := i, isLt := h } = a) ↔\n ∃ i h, List.get (toList v) (↑(Fin.cast (_ : n = List.length (toList v))) { val := i, isLt := h }) = a",
"state_before": "α : Type u_1\nβ : Type ?u.160\nn : ℕ\na... | [
38,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
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Std/Data/List/Lemmas.lean | List.get_mem | [] | [
527,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
525,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_ι_app_none | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
1871,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1870,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegrable_iff_integrable_Ioc_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.462744\n𝕜 : Type ?u.462747\nE : Type u_1\nF : Type ?u.462753\nA : Type ?u.462756\ninst✝ : NormedAddCommGroup E\nf : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhab : a ≤ b\n⊢ IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b)",
"tactic": "rw... | [
96,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/Height.lean | Set.nil_mem_subchain | [] | [
68,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/Convex/Segment.lean | mem_segment_iff_sameRay | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.214396\nG : Type ?u.214399\nι : Type ?u.214402\nπ : ι → Type ?u.214407\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx y z : E\nh : SameRay 𝕜 (x - y) (z - x)\n⊢ x ∈ [y-[𝕜]z]",
"state_before": "𝕜 : Type u_2\nE : Ty... | [
380,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Control/Fold.lean | Traversable.foldrm_toList | [
{
"state_after": "α β γ : Type u\nt : Type u → Type u\ninst✝³ : Traversable t\ninst✝² : IsLawfulTraversable t\nm : Type u → Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → β → m β\nx : β\nxs : t α\n⊢ foldrm f x xs = ↑(foldrM.ofFreeMonoid f) (↑FreeMonoid.ofList (toList xs)) x",
"state_before": "α β ... | [
420,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.exists_succAbove_eq_iff | [
{
"state_after": "n m : ℕ\nx y : Fin (n + 1)\n⊢ (∃ z, ↑(succAbove x) z = y) → y ≠ x",
"state_before": "n m : ℕ\nx y : Fin (n + 1)\n⊢ (∃ z, ↑(succAbove x) z = y) ↔ y ≠ x",
"tactic": "refine' ⟨_, exists_succAbove_eq⟩"
},
{
"state_after": "case intro\nn m : ℕ\nx : Fin (n + 1)\ny : Fin n\n⊢ ↑(succAb... | [
2164,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2161,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_single | [] | [
302,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.StronglyMeasurable.integral_prod_right' | [
{
"state_after": "α : Type u_2\nα' : Type ?u.2378632\nβ : Type u_1\nβ' : Type ?u.2378638\nγ : Type ?u.2378641\nE : Type u_3\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MeasurableSpace α'\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : MeasurableSpace β'\ninst✝⁴ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Measu... | [
130,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_eq_prod_fintype | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝ : CommMonoid γ\nv : Π₀ (i : ι), β i\nf : (i : ι) → β i → γ\nhf : ∀ (i : ι), f i 0 = 1\n⊢ ∏... | [
1857,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1849,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.neg_right | [
{
"state_after": "α : Type u_2\nβ : Type ?u.628486\nm : MeasurableSpace α\nL : Type ?u.628492\nM : Type u_3\nN✝ : Type ?u.628498\ninst✝⁸ : AddCommMonoid L\ninst✝⁷ : TopologicalSpace L\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : AddCommMonoid N✝\ninst✝³ : TopologicalSpace N✝\nv✝ : VectorMeas... | [
1124,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.Coprime.gcd_mul_left_cancel | [
{
"state_after": "m n k : ℕ+\nh : Coprime k n\n⊢ gcd (k * m) n = gcd m n",
"state_before": "m n k : ℕ+\n⊢ Coprime k n → gcd (k * m) n = gcd m n",
"tactic": "intro h"
},
{
"state_after": "case a\nm n k : ℕ+\nh : Coprime k n\n⊢ ↑(gcd (k * m) n) = ↑(gcd m n)",
"state_before": "m n k : ℕ+\nh : C... | [
210,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_of_fact_finrank_eq_two | [] | [
744,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
src/lean/Init/SimpLemmas.lean | beq_self_eq_true | [] | [
148,
98
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
148,
9
] |
Mathlib/Algebra/Hom/Commute.lean | SemiconjBy.map | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝² : Mul M\ninst✝¹ : Mul N\na x y : M\ninst✝ : MulHomClass F M N\nh : SemiconjBy a x y\nf : F\n⊢ SemiconjBy (↑f a) (↑f x) (↑f y)",
"tactic": "simpa only [SemiconjBy, map_mul] using congr_arg f h"
}
] | [
27,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
11
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | span_singleton_dvd_span_singleton_iff_dvd | [] | [
1414,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.embDomain_mapRange | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.236087\nι : Type ?u.236090\nM : Type u_3\nM' : Type ?u.236096\nN : Type u_4\nP : Type ?u.236102\nG : Type ?u.236105\nH : Type ?u.236108\nR : Type ?u.236111\nS : Type ?u.236114\ninst✝¹ : Zero M\ninst✝ : Zero N\nf : α ↪ β\ng : M → N\np : α →₀ M\nhg... | [
891,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Data/Rat/Cast.lean | eq_ratCast | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\nι : Type ?u.81845\nα : Type ?u.81848\nβ : Type ?u.81851\nk : Type u_1\ninst✝¹ : DivisionRing k\ninst✝ : RingHomClass F ℚ k\nf : F\nr : ℚ\n⊢ ↑f r = ↑r",
"tactic": "rw [← map_ratCast f, Rat.cast_id]"
}
] | [
444,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
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