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/Order/Max.lean | IsMin.eq_of_le | [] | [
386,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
11
] |
Mathlib/Analysis/NormedSpace/DualNumber.lean | DualNumber.exp_smul_eps | [
{
"state_after": "no goals",
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"tactic": "rw [eps, ← inr_smul, exp_inr, ... | [
43,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Std/Data/Int/Lemmas.lean | Int.negSucc_ne_zero | [] | [
76,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
76,
9
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Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_ciInf | [] | [
262,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.dNext_succ_chainComplex | [
{
"state_after": "ι : Type ?u.303893\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf✝ g : C ⟶ D\nh k : D ⟶ E\ni✝ : ι\nP Q : ChainComplex V ℕ\nf : (i j : ℕ) → X P i ⟶ X Q j\ni : ℕ\n⊢ d P (i + 1) (ComplexShape.next (ComplexShape.down ℕ) (i + 1)) ≫\n ... | [
474,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
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Mathlib/Topology/Instances/NNReal.lean | NNReal.hasSum_nat_add_iff | [
{
"state_after": "α : Type ?u.37164\nf : ℕ → ℝ≥0\nk : ℕ\na : ℝ≥0\n⊢ HasSum (fun n => ↑(f n)) (↑a + ∑ i in Finset.range k, ↑(f i)) ↔ HasSum f (a + ∑ i in Finset.range k, f i)",
"state_before": "α : Type ?u.37164\nf : ℕ → ℝ≥0\nk : ℕ\na : ℝ≥0\n⊢ HasSum (fun n => f (n + k)) a ↔ HasSum f (a + ∑ i in Finset.range... | [
220,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.iInf_eq | [
{
"state_after": "α : Type u_2\nβ : Type ?u.72956\nγ : Type u_1\nι : Type u_3\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\nu : ι → UniformSpace γ\n⊢ (⨅ (s : Set α) (_ : s ∈ 𝔖) (i : ι), UniformSpace.comap (restrict s) (UniformFun.uniformSpace (↑s) γ)) =\n ⨅ (i : ι)... | [
733,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
11
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.injective_trop | [] | [
144,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_mono | [] | [
114,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.contSupp_comp | [] | [
1881,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
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Mathlib/Analysis/Convex/Join.lean | convexJoin_union_left | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.38083\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns t✝ s₁✝ s₂✝ t₁ t₂ u : Set E\nx y : E\ns₁ s₂ t : Set E\n⊢ convexJoin 𝕜 (s₁ ∪ s₂) t = convexJoin 𝕜 s₁ t ∪ convexJoin 𝕜 s₂ t",
"tacti... | [
86,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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src/lean/Init/SimpLemmas.lean | forall_congr | [] | [
42,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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1
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Mathlib/Topology/NhdsSet.lean | bUnion_mem_nhdsSet | [] | [
56,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.liftOn_zero | [
{
"state_after": "no goals",
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1844,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1843,
1
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Mathlib/Algebra/Invertible.lean | mul_invOf_mul_self_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Monoid α\na b : α\ninst✝ : Invertible b\n⊢ a * ⅟b * b = a",
"tactic": "simp [mul_assoc]"
}
] | [
139,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Logic/Basic.lean | forall_or_left | [] | [
848,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.toZNum_succ | [] | [
1240,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.wellFounded_characterisations | [
{
"state_after": "case tfae_1_to_2\nι : Sort ?u.77139\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\n⊢ (WellFounded fun x x_1 => x > x_1) → IsSupFiniteCompact α\n\nι : Sort ?u.77139\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\ntfae_1_to_2 : (WellFounded fun x x_1 => x > x_1) → IsSupFiniteCompact α... | [
276,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Std/Data/List/Lemmas.lean | List.filterMap_cons | [] | [
1154,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1150,
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.comp_assoc | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Order/Filter/Extr.lean | isMinOn_iff | [] | [
135,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_subset | [] | [
594,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.join_map_ret | [
{
"state_after": "case H\nα : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ ∀ (s : Seq α),\n BisimO (fun s1 s2 => ∃ s, s1 = Seq.join (Seq.map ret s) ∧ s2 = s) (destruct (Seq.join (Seq.map ret s))) (destruct s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ Seq.join (Seq.map ret s) = s... | [
969,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
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Mathlib/Data/Real/Irrational.lean | Irrational.of_pow | [
{
"state_after": "q : ℚ\nx y : ℝ\nh : Irrational 1\n⊢ Irrational x",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational (x ^ 0)\n⊢ Irrational x",
"tactic": "rw [pow_zero] at h"
},
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational 1\n⊢ Irrational x",
"tactic": "exa... | [
480,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Set/Function.lean | Set.InjOn.comp | [] | [
664,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.exists_dvd_of_not_prime2 | [] | [
458,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.apply_symm_apply | [] | [
2037,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2036,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.typevecCasesCons₂_appendFun | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/Set/Semiring.lean | SetSemiring.up_le_up | [] | [
76,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrable_indicatorConstLp | [
{
"state_after": "α : Type u_2\nβ : Type ?u.1643027\nE✝ : Type ?u.1643030\nF : Type ?u.1643033\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E✝\nf g : α → E✝\ns✝ t : Set α\nμ ν : Measure α\nE : Type u_1\ninst✝ : NormedAddCommGroup E\np : ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\nhμs : ↑↑μ s ≠ ⊤\nc : E\n... | [
287,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
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Mathlib/CategoryTheory/Products/Bifunctor.lean | CategoryTheory.Bifunctor.diagonal | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Category E\nF : C × D ⥤ E\nX X' : C\nf : X ⟶ X'\nY Y' : D\ng : Y ⟶ Y'\n⊢ F.map (𝟙 X, g) ≫ F.map (f, 𝟙 Y') = F.map (f, g)",
"tactic": "rw [← Functor.map_comp, prod_comp... | [
52,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | affineIndependent_iff_finrank_vectorSpan_eq | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\nι : Type u_1\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : Fintype ι\np : ι → P\nn : ℕ\nhc : Fintype.card ι = n + 1\nhn : Nonempty ι\n⊢ AffineIndependent k p ↔ finrank k { x // x ∈ vectorSpan ... | [
179,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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] |
Std/Data/Nat/Lemmas.lean | Nat.le_of_not_le | [] | [
35,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
35,
11
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.fork_ι_comp_cofork_π | [] | [
292,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | Continuous.clm_comp | [] | [
534,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
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] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubVSubWeights_apply_right | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type ?u.422233\nP : Type ?u.422236\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.422892\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni j : ι\nh : i ≠ j\n⊢ weightedVSubVS... | [
691,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolRing_symm_eq | [] | [
404,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformLeft_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CommGroup α\ne : α\nx : Finset α × Finset α\n⊢ mulEtransformLeft e⁻¹ x = Prod.swap (mulEtransformRight e (Prod.swap x))",
"tactic": "simp [-op_inv, op_smul_eq_smul, mulEtransformLeft, mulEtransformRight]"
}
] | [
193,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | StrictMono.mul_const | [] | [
590,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Init/CcLemmas.lean | imp_eq_of_eq_true_right | [] | [
55,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.inter_mem_iff | [] | [
164,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_sum | [] | [
982,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.restrict_scalars | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\ninst✝¹⁶ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁵ : NormedAddCommGroup D\ninst✝¹⁴ : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : NormedSpace 𝕜 F... | [
2220,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2217,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inv_smul_mem_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.829527\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.829536\ninst✝² : DecidableEq β\ninst✝¹ : Group α\ninst✝ : MulAction α β\ns t : Finset β\na : α\nb : β\n⊢ a⁻¹ • b ∈ s ↔ b ∈ a • s",
"tactic": "rw [← smul_mem_smul_finset_iff a, smul_inv_smul]"
}
] | [
1958,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1957,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst | [] | [
600,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_zero | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuousOn_inv | [] | [
205,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Icc | [] | [
143,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.sup_mem_subalgebra_closure | [
{
"state_after": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf g : { x // x ∈ A }\n⊢ 2⁻¹ • (↑f + ↑g + Abs.abs (↑f - ↑g)) ∈ Subalgebra.topologicalClosure A",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ ... | [
154,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Computability/Halting.lean | RePred.of_eq | [] | [
152,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.map_mul_left_ae | [] | [
301,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.mulVecLin_reindex | [] | [
243,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.nontrivial_of_char_ne_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : NonAssocSemiring R\nv : ℕ\nhv : v ≠ 1\nhr : CharP R v\nh : ↑1 = 0\n⊢ v = 1",
"tactic": "rwa [CharP.cast_eq_zero_iff _ v, Nat.dvd_one] at h"
}
] | [
604,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.not_bddAbove | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.22760\nγ : Type ?u.22763\nι : Sort ?u.22766\nκ : ι → Sort ?u.22771\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns : Set α\np : α → Prop\na✝ : α\ninst✝ : NoMaxOrder α\nhs : IsUpperSet s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ upperBounds s\n⊢ False",
"s... | [
328,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_ring | [] | [
534,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Algebra/Group/Commute.lean | inv_mul_cancel_comm_assoc | [] | [
430,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.null_of_frequently_le_of_frequently_ge | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.1791566\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
235,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientEquivAlgOfEq_symm | [
{
"state_after": "case h\nR : Type u\nS : Type v\nF : Type w\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\nR₁ : Type u_2\nR₂ : Type ?u.1696123\nA : Type u_1\nB : Type ?u.1696129\ninst✝⁶ : CommSemiring R₁\ninst✝⁵ : CommSemiring R₂\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : Algebra R₁ A\ninst✝¹ : Algebra R₂... | [
498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/CategoryTheory/Sites/InducedTopology.lean | CategoryTheory.LocallyCoverDense.inducedTopology_coverPreserving | [] | [
110,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_coe | [] | [
1804,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1803,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.zero_eq' | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
198,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.deterministic_apply' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type ?u.395518\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nf : α → β\nhf : Measurable f\na : α\ns : Set β\nhs : MeasurableSet s\n⊢ ↑↑(↑{ val := fun a => Measure.dirac (f a), property := (_ : Measurable fun a => Measure.dirac (f ... | [
363,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/List/Basic.lean | List.reverse_eq_nil | [] | [
638,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_pow_apply_nthLe | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.779543\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nh : Nodup l\nk : ℕ\nhk : k < length l\n⊢ ↑(formPerm l ^ Nat.zero) (nthLe l k hk) =\n nthLe l ((k + Nat.zero) % length l) (_ : (k + Nat.zero) % length l < length l)\n\ncase succ\nα : Type u_1\... | [
333,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.mkContinuous_norm_le' | [] | [
715,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.zpow | [
{
"state_after": "case ofNat\nα : Type u_1\nβ : Type ?u.46731\nE : Type ?u.46734\nF : Type ?u.46737\nG : Type ?u.46740\nE' : Type ?u.46743\nF' : Type ?u.46746\nG' : Type ?u.46749\nE'' : Type ?u.46752\nF'' : Type ?u.46755\nG'' : Type ?u.46758\nR : Type ?u.46761\nR' : Type ?u.46764\n𝕜 : Type u_2\n𝕜' : Type u_3\... | [
257,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_castSucc | [
{
"state_after": "case h\nn m n' : ℕ\nh : n + 1 = n' + 1\ni : Fin n\n⊢ ↑(↑(cast h) (↑castSucc i)) = ↑(↑castSucc (↑(cast (_ : n = n')) i))",
"state_before": "n m n' : ℕ\nh : n + 1 = n' + 1\ni : Fin n\n⊢ ↑(cast h) (↑castSucc i) = ↑castSucc (↑(cast (_ : n = n')) i)",
"tactic": "ext"
},
{
"state_aft... | [
1220,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_iInf | [] | [
1275,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | tendsto_norm_div_self_punctured_nhds | [] | [
2027,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2024,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.nonneg_smul_left | [] | [
156,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
src/lean/Init/Data/String/Extra.lean | String.Iterator.sizeOf_next_lt_of_atEnd | [] | [
44,
32
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
42,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.aut_one | [] | [
667,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | pow_orderOf_eq_one | [
{
"state_after": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nx : G\n⊢ x ^ minimalPeriod (fun x_1 => x * x_1) 1 = (fun x_1 => x ^ minimalPeriod (fun x_2 => x * x_2) 1 * x_1) 1",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Mono... | [
161,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.ediam_Ioo | [
{
"state_after": "case inl\nα : Type ?u.555240\nβ : Type ?u.555243\nγ : Type ?u.555246\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : b ≤ a\n⊢ EMetric.diam (Ioo a b) = ENNReal.ofReal (b - a)\n\ncase inr\nα : Type ?u.555240\nβ : Type ?u.555243\nγ : Type ?u.555246\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : a < b\n⊢... | [
1533,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | MulHom.eqOn_closure | [] | [
486,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | Units.sq_eq_sq_iff_eq_or_eq_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.134487\nM : Type ?u.134490\ninst✝¹ : CommRing R\ninst✝ : NoZeroDivisors R\na✝ b✝ : R\na b : Rˣ\n⊢ a ^ 2 = b ^ 2 ↔ a = b ∨ a = -b",
"tactic": "simp_rw [ext_iff, val_pow_eq_pow_val, sq_eq_sq_iff_eq_or_eq_neg, Units.val_neg]"
}
] | [
308,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
11
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.cancel_right | [] | [
816,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.smul_im | [] | [
378,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
9
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.abelian_derivedAbelianOfIdeal | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI✝ J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nI : LieIdeal R L\n⊢ IsLieAbelian\n { x //\n x ∈\n ↑(match derivedLengthOfIdeal R... | [
351,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_im_lt_abs | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ Abs.abs z.im < ↑abs z ↔ z.re ≠ 0",
"tactic": "simpa using @abs_re_lt_abs (z * I)"
}
] | [
1058,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasStrictDerivAt.const_smul | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : F... | [
127,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
8
] |
Mathlib/Data/FunLike/Basic.lean | FunLike.ext' | [] | [
172,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.measure_union₀' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.20428\nα : Type u_1\nβ : Type ?u.20434\nγ : Type ?u.20437\nm0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\nhs : NullMeasurableSet s\nhd : AEDisjoint μ s t\n⊢ ↑↑μ (s ∪ t) = ↑↑μ s + ↑↑μ t",
"tactic": "rw [union_comm, measure_union₀ hs (AEDisjoi... | [
340,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AlgHom.fieldRange_eq_map | [] | [
276,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.prod_map | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nι' : Type u_1\nα' : Type u_2\nβ' : Type u_3\ninst✝ : UniformSpace β'\nF' : ι' → α' → β'\nf' : α' → β'\nq : Filter ι'\nq' : Filter α'\n... | [
282,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | CategoryTheory.Functor.mapPresheaf_obj_X | [] | [
543,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Algebra/Ring/CompTypeclasses.lean | RingHomCompTriple.comp_apply | [] | [
67,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.monotone | [] | [
421,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.inv | [] | [
1311,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
11
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.isBigO | [] | [
87,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
8
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to0.tr_supports | [
{
"state_after": "case left\nΓ : Type u_2\ninst✝³ : Inhabited Γ\nΛ : Type u_1\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nM : Λ → Stmt₁\ninst✝ : Fintype σ\nS : Finset Λ\nss : TM1.Supports M S\n⊢ default ∈ ↑(trStmts M S)\n\ncase right\nΓ : Type u_2\ninst✝³ : Inhabited Γ\nΛ : Type u_1\ninst✝² : Inh... | [
1580,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Order/Bounds/Basic.lean | image2_upperBounds_lowerBounds_subset_lowerBounds_image2 | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Monotone (f a)\na : α\nb : β\nha : a ∈ upperBoun... | [
1524,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
] |
Mathlib/Data/Bool/Set.lean | Bool.compl_singleton | [] | [
36,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
9
] |
Mathlib/RingTheory/Bezout.lean | IsBezout.gcd_dvd_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsBezout R\nx y : R\n⊢ x ∈ {x, y}",
"tactic": "simp"
}
] | [
72,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_le | [] | [
33,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
33,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.ext | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nh : ∀ (x : X), x ∈ s₁ ↔ x ∈ s₂\n⊢ toList s₁ ~ toList s₂",
"tactic": "classical\nexact List.perm_of_nodup_nodup_toFinset_eq s₁.toList_nodup s₂.toList_nodup\n (Finset.... | [
326,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Order/PartialSups.lean | iSup_eq_iSup_of_partialSups_eq_partialSups | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nf g : ℕ → α\nh : partialSups f = partialSups g\n⊢ (⨆ (n : ℕ), f n) = ⨆ (n : ℕ), g n",
"tactic": "simp_rw [← iSup_partialSups_eq f, ← iSup_partialSups_eq g, h]"
}
] | [
193,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_univ | [] | [
1248,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.inverse_continuousOn | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.397883\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedSpace 𝕜 G\nG' : Type ?u.397986\... | [
418,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioc_eq_nhdsWithin_Ioi | [] | [
434,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
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