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/Init/Data/Ordering/Lemmas.lean | Ordering.ite_eq_gt_distrib | [
{
"state_after": "no goals",
"state_before": "c : Prop\ninst✝ : Decidable c\na b : Ordering\n⊢ ((if c then a else b) = gt) = if c then a = gt else b = gt",
"tactic": "by_cases c <;> simp [*]"
}
] | [
39,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_id | [] | [
370,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_add_of_pos_right | [] | [
90,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
89,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | tendsto_one_plus_div_rpow_exp | [
{
"state_after": "t : ℝ\n⊢ (exp ∘ fun x => x * log (1 + t / x)) =ᶠ[atTop] fun x => (1 + t / x) ^ x",
"state_before": "t : ℝ\n⊢ Tendsto (fun x => (1 + t / x) ^ x) atTop (𝓝 (exp t))",
"tactic": "apply ((Real.continuous_exp.tendsto _).comp (tendsto_mul_log_one_plus_div_atTop t)).congr' _"
},
{
"st... | [
621,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.FG.stablizes_of_iSup_eq | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nP : Type ?u.311147\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : M →ₗ[R] P\nM' : Submodule R M\nN : ℕ →o Submodule R M\nH : iSup ↑N = M'\nS : Finset M\nhS : span R ↑S = M'\n⊢ ∃ n, M... | [
388,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.rangeS_subtype | [] | [
1241,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_add_left | [
{
"state_after": "m n : Nat\n⊢ (match m - (m + n) with\n | 0 => ofNat (m + n - m)\n | succ k => -[k+1]) =\n ↑n",
"state_before": "m n : Nat\n⊢ subNatNat (m + n) m = ↑n",
"tactic": "unfold subNatNat"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ (match m - (m + n) wit... | [
116,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
114,
1
] |
Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.ad_ker_eq_bot_of_semisimple | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\ninst✝ : IsSemisimple R L\n⊢ LieHom.ker (ad R L) = ⊥",
"tactic": "simp"
}
] | [
121,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/Convex/Caratheodory.lean | Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull | [
{
"state_after": "𝕜 : Type u_1\nE : Type u\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nx : E\nhx : x ∈ ↑(convexHull 𝕜).toOrderHom s\nk : ℕ := card (minCardFinsetOfMemConvexHull hx) - 1\n⊢ AffineIndependent 𝕜 Subtype.val",
"state_before": "𝕜 : Type u_1\nE : T... | [
148,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | constant_of_derivWithin_zero | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.49446\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → E\na b : ℝ\nhdiff : DifferentiableOn ℝ f (Icc a b)\nhderiv : ∀ (x : ℝ), x ∈ Ico a b → derivWithin f (Icc a b) x = 0\nH : ∀ (x : ℝ), x ∈ Ico ... | [
409,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/Basic.lean | continuousAt_def | [] | [
1593,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1592,
1
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_inter_Ico_of_le | [] | [
217,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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] |
Mathlib/Analysis/Normed/Group/Basic.lean | AntilipschitzWith.mul_lipschitzWith | [
{
"state_after": "𝓕 : Type ?u.1208856\n𝕜 : Type ?u.1208859\nα : Type u_1\nι : Type ?u.1208865\nκ : Type ?u.1208868\nE : Type u_2\nF : Type ?u.1208874\nG : Type ?u.1208877\ninst✝² : SeminormedCommGroup E\ninst✝¹ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ninst✝ : PseudoEMetricSpace α\nK Kf Kg : ... | [
1898,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1887,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.sub_mulVec | [
{
"state_after": "no goals",
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1917,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1916,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Ici | [] | [
175,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_prod | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.191238\nι : Sort ?u.191241\nκ : ι → Sort ?u.191246\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns : Set α\nt : Set β\nx✝ : α × β\n⊢ x✝ ∈ ↑(upperClosure (s ×ˢ t)) ↔ x✝ ∈ ↑(upperClosure s ×ˢ upperClosure t)",
"state_before": "α : Type u_1\nβ : T... | [
1752,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1749,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_think | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\na : α\nf : Stream' (Option (Option α))\nal : IsSeq f\n⊢ a ∈ think { val := f, property := al } ↔ a ∈ { val := f, property := al }",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\n⊢ a ∈ think s ↔ a ∈ s",
"tactic": "ca... | [
932,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_toLinearEquiv | [] | [
72,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_exp | [] | [
33,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Order/RelClasses.lean | IsAsymm.swap | [] | [
88,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.prop_fst | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.eqOn | [] | [
357,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
11
] |
Mathlib/Data/Part.lean | Part.right_dom_of_mul_dom | [] | [
729,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_sum | [
{
"state_after": "case empty\nK : Type u_3\nL : Type u_2\nL' : Type ?u.104812\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Field L'\ninst✝² : Algebra K L\ninst✝¹ : Algebra K L'\nS : IntermediateField K L\nι : Type u_1\ninst✝ : Fintype ι\nf : ι → { x // x ∈ S }\n⊢ ↑(∑ i in ∅, f i) = ∑ i in ∅, ↑(f i)\n\ncase ins... | [
354,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRel.swap_lem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\ns1 : WSeq α\ns2 : WSeq β\nh✝ : LiftRel R s1 s2\ns : WSeq β\nt : WSeq α\nh : LiftRel R t s\n⊢ Computation.LiftRel (LiftRelO (swap R) (swap (LiftRel R))) (destruct s) (destruct t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR :... | [
559,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.hasFiniteIntegral | [] | [
461,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Order/Chain.lean | ChainClosure.isChain | [
{
"state_after": "case succ\nα : Type u_1\nβ : Type ?u.13781\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\ns✝ : Set α\na✝ : ChainClosure r s✝\na_ih✝ : IsChain r s✝\n⊢ IsChain r (SuccChain r s✝)\n\ncase union\nα : Type u_1\nβ : Type ?u.13781\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\ns✝ : ... | [
270,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.map_id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.135359\nγ : Type ?u.135362\ndec : DecidableEq α\na b : α\nR S : RegularExpression α\n⊢ map id (R + S) = R + S",
"tactic": "simp_rw [map, map_id]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u... | [
432,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.disjoint_iUnion₂_right | [] | [
2096,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2094,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.untop_one' | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.card_Ioo_finset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\n⊢ card (Ioo s t) = 2 ^ (card t - card s) - 2",
"tactic": "rw [card_Ioo_eq_card_Icc_sub_two, card_Icc_finset h]"
}
] | [
119,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.sInf_neBot_of_directed | [] | [
934,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformInducing_id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\n⊢ comap (fun x => (id x.fst, id x.snd)) (𝓤 α) = 𝓤 α",
"tactic": "rw [← Prod.map_def, Prod.map_id, comap_id]"
}
] | [
68,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.to_openEmbedding | [
{
"state_after": "case h₁\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.108605\nδ : Type ?u.108608\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\nh : e.source = univ\n⊢ Continuous ↑e\n\ncase h₂\nα ... | [
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74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.eq_generate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15440\nγ : Type ?u.15443\nι : Sort u_2\nι' : Sort ?u.15449\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nh : HasBasis l p s\n⊢ l = generate {U | ∃ i, p i ∧ s i = U}",
"tac... | [
328,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.empty_left | [] | [
155,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/CategoryTheory/SingleObj.lean | MonoidHom.comp_toFunctor | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | eq_intCast' | [] | [
250,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Opposites.lean | AddOpposite.op_inv | [] | [
412,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.union_mul_inter_subset | [] | [
774,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.not_top_le_coe | [] | [
659,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/CategoryTheory/Sites/InducedTopology.lean | CategoryTheory.LocallyCoverDense.pushforward_cover_iff_cover_pullback | [
{
"state_after": "case mp\nC : Type u_2\ninst✝⁴ : Category C\nD : Type u_4\ninst✝³ : Category D\nG : C ⥤ D\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nA : Type v\ninst✝² : Category A\ninst✝¹ : Full G\ninst✝ : Faithful G\nHld : LocallyCoverDense K G\nX : C\nS : Sieve X\n⊢ GrothendieckTopology.sieves... | [
70,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
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] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.finset_inf_coe | [
{
"state_after": "R : Type u_2\nS : Type ?u.133565\nM : Type u_3\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S M\ninst✝¹ : SMul S R\ninst✝ : IsScalarTower S R M\np✝ q : Submodule R M\nι : Type u_1\ns : Finset ι\np : ι → Submodule R M\nthis : Decidabl... | [
254,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.lt_nfp | [
{
"state_after": "f : Ordinal → Ordinal\na b : Ordinal\n⊢ a < (fun a => sup fun n => (f^[n]) a) b ↔ ∃ n, a < (f^[n]) b",
"state_before": "f : Ordinal → Ordinal\na b : Ordinal\n⊢ a < nfp f b ↔ ∃ n, a < (f^[n]) b",
"tactic": "rw [← sup_iterate_eq_nfp]"
},
{
"state_after": "no goals",
"state_be... | [
449,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
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Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.natDegree_pos | [
{
"state_after": "A : Type u_2\nB : Type u_1\nB' : Type ?u.58941\ninst✝³ : CommRing A\ninst✝² : Ring B\ninst✝¹ : Algebra A B\nx : B\ninst✝ : Nontrivial B\nhx : IsIntegral A x\n⊢ natDegree (minpoly A x) ≠ 0",
"state_before": "A : Type u_2\nB : Type u_1\nB' : Type ?u.58941\ninst✝³ : CommRing A\ninst✝² : Ring ... | [
194,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.symm_image_image | [] | [
79,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isLeast_csInf | [
{
"state_after": "α : Type u_1\nβ : Type ?u.69153\nγ : Type ?u.69156\nι : Sort ?u.69159\ninst✝¹ : ConditionallyCompleteLinearOrder α\ns t : Set α\na b : α\ninst✝ : IsWellOrder α fun x x_1 => x < x_1\nhs : Set.Nonempty s\n⊢ IsLeast s (argminOn id (_ : WellFounded fun x x_1 => x < x_1) s hs)",
"state_before":... | [
975,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.isIso_ι_of_isInitial | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nJ : Type u\ninst✝² : Category J\nj : J\nI : IsInitial j\nF : J ⥤ C\ninst✝¹ : HasColimit F\ninst✝ : ∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)\n⊢ colimit.ι F j ≫ colimit.desc F (coconeOfDiagramInitial I F) = 𝟙 (F.obj j)",
"state_before": "C : Type u₁\ninst✝³... | [
748,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.nonpos_iff_eq_zero' | [] | [
1091,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bfamilyOfFamily_typein | [] | [
1150,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_mono | [] | [
165,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.eq_iff | [] | [
230,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.bijective_iff_has_inverse | [] | [
512,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Computability/Partrec.lean | Nat.Partrec.prec' | [
{
"state_after": "no goals",
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215,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.degree_add_divByMonic | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\nhq : Monic q\nh : degree q ≤ degree p\n✝ : Nontrivial R\n⊢ degree q + degree (p /ₘ q) = degree p",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRi... | [
281,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measure_mul_measure_eq | [
{
"state_after": "G : Type u_1\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : Group G\ninst✝⁵ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝⁴ : SigmaFinite ν\ninst✝³ : SigmaFinite μ\ns✝ : Set G\ninst✝² : MeasurableInv G\ninst✝¹ : IsMulLeftInvariant μ\ninst✝ : IsMulLeftInvariant ν\ns t : Set G\nhs : MeasurableSet s\nht : Mea... | [
348,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.ext | [] | [
662,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.smul_toInvSubmonoid | [
{
"state_after": "case h.e'_2.h.e\nR : Type u_1\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.131549\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\nm : { x // x ∈ M }\n⊢ HSMul.hSMul m = HMul.hMul (↑(algebraMap R S) ↑m)",
"state_before": "R : T... | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformEmbedding_translate_mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.112462\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\na : α\n⊢ 𝓤 α = 𝓤 α\n\nα : Type u_1\nβ : Type ?u.112462\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\na : α\n⊢ Function.Injective fun x => (x.fst * a, x.snd * a)",
"s... | [
189,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.val_eq_coe | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/List/MinMax.lean | List.argAux_self | [] | [
67,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_ofEq_apply | [] | [
1179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_add_distrib' | [] | [
894,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.mapsTo_compl | [] | [
877,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map_eq_lift | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\nf : α → β\nx✝ y : FreeGroup α\nx : α\n⊢ ↑(↑lift (of ∘ f)) (of x) = of (f x)",
"tactic": "simp"
}
] | [
848,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.pointwise_smul_le_iff | [] | [
434,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_erase | [] | [
1860,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1859,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ppow_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\n⊢ ppow f 0 = ↑ζ",
"tactic": "rw [ppow, dif_pos rfl]"
}
] | [
551,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.dart_card_eq_sum_degrees | [
{
"state_after": "V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype (Sym2 V)\nthis : DecidableEq V\n⊢ Fintype.card (Dart G) = ∑ v : V, degree G v",
"state_before": "V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype (... | [
81,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.combo_interior_closure_subset_interior | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.39791\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\na b : 𝕜\nh... | [
125,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.right_le_opow | [] | [
177,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_inv_cancel_right_of_invertible | [] | [
356,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsSeparable.image | [
{
"state_after": "case intro.intro\nα : Type u\nt : TopologicalSpace α\nβ : Type u_1\ninst✝ : TopologicalSpace β\ns : Set α\nf : α → β\nhf : Continuous f\nc : Set α\nc_count : Set.Countable c\nhc : s ⊆ _root_.closure c\n⊢ IsSeparable (f '' s)",
"state_before": "α : Type u\nt : TopologicalSpace α\nβ : Type u... | [
438,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.map | [] | [
290,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
8
] |
Mathlib/Data/ZMod/Parity.lean | ZMod.ne_zero_iff_odd | [
{
"state_after": "case mpr\nn : ℕ\n⊢ ¬↑n ≠ 0 → ¬Odd n",
"state_before": "case mpr\nn : ℕ\n⊢ Odd n → ↑n ≠ 0",
"tactic": "contrapose"
},
{
"state_after": "no goals",
"state_before": "case mpr\nn : ℕ\n⊢ ¬↑n ≠ 0 → ¬Odd n",
"tactic": "simp [eq_zero_iff_even]"
}
] | [
39,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | dense_of_mem_residual | [] | [
253,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_smul | [
{
"state_after": "case ofFinsupp\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝¹ : Semiring R\np q r✝ : R[X]\ninst✝ : SMulZeroClass S R\nr : S\nn : ℕ\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ coeff (r • { toFinsupp := toFinsupp✝ }) n = r • coeff { toFinsupp := toFinsupp✝ } n",
"state_before": "R : Type u\nS ... | [
64,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_of_lipschitz | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.274096\nE : Type u_3\nEₗ : Type ?u.274102\nF : Type u_4\nFₗ : Type ?u.274108\nG : Type ?u.274111\nGₗ : Type ?u.274114\n𝓕 : Type ?u.274117\ninst✝¹⁵ : SeminormedAddCommGroup E\ninst✝¹⁴ : SeminormedAddCommGroup Eₗ\ninst... | [
176,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_induction | [] | [
966,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_bot_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ relindex H ⊥ = 1",
"tactic": "rw [relindex, subgroupOf_bot_eq_top, index_top]"
}
] | [
267,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiff.sin | [] | [
1036,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousWithinAt_iff_continuousWithinAt_comp_right | [] | [
1143,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_C_mul_X_pow' | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nc : R\n⊢ support (↑C c * X ^ n) ⊆ {n}",
"tactic": "simpa only [C_mul_X_pow_eq_monomial] using support_monomial' n c"
}
] | [
858,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Agrees.set | [
{
"state_after": "case mk\nα : Type u_1\nβ : Sort u_2\nf : α → β\narr : Array α\ni : Fin (Array.size arr)\nx : α\nm' : Fin (Array.size arr) → β\nhm₂ : ∀ (h : ↑i < Array.size arr), f x = m' { val := ↑i, isLt := h }\nhm₁ : ∀ (j : Fin (Array.size arr)), ↑j ≠ ↑i → m' j = (fun i => f (Array.get arr i)) j\n⊢ Agrees (... | [
113,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_eq_top | [] | [
549,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.map_neg | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁴ : StrictOrderedCommRing R\nM : Type u_2\nN : Type u_3\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\nx y : M\nf : M ≃ₗ[R] N\ng : M\nhg : g ≠ 0\n⊢ ↑(map f) (-rayOfNeZero R g hg) = -↑(map f) (rayOfNeZero R g hg)",
"sta... | [
498,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_singleton | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.59247\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\n⊢ infDist x {y} = dist x y",
"tactic": "simp [infDist, dist_edist]"
}
] | [
505,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.preimage_subset | [] | [
110,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableWithinAt.cexp | [] | [
140,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.relabel_moveRight' | [] | [
1162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_add | [
{
"state_after": "no goals",
"state_before": "p q : ℚ\nhq : 0 ≤ q\nhp : 0 ≤ p\n⊢ ↑(toNNRat (q + p)) = ↑(toNNRat q + toNNRat p)",
"tactic": "simp [toNNRat, hq, hp, add_nonneg]"
}
] | [
379,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_pos | [] | [
290,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.map_add | [] | [
123,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.smul_inv | [] | [
2204,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2203,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.eq_zero_iff_mem | [] | [
137,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnityEquivNthRoots_apply | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/List/Card.lean | List.card_nil | [] | [
79,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
9
] |
Mathlib/Computability/Primrec.lean | Primrec₂.right | [] | [
434,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_to_list | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.290155\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\n⊢ List.prod (List.map f (toList s)) = Finset.prod s f",
"tactic": "rw [Finset.prod, ← Multiset.coe_prod, ← Multis... | [
430,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_Icc | [] | [
274,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
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