file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Logic/Basic.lean | exists_unique_eq' | [
{
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_is_coproduct | [
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Mathlib/Order/Interval.lean | NonemptyInterval.coe_pure | [] | [
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.mk₂_funext | [] | [
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Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_atTop | [
{
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Mathlib/Algebra/Ring/Commute.lean | Commute.neg_right_iff | [] | [
100,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_inv | [
{
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}
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63
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | DifferentiableAt.derivWithin | [
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Mathlib/GroupTheory/Perm/Option.lean | Finset.univ_perm_option | [] | [
89,
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Mathlib/LinearAlgebra/Span.lean | LinearMap.span_singleton_eq_range | [
{
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29
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_const_smul_le | [] | [
1470,
11
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_foldr_sup | [
{
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.add_apply | [] | [
81,
28
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80,
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Mathlib/Algebra/BigOperators/Ring.lean | Finset.mul_sum | [] | [
59,
39
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Mathlib/Algebra/BigOperators/Fin.lean | List.prod_ofFn | [
{
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_toAddSubmonoid | [] | [
73,
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Mathlib/Data/Set/Image.lean | Set.subsingleton_of_preimage | [
{
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... | [
1238,
31
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1235,
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Mathlib/Order/Filter/Extr.lean | IsMinOn.min | [] | [
600,
24
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598,
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Mathlib/Order/SuccPred/Basic.lean | Succ.rec | [
{
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"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹... | [
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55
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1387,
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Mathlib/Algebra/Lie/SkewAdjoint.lean | skewAdjointMatricesLieSubalgebraEquiv_apply | [
{
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"tactic"... | [
148,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_const_apply | [
{
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1100,
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1097,
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Mathlib/Order/Filter/Cofinite.lean | Filter.eventually_cofinite | [] | [
49,
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Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsMinOn.closure | [] | [
37,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_apply_inter_support | [
{
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"tactic": "simp [p.toMeasure_apply_eq_toOuter... | [
281,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_mul_X' | [
{
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793,
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Mathlib/Data/Setoid/Basic.lean | Setoid.ker_iff_mem_preimage | [] | [
290,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.T_complex_cos | [
{
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"tactic": "simp only [T_zero, eval_one, Nat.cast_zero, MulZeroClass.zero_mul, cos_zero]"
},
{
"state... | [
88,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.basicOpen_le_basicOpen_iff | [
{
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"tactic": "rw [← SetLike.coe_subset_coe, basicOpen_eq_zeroLocus_compl, basicOpen_eq_zeroLocus_compl,\n Set.compl_sub... | [
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796,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.EqOnSource.source_inter_preimage_eq | [
{
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"tactic": "rw [he.eqOn.inter_preimage_eq, source_eq he... | [
886,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_succ' | [
{
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308,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_iff_of_mem | [
{
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Mathlib/Topology/Semicontinuous.lean | ContinuousWithinAt.lowerSemicontinuousWithinAt | [] | [
286,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/FieldTheory/Laurent.lean | RatFunc.taylor_mem_nonZeroDivisors | [
{
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Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.setOf_subset_eq_empty_iff | [
{
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Mathlib/Algebra/BigOperators/Finprod.lean | mul_finsum | [] | [
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40
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Mathlib/Data/ENat/Basic.lean | ENat.some_eq_coe | [] | [
63,
72
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63,
9
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.π_of_eq | [] | [
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67
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1055,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.top_rpow_of_pos | [
{
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] | [
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94
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315,
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Mathlib/Data/Sum/Order.lean | Sum.Lex.inr_strictMono | [] | [
418,
43
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_pow | [] | [
274,
12
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11
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Std/Data/List/Lemmas.lean | List.subset_append_left | [] | [
249,
98
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Mathlib/Data/List/AList.lean | AList.toAList_cons | [] | [
345,
6
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343,
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Mathlib/Data/Set/Function.lean | Function.Semiconj.injOn_range | [
{
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41
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1646,
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectMap_id | [
{
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"tactic": "aesop_cat"
... | [
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90
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Mathlib/Order/RelClasses.lean | Set.not_bounded_iff | [
{
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"tactic": "simp only [Bounded, Unbounded, not_forall, not_exists, exists_prop, not_and, not_not]"
}
] | [
538,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_add | [
{
"state_after": "case h\nθ₂ : Angle\nx✝ : ℝ\n⊢ sin (↑x✝ + θ₂) = sin ↑x✝ * cos θ₂ + cos ↑x✝ * sin θ₂",
"state_before": "θ₁ θ₂ : Angle\n⊢ sin (θ₁ + θ₂) = sin θ₁ * cos θ₂ + cos θ₁ * sin θ₂",
"tactic": "induction θ₁ using Real.Angle.induction_on"
},
{
"state_after": "case h.h\nx✝¹ x✝ : ℝ\n⊢ sin (↑x... | [
434,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.image_subset_iff_subset_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : DecidableEq β\nf : α → β\ns : Finset α\nt : Finset β\nhf : InjOn f (f ⁻¹' ↑t)\n⊢ (∀ (x : α), x ∈ s → f x ∈ t) ↔ s ⊆ preimage t f hf",
"tactic": "simp only [subset_iff, mem_preimage]"
}
] | [
89,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.inv_zero | [
{
"state_after": "n : ℕ\n⊢ ↑(Nat.gcdA 0 (n + 1)) = 0",
"state_before": "n : ℕ\n⊢ ↑(Nat.gcdA (val 0) (n + 1)) = 0",
"tactic": "rw [val_zero]"
},
{
"state_after": "n : ℕ\n⊢ ↑(n + 1, 0, 1).snd.fst = 0",
"state_before": "n : ℕ\n⊢ ↑(Nat.gcdA 0 (n + 1)) = 0",
"tactic": "unfold Nat.gcdA Nat.xgc... | [
642,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
src/lean/Init/SimpLemmas.lean | and_false | [] | [
85,
77
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
85,
9
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.cutMap_bddAbove | [
{
"state_after": "case intro\nF : Type ?u.11263\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.11272\ninst✝² : LinearOrderedField α\ninst✝¹ : LinearOrderedField β\na✝ a₁ a₂ : α\nb : β\nq✝ : ℚ\ninst✝ : Archimedean α\na : α\nq : ℚ\nhq : a < ↑q\n⊢ BddAbove (cutMap β a)",
"state_before": "F : Type ?u.11263\nα : Type ... | [
149,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_add_not_infinite | [] | [
574,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_dist | [] | [
196,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.comp_assoc | [
{
"state_after": "case refine_3\nR✝ : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R✝\nm n : ℕ\ninst✝¹ : Semiring R✝\np q r : R✝[X]\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ χ : R[X]\nn✝ : ℕ\na✝¹ : R\na✝ : comp (comp (↑C a✝¹ * X ^ n✝) ψ) χ = comp (↑C a✝¹ * X ^ n✝) (comp ψ χ)\n⊢ comp (comp (↑C a✝¹ * X ^ (n... | [
662,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_range | [] | [
207,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.surjective_comp_right | [] | [
791,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Function.Bijective.cauchySeq_comp_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nf : ℕ → ℕ\nhf : Bijective f\nu : ℕ → α\nH : CauchySeq (u ∘ f)\n⊢ CauchySeq u",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nf : ℕ → ℕ\nhf : Bijective f\nu : ℕ → α\n⊢ CauchySeq (u ∘ f) ↔ CauchySeq u",
"tactic": "refine'... | [
216,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
src/lean/Init/Control/Lawful.lean | ExceptT.ext | [
{
"state_after": "m : Type u_1 → Type u_2\nε α : Type u_1\ninst✝ : Monad m\nx y : ExceptT ε m α\nh : x = y\n⊢ x = y",
"state_before": "m : Type u_1 → Type u_2\nε α : Type u_1\ninst✝ : Monad m\nx y : ExceptT ε m α\nh : run x = run y\n⊢ x = y",
"tactic": "simp [run] at h"
},
{
"state_after": "no g... | [
106,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
104,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.norm_exp | [
{
"state_after": "no goals",
"state_before": "q : ℍ\n⊢ ‖exp ℝ q‖ = ‖exp ℝ q.re‖",
"tactic": "rw [norm_eq_sqrt_real_inner (exp ℝ q), inner_self, normSq_exp, Real.sqrt_sq_eq_abs,\n Real.norm_eq_abs]"
}
] | [
142,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/SubsetProperties.lean | Set.Subsingleton.isCompact | [] | [
402,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.47735\nδ : Type ?u.47738\ne : LocalEquiv α β\ne' : LocalEquiv β γ\n⊢ (LocalEquiv.trans (LocalEquiv.refl α) e).source = e.source",
"tactic": "simp [trans_source, preimage_id]"
}
] | [
754,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | act_rel_of_act_rel_of_rel_act_rel | [] | [
235,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_iff_prime_squarefree | [] | [
38,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciInf_set_iff | [] | [
529,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | MonoidHom.toFreimanHom_injective | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.80415\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.80424\nδ : Type ?u.80427\nG : Type ?u.80430\ninst✝⁵ : FunLike F α fun x => β\ninst✝⁴ : CommMonoid α\ninst✝³ : CommMonoid β\ninst✝² : CommMonoid γ\ninst✝¹ : CommMonoid δ\ninst✝ : CommGroup G\nA : Set α\nB... | [
483,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.pow_succ | [] | [
474,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
473,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.monoidOf_eq_algebraMap | [] | [
1021,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.exp_pow_sum | [
{
"state_after": "A : Type u_1\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn : ℕ\n⊢ (Finset.sum (Finset.range n) fun x =>\n ↑{\n toMonoidHom :=\n {\n toOneHom :=\n { toFun := fun f => mk fun n => ↑x ^ n * ↑(coeff A n) f,\n map_one' :... | [
209,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isAdjointPair_id | [] | [
450,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.ne_zero | [] | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_of_dist_bounded | [] | [
708,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | rightLim_eq_of_tendsto | [] | [
67,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.lt_add_of_tsub_lt_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.38298\ninst✝³ : PartialOrder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhb : AddLECancellable b\nh : a - b < c\n⊢ a - b ≤ c ∧ a ≠ b + c",
"state_before": "α : Type u_1\nβ : Type ?u.38298\ninst✝³ : PartialOrder α\ninst✝² : Ad... | [
315,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
11
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.prod_le_iff | [
{
"state_after": "case mp\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.377212\nM₆ : Type ?u.377215\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂... | [
723,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Topology/SubsetProperties.lean | isPreirreducible_iff_closed_union_closed | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.198320\nπ : ι → Type ?u.198325\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s z₁ z₂ : Set α\n⊢ IsOpen (z₁ᶜ) → IsOpen (z₂ᶜ) → Set.Nonempty (s ∩ z₁ᶜ) → Set.Nonempty (s ∩ z₂ᶜ) → Set.Nonempty (s ∩ (z₁ᶜ ∩ z₂ᶜ)) ↔\n IsClosed z₁ → IsClosed z₂ →... | [
1932,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1925,
1
] |
Mathlib/Order/Heyting/Basic.lean | IsCompl.eq_compl | [] | [
864,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.exists_mem | [] | [
299,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_pow | [] | [
235,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_eq_self | [] | [
1148,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.summable_of_le | [] | [
1120,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_add | [] | [
481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Algebra/Lie/SkewAdjoint.lean | Matrix.lie_transpose | [
{
"state_after": "no goals",
"state_before": "R : Type u\nn : Type w\ninst✝² : CommRing R\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\nJ A B : Matrix n n R\n⊢ (A * B - B * A)ᵀ = Bᵀ * Aᵀ - Aᵀ * Bᵀ",
"tactic": "simp"
}
] | [
102,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.AbsTheory.abs_conj | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ Real.sqrt (↑normSq (↑(starRingEnd ℂ) z)) = Real.sqrt (↑normSq z)",
"tactic": "simp"
}
] | [
913,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.mul_left | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nF : Type ?u.77288\nα : Type u_1\nβ : Type ?u.77294\n𝕜 : Type ?u.77297\nE : Type ?u.77300\ninst✝ : CancelCommMonoid α\ns : Set α\na : α\nhs : MulSalemSpencer s\nb : α\nhb : b ∈ s\nc : α\nhc : c ∈ s\nd : α\nhd : d ∈ s\nh : (fun x x_1 => x * x_1) a b * (... | [
183,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
src/lean/Init/SimpLemmas.lean | bne_self_eq_false | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na : α\n⊢ (a != a) = false",
"tactic": "simp [bne]"
}
] | [
151,
100
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
151,
9
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iUnion | [] | [
433,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.mul_lt_omega_opow | [
{
"state_after": "case inl\na b : Ordinal\nhb : b < ω\nc0 : 0 < 0\nha : a < ω ^ 0\n⊢ a * b < ω ^ 0\n\ncase inr.inl.intro\na b : Ordinal\nhb : b < ω\nc : Ordinal\nc0 : 0 < succ c\nha : a < ω ^ succ c\n⊢ a * b < ω ^ succ c\n\ncase inr.inr\na b c : Ordinal\nc0 : 0 < c\nha : a < ω ^ c\nhb : b < ω\nl : IsLimit c\n⊢ ... | [
363,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.exists_reduced_fraction | [
{
"state_after": "case intro.mk.intro\nR : Type ?u.2417\ninst✝⁹ : CommRing R\nM : Submonoid R\nS : Type ?u.2623\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nP : Type ?u.2877\ninst✝⁶ : CommRing P\nA : Type u_1\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : UniqueFactorizationMonoid A\nK : Type u_2\ninst✝² : ... | [
52,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_lt_nadd_right | [] | [
231,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Topology/Separation.lean | nhds_basis_clopen | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\ninst✝² : T2Space α\ninst✝¹ : CompactSpace α\ninst✝ : TotallyDisconnectedSpace α\nx : α\nU : Set α\n⊢ U ∈ 𝓝 x → ∃ i, (x ∈ i ∧ IsClopen i) ∧ id i ⊆ U\n\ncase mpr\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\ninst✝² : T2Space ... | [
1975,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_mem_pointwise_smul | [] | [
291,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.isNoetherianRing_fin_0 | [
{
"state_after": "case f\nR : Type u\nS : Type ?u.780222\nσ : Type v\nM : Type w\ninst✝⁴ : CommRing R\ninst✝³ : CommRing S\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsNoetherianRing R\n⊢ R ≃+* MvPolynomial (Fin 0) R",
"state_before": "R : Type u\nS : Type ?u.780222\nσ : Type v\nM : Type w\ninst... | [
1064,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | WithTop.sum_lt_top | [] | [
733,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Topology/UniformSpace/CompleteSeparated.lean | IsComplete.isClosed | [
{
"state_after": "α : Type u_1\ninst✝¹ : UniformSpace α\ninst✝ : SeparatedSpace α\ns : Set α\nh : IsComplete s\na : α\nha : ClusterPt a (𝓟 s)\nf : Filter α := 𝓝[s] a\n⊢ a ∈ s",
"state_before": "α : Type u_1\ninst✝¹ : UniformSpace α\ninst✝ : SeparatedSpace α\ns : Set α\nh : IsComplete s\na : α\nha : Cluste... | [
35,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.update_piecewise_of_not_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.308822\nγ : Type ?u.308825\nδ : α → Sort u_2\ns : Finset α\nf g : (i : α) → δ i\ninst✝¹ : (j : α) → Decidable (j ∈ s)\ninst✝ : DecidableEq α\ni : α\nhi : ¬i ∈ s\nv : δ i\n⊢ piecewise s (update f i v) (update g i v) = piecewise s f (update g i v)",
"state_before": ... | [
2554,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2550,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.weaken | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.29021\nE : Type u_2\nF : Type ?u.29027\nG : Type ?u.29030\nE' : Type ?u.29033\nF' : Type u_3\nG' : Type ?u.29039\nE'' : Type ?u.29042\nF'' : Type ?u.29045\nG'' : Type ?u.29048\nR : Type ?u.29051\nR' : Type ?u.29054\n𝕜 : Type ?u.29057\n... | [
199,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_two_two_eq_four | [
{
"state_after": "case zero\n\n⊢ hyperoperation (Nat.zero + 1) 2 2 = 4\n\ncase succ\nnn : ℕ\nnih : hyperoperation (nn + 1) 2 2 = 4\n⊢ hyperoperation (Nat.succ nn + 1) 2 2 = 4",
"state_before": "n : ℕ\n⊢ hyperoperation (n + 1) 2 2 = 4",
"tactic": "induction' n with nn nih"
},
{
"state_after": "no... | [
106,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_Ico_ae_eq_pi_Icc | [] | [
536,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_mono | [
{
"state_after": "α : Type u_1\nE : Type ?u.748247\nF : Type ?u.748250\nF' : Type ?u.748253\nG : Type ?u.748256\n𝕜 : Type ?u.748259\np : ℝ≥0∞\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedAddCommGroup F'\ninst✝⁷ : NormedSpac... | [
864,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Data/Finsupp/AList.lean | AList.lookupFinsupp_support | [
{
"state_after": "α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x => M\n⊢ toFinset (List.keys (filter (fun x => decide ¬x.snd = 0) l.entries)) =\n toFinset (List.keys (filter (fun x => decide ¬x.snd = 0) l.entries))",
"state_before": "α : Type ... | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq_one | [
{
"state_after": "no goals",
"state_before": "⊢ stirlingSeq 1 = exp 1 / Real.sqrt 2",
"tactic": "rw [stirlingSeq, pow_one, factorial_one, cast_one, mul_one, mul_one_div, one_div_div]"
}
] | [
67,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
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