file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.epi_of_cancel_zero | [] | [
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85
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq | [
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toRingHom_apply_symm_toRingHom_apply | [] | [
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Mathlib/Data/Matrix/Notation.lean | Matrix.tail_transpose | [
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_one | [] | [
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.exists_mem_frontier_isMaxOn_norm | [
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_pow | [] | [
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Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.on_subset | [] | [
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.injective_coe | [
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Mathlib/Topology/SubsetProperties.lean | irreducibleSpace_def | [] | [
1842,
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Mathlib/Algebra/CharP/Basic.lean | CharP.neg_one_pow_char_pow | [
{
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"tactic": "rw [eq_neg_iff_add_eq_zero]... | [
322,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc | [
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463,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_id_le | [
{
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Mathlib/Data/Nat/Pow.lean | Nat.pow_dvd_of_le_of_pow_dvd | [] | [
232,
33
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Mathlib/Order/Bounds/Basic.lean | Monotone.mem_upperBounds_image | [] | [
1265,
42
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1264,
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Mathlib/Data/Sum/Order.lean | OrderIso.sumAssoc_apply_inl_inr | [] | [
579,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_toSubsemiring | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback | [
{
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177,
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Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.restrict_invariant | [] | [
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79
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132,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_eq_top_or_isMaximal_of_surjective | [
{
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.cast_eq_of_cons_eq_cons | [
{
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142,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.mul_lt_one_of_le_of_lt | [] | [
847,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.map₂Right_nil_left | [
{
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}
] | [
4136,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.snorm_lim_le_liminf_snorm | [
{
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_iff_lt_rowLen | [
{
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},
{
"state_after": "μ : YoungDiagram\ni j : ℕ\n⊢ (i, j) ∈ μ ↔ ∀ (m : ℕ), m ≤ j → (i,... | [
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Std/Data/List/Lemmas.lean | List.length_eraseP_of_mem | [
{
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.congr_fun | [] | [
606,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
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Mathlib/Order/Filter/Bases.lean | Filter.IsBasis.mem_filter_iff | [
{
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"tactic": "simp only [IsBasis.filter, FilterBasis.mem_filter_iff, mem_fi... | [
221,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Sigma.lean | List.dlookup_kerase | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/UpperLower.lean | mul_upperClosure | [
{
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291,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.aemeasurable | [] | [
222,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
11
] |
Mathlib/RingTheory/Derivation/Lie.lean | Derivation.commutator_coe_linear_map | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.neighborFinset_disjoint_singleton | [] | [
1362,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
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Mathlib/Topology/UniformSpace/Basic.lean | mem_uniformity_of_uniformContinuous_invariant | [
{
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87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOnFilter.tendstoUniformlyOnFilter_of_tendsto | [
{
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Mathlib/Order/Disjointed.lean | disjointed_eq_inter_compl | [] | [
175,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.degree_pos | [] | [
199,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/CategoryTheory/Monad/Coequalizer.lean | CategoryTheory.Monad.FreeCoequalizer.condition | [] | [
69,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/Order/Bounds/Basic.lean | mem_upperBounds_image2 | [] | [
1358,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1356,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsPrime.ne_top | [] | [
249,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.fromStructuredArrow_map | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/Data/Sym/Basic.lean | Sym.coe_map | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.map_injective_iff | [
{
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Mathlib/Data/List/Rotate.lean | List.rotate'_cons_succ | [
{
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}
] | [
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.isIso_map_iff | [
{
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259,
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Mathlib/Algebra/Quaternion.lean | Quaternion.coe_pow | [] | [
973,
32
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972,
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Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.Monad.ForgetCreatesColimits.commuting | [] | [
178,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/Algebra/Order/UpperLower.lean | lowerClosure_one | [] | [
271,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_sup | [] | [
1510,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1509,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.enum_lt_enum | [
{
"state_after": "no goals",
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"tactic":... | [
539,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eqToHom_map | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y : C\np : X = Y\n⊢ F.map (eqTo... | [
274,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Std/Logic.lean | and_rotate | [
{
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"tactic": "simp only [and_left_comm, and_comm]"
}
] | [
187,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
186,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_zsmul | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_singleton_zero | [] | [
274,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_equiv_symm_const' | [
{
"state_after": "no goals",
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927,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.unique_quotient_iff_eq_top | [
{
"state_after": "R : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np' : Submodule R M\n⊢ Nonempty (Unique (M ⧸ ⊤))",
"state_before": "R : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' : Subm... | [
294,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_apply_left | [
{
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"tactic": "rw [← Finsupp.sum_apply, ← Finsupp.sum_mul g f, f.sum_single]"
},
{
... | [
1066,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | LipschitzWith.inv | [] | [
1858,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_one_zero | [
{
"state_after": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ (if 0 = 0 then 1 else 0) = 1",
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"tactic": "rw [← monomial_zero_one, coeff_monomial]"
},
{
"state_after": "no goals",
... | [
686,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.bijOn_ptsOfPeriod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5460\nf✝ fa : α → α\nfb : β → β\nx✝ y : α\nm n✝ : ℕ\nf : α → α\nn : ℕ\nhn : 0 < n\nx : α\nhx : x ∈ ptsOfPeriod f n\n⊢ f ((f^[Nat.pred n]) x) = x",
"tactic": "rw [← comp_apply (f := f), comp_iterate_pred_of_pos f hn, hx.eq]"
}
] | [
214,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.frequently_iff_seq_frequently | [
{
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1861,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1846,
1
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Mathlib/Data/Set/Lattice.lean | Set.compl_iInter₂ | [
{
"state_after": "no goals",
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508,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_union_inter | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.326633\nι : Type ?u.326636\nG : Type ?u.326639\nM : Type u_2\nN : Type ?u.326645\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\nt : Set α\nht : Set.Finite t\ns : Finset α\n⊢ ((∏ᶠ (i : α) (_ : i ∈ ↑s ∪ t), f i) * ∏ᶠ (i : α) (_ : i ∈ ↑s ... | [
772,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_subset_prod_iff | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.87049\nδ : Type ?u.87052\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nh : s ×ˢ t = ∅\n⊢ s ×ˢ t ⊆ s₁ ×ˢ t₁ ↔ s ⊆ s₁ ∧ t ⊆ t₁ ∨ s = ∅ ∨ t = ∅\n\ncase inr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.87049\nδ : Type ?u.87052\ns s₁ s₂ : Set α\nt t₁... | [
394,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
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Mathlib/Data/Multiset/Functor.lean | Multiset.map_traverse | [
{
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127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_equiv_symm_const | [
{
"state_after": "no goals",
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917,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csSup_empty | [
{
"state_after": "no goals",
"state_before": "⊢ ¬(Set.Nonempty ∅ ∧ BddAbove ∅)",
"tactic": "simp"
}
] | [
75,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_eq_zero | [
{
"state_after": "case zero\nx : ZMod Nat.zero\n⊢ valMinAbs x = 0 ↔ x = 0\n\ncase succ\nn : ℕ\nx : ZMod (Nat.succ n)\n⊢ valMinAbs x = 0 ↔ x = 0",
"state_before": "n : ℕ\nx : ZMod n\n⊢ valMinAbs x = 0 ↔ x = 0",
"tactic": "cases' n with n"
},
{
"state_after": "case succ\nn : ℕ\nx : ZMod (Nat.succ ... | [
1001,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nβ₂ : Type ?u.114350\nγ : Type ?u.114353\nι : Sort ?u.114356\nι' : Sort ?u.114359\nκ : ι → Sort ?u.114364\nκ' : ι' → Sort ?u.114369\ninst✝ : CompleteLattice α\nf✝ g s✝ t✝ : ι → α\na b : α\nf : β → α\ns t : Set β\n⊢ (⨆ (x : β) (_ : x ∈ ... | [
1415,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.toBasis_adjustToOrientation | [] | [
120,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Data/Int/CharZero.lean | Int.cast_ne_zero | [] | [
46,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsFractionRing.coeSubmodule_isPrincipal | [] | [
213,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/List/Basic.lean | List.choose_mem | [] | [
3979,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3978,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_spec' | [
{
"state_after": "A : Type ?u.179006\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn : ℕ\n⊢ ∑ k in range (succ n),\n ↑(Nat.choose ((k, n - k).fst + (k, n - k).snd) (k, n - k).snd) / (↑(k, n - k).snd + 1) *\n bernoulli' (k, n - k).fst =\n ∑ k in range (succ n), ↑(Nat.choose n (n - k)) / (↑n - ↑k + 1)... | [
97,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_insert | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.81246\nα : Type u_1\nβ : Type ?u.81252\nr : α → α → Prop\nr' : β → β → Prop\nf : α → β\ns t : Set α\na : α\ninst✝ : IsRefl α r\n⊢ PartiallyWellOrderedOn (insert a s) r ↔ PartiallyWellOrderedOn s r",
"tactic": "simp only [← singleton_union, partia... | [
318,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_I_im | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (z * I).im = z.re",
"tactic": "simp"
}
] | [
342,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Order/CompleteLattice.lean | Prod.swap_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.211513\nγ : Type ?u.211516\nι : Sort u_3\nι' : Sort ?u.211522\nκ : ι → Sort ?u.211527\nκ' : ι' → Sort ?u.211532\ninst✝¹ : InfSet α\ninst✝ : InfSet β\nf : ι → α × β\n⊢ swap (iInf f) = ⨅ (i : ι), swap (f i)",
"tactic": ... | [
1866,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1865,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_eq_add_interpolate_erase | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\nhvs : Set.InjOn v ↑s\nhi : i ∈ s\nhj : j ∈ s\nhij : i ≠ j\n⊢ {i, j} ⊆ s",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j ... | [
468,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | DifferentiableOn.of_dslope | [] | [
142,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_monomial | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nha : a ≠ 0\n⊢ Finset.max {n} = ↑n",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nha : a ≠ 0\n⊢ degree (↑(monomial n) a) = ↑n",
"tactic": "... | [
290,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_comp | [
{
"state_after": "case h.h\nα : Type u_4\nM : Type u_1\nN : Type ?u.445605\nP : Type ?u.445608\nR : Type u_2\nS : Type ?u.445614\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R... | [
746,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/CategoryTheory/Category/Cat/Limit.lean | CategoryTheory.Cat.HasLimits.limit_π_homDiagram_eqToHom | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ Cat\nX : limit (F ⋙ objects)\nj : J\n⊢ limit.π (homDiagram X X) j (eqToHom (_ : X = X)) = eqToHom (_ : limit.π (F ⋙ objects) j X = limit.π (F ⋙ objects) j X)",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ Cat\nX Y : limit (F ⋙ o... | [
135,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.X_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\nH : X = 0\n⊢ False",
"tactic": "simpa only [coeff_one_X, one_ne_zero, map_zero] using congr_arg (coeff R 1) H"
}
] | [
1447,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.single_trans_single_of_ne | [] | [
410,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_singleton | [
{
"state_after": "case a.mk\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.70206\ns s' : Finset α\nt t' : Finset β\na : α\nb✝ b : β\nx : α\ny : β\n⊢ (x, y) ∈ s ×ˢ {b} ↔ (x, y) ∈ map { toFun := fun i => (i, b), inj' := (_ : Function.Injective fun a => (a, b)) } s",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : ... | [
226,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nf : α → β → γ\na : Option α\nb : Option β\nc : Option γ\ng : β → α → γ\nh_comm : ∀ (a : α) (b : β), f a b = g b a\n⊢ map₂ f a b = map₂ g b a",
"tactic": "cases a <;> cases b <;> simp [h_comm]"
}
] | [
131,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.X_pow_add_C_ne_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\na : R\nh : X ^ n + ↑C a = 1\n⊢ n = 0",
"tactic": "simpa only [natDegree_X_pow_add_C, natDegree_one] using congr_arg natDegree h"
}
] | [
1408,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.left_inv | [
{
"state_after": "case refine_1\nR : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nx : A ⊗[R] R[X]\n⊢ invFun R A (↑(toFunAlgHom R A) 0) = 0\n\ncase refine_2\nR : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nx : A ⊗[R] R[X... | [
167,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finiteAt_nhdsWithin | [] | [
4150,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4148,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.bot_pow | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.242140\nα : Type u_1\nβ : Type ?u.242146\nγ : Type ?u.242149\nδ : Type ?u.242152\nε : Type ?u.242155\ninst✝ : Monoid α\nf g : Filter α\ns : Set α\na : α\nm n✝ n : ℕ\nhn : n ≠ 0\n⊢ ⊥ ^ n = ⊥",
"tactic": "rw [← tsub_add_cancel_of_le (Nat.succ_le_of... | [
686,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_toEquiv | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_add | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\ng : σ → S₁\n⊢ eval₂ f g (p + q) = eval₂ f g p + eval₂ f g q",
... | [
957,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.snd_sumFinsuppLEquivProdFinsupp | [] | [
951,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv | [] | [
767,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.uncurry0_apply | [] | [
1642,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_sub_C_le | [] | [
1320,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1319,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.id_linear | [] | [
391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.one_apply | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_congr | [] | [
440,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Finsupp.linearEquivFunOnFinite_symm_coe | [] | [
124,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
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