file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Polynomial/Eval.lean | Polynomial.coe_eval₂RingHom | [] | [
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6
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282,
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Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.convexHull_inter_convexHull | [] | [
103,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.image_coe_Ioc | [
{
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"tactic": "rw [← preimage_coe_Ioc, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left\n (Subset.trans Ioc_subset_Iic_self <| Iic_subset_Iio.2 <| coe_lt_t... | [
122,
78
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Mathlib/Order/Filter/Extr.lean | IsMaxOn.inf | [] | [
574,
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573,
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Mathlib/Topology/Order/Basic.lean | comap_coe_Ioo_nhdsWithin_Ioi | [] | [
2498,
41
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2496,
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Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_one | [] | [
668,
22
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667,
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_coprod_of_isSeparator_right | [
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"tactic": "simp"
}
] | [
569,
64
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567,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.dvd_of_mod_eq_zero | [
{
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}
] | [
1066,
53
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1065,
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Mathlib/Data/List/Cycle.lean | Cycle.length_subsingleton_iff | [] | [
601,
10
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600,
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.sub_singleton_eq | [
{
"state_after": "no goals",
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"tactic": "simpa only [neg_sub, neg_eq] using congr_arg Neg.neg (singleton_sub_eq a r)"
}
] | [
319,
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.toOuterMeasure_ofFinset_apply | [] | [
188,
45
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186,
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_le_card | [] | [
262,
51
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260,
1
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Mathlib/Order/UpperLower/Basic.lean | coe_upperClosure | [
{
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"state_before": "α : Type u_1\nβ : Type ... | [
1284,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
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Mathlib/LinearAlgebra/Pi.lean | LinearMap.proj_pi | [] | [
100,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_conj_symm | [] | [
444,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.eq_X_sub_C_of_splits_of_single_root | [
{
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"state_before": "F : Type u\nK : Type v\nL : Type... | [
373,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_map | [] | [
224,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_set | [
{
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}
] | [
639,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
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Mathlib/Data/Subtype.lean | Subtype.map_id | [] | [
216,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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Mathlib/Topology/UniformSpace/AbsoluteValue.lean | AbsoluteValue.hasBasis_uniformity | [] | [
47,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/CategoryTheory/Abelian/InjectiveResolution.lean | CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι | [
{
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"tactic": "simp [homotopyEquiv]"
}
] | [
188,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.sub_isLittleO | [
{
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"tactic": "simpa only [sub_eq_add_neg] using huv.add_isLittleO hwv.neg_left"
}
] | [
173,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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Mathlib/Data/Nat/Factors.lean | Nat.perm_factors_mul_of_coprime | [
{
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"state_before": "a b : ℕ\nhab : coprime a b\n⊢ factors (a * b) ~ factors a ++ factors b",
"tactic": "rcases a... | [
217,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.natDegree_multiset_prod_X_sub_C_eq_card | [
{
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757,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_isClosed | [] | [
115,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Order/Partition/Equipartition.lean | Finpartition.isEquipartition_iff_card_parts_eq_average | [
{
"state_after": "no goals",
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41,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Pointwise.lean | Real.sInf_smul_of_nonneg | [
{
"state_after": "case inl\nι : Sort ?u.200\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : MulActionWithZero α ℝ\ninst✝ : OrderedSMul α ℝ\na : α\nha : 0 ≤ a\n⊢ sInf (a • ∅) = a • sInf ∅\n\ncase inr\nι : Sort ?u.200\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : MulActionWithZero α ℝ\ninst✝ : Ord... | [
48,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Pointwise.lean | Set.Finite.toFinset_mul | [] | [
2213,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2211,
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Mathlib/Data/List/Basic.lean | List.get_zero_scanl | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.hom_ext | [] | [
159,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.support_cycleOf_le | [
{
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"state_before": "ι : Type ?u.2513584\nα : Type u_1\nβ : Type ?u.2513590\ninst✝¹ : DecidableEq ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
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Mathlib/Data/Stream/Init.lean | Stream'.nth_zero_cons | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_restrict_biUnion_iff | [
{
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2777,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2775,
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Mathlib/Data/Finset/Image.lean | Finset.image_empty | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
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] |
Mathlib/Algebra/Support.lean | Function.mulSupport_prod_mk | [
{
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231,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_cons_concat_apply_last | [
{
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132,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Data/Sign.lean | sign_mul_abs | [
{
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410,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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Mathlib/Data/List/Cycle.lean | Cycle.length_reverse | [] | [
588,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
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Mathlib/Data/Int/CharZero.lean | Int.cast_injective | [] | [
42,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
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Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousComponent_homogeneous_polynomial | [
{
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"state_before": "σ : Type u_1\nτ : Type ?u.368740\nR : ... | [
328,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Mathlib/Topology/Separation.lean | infinite_of_mem_nhds | [
{
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"state_before": "α✝ : Type u\nβ : Type v\ninst✝² : TopologicalSpace α✝\nα : ... | [
782,
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778,
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_singleton | [] | [
98,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/Algebra/GroupPower/Lemmas.lean | Units.conj_pow' | [] | [
1246,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1244,
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Mathlib/Algebra/Lie/BaseChange.lean | LieAlgebra.ExtendScalars.bracket'_tmul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type w\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\ns t : A\nx y : L\n⊢ ↑(↑(LieAlgebra.ExtendScalars.bracket' R A L) (s ⊗ₜ[R] x)) (t ⊗ₜ[R] y) = (s * t) ⊗ₜ[R] ⁅x, y⁆",
... | [
54,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_zero | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_iSup_comap_of_surjective | [] | [
499,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.eq_of_comp_left_eq' | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z✝ : C\nf g : X ⟶ Y\nw : (fun {Z} h => f ≫ h) = fun {Z} h => g ≫ h\nZ : C\nh : Y ⟶ Z\n⊢ f ≫ h = g ≫ h",
"tactic": "convert congr_fun (congr_fun w Z) h"
}
] | [
224,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Std/Logic.lean | Bool.eq_iff_iff | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ a = b ↔ (a = true ↔ b = true)",
"tactic": "cases b <;> simp"
}
] | [
770,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
770,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.prod_ext_iff | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_sq_le_normSq | [] | [
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Mathlib/Data/List/Chain.lean | List.chain_of_chain_map | [] | [
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_submatrix_equiv_self | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.bot_adj | [] | [
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.degreeOf_coeff_finSuccEquiv | [
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Mathlib/Algebra/Star/Pointwise.lean | Set.star_inv' | [
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_mul' | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_le_of_limit | [
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803,
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Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsInt.neg_to_eq | [
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Mathlib/Order/Chain.lean | Flag.mk_coe | [] | [
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mul_right_mono | [
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Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.leftAdjointUniq_hom_counit | [
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.aut_mul | [] | [
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Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable_aux₁ | [
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coordChange_same | [] | [
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Std/Data/Int/DivMod.lean | Int.mul_ediv_mul_of_pos_left | [
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Mathlib/Data/Int/Lemmas.lean | Int.toNat_of_nonpos | [
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_inv_cancel_iff | [
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Mathlib/Topology/Sequences.lean | IsSeqCompact.isCompact | [] | [
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Mathlib/Logic/Basic.lean | ite_ne_left_iff | [
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Mathlib/Analysis/Complex/Isometry.lean | rotation_trans | [
{
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Mathlib/Topology/Homeomorph.lean | Homeomorph.symm_symm | [] | [
82,
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_strict_mono | [] | [
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25
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_apply | [] | [
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Mathlib/Order/Lattice.lean | inf_eq_minDefault | [
{
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubgroup_le | [] | [
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10
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Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.exists_smul_eq | [
{
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_ne_zero_iff | [] | [
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31
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_self_apply | [] | [
1277,
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1276,
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Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_id | [] | [
201,
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200,
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Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ioi | [] | [
103,
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafify_isSheaf | [] | [
610,
50
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Mathlib/Algebra/AddTorsor.lean | Equiv.pointReflection_symm | [
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Mathlib/Data/Vector3.lean | Vector3.append_cons | [] | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_self_iff | [
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Mathlib/Analysis/MeanInequalitiesPow.lean | Real.pow_sum_div_card_le_sum_pow | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.eq_one_iff_unique | [] | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_succ_X_mul | [
{
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Mathlib/Data/Set/Intervals/Basic.lean | Set.right_mem_Ioc | [
{
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65
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_iUnion₀ | [
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Std/Data/Nat/Gcd.lean | Nat.coprime_zero_right | [
{
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Mathlib/Algebra/Order/Group/Defs.lean | OrderedCommGroup.to_contravariantClass_left_le | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycle_is_cycleOf | [
{
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Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.one_def | [] | [
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Std/Classes/LawfulMonad.lean | SatisfiesM.mapConst | [] | [
117,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
115,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.eq_of_mono_cofork_π | [] | [
1072,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sinOrderIso_apply | [] | [
925,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_smul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.74308\nβ : Type ?u.74311\na b c d : ℝ≥0∞\nr✝ p q : ℝ≥0\nR : Type u_1\nr : R\ns : ℝ≥0\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0\ninst✝ : IsScalarTower R ℝ≥0 ℝ≥0∞\n⊢ ↑(r • s) = r • ↑s",
"tactic": "rw [← smul_one_s... | [
514,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.cof_eq | [
{
"state_after": "α : Type ?u.67959\nr : α → α → Prop\na o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal\nhf : IsFundamentalSequence a o f\n⊢ ord (cof (blsub o f)) ≤ o",
"state_before": "α : Type ?u.67959\nr : α → α → Prop\na o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal\nhf : IsFundamentalSequence a o ... | [
559,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.491428\nι : Type ?u.491431\ninst✝ : PseudoMetricSpace α\nx : α\ns t : Set α\nr : ℝ\n⊢ Bounded (s ∪ t) ↔ Bounded s ∧ Bounded t",
"tactic": "simp only [bounded_iff_isBounded, isBounded_union]"
}
] | [
2372,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2371,
9
] |
Std/Data/List/Basic.lean | List.removeNth_eq_removeNthTR | [
{
"state_after": "case h.h.h\nα : Type u_1\nl : List α\nn : Nat\n⊢ removeNth l n = removeNthTR l n",
"state_before": "⊢ @removeNth = @removeNthTR",
"tactic": "funext α l n"
},
{
"state_after": "case h.h.h\nα : Type u_1\nl : List α\nn : Nat\n⊢ removeNth l n = removeNthTR.go l l n #[]",
"state... | [
384,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
375,
10
] |
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