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/Data/Part.lean | Part.mod_get_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73049\nγ : Type ?u.73052\ninst✝ : Mod α\na b : Part α\nhab : (a % b).Dom\n⊢ get (Part.bind a fun y => map (fun x => y % x) b) (_ : (Part.bind a fun y => map (fun x => y % x) b).Dom) =\n get a (_ : a.Dom) % get b (_ : b.Dom)",
"state_before": "α : Type u_1\nβ : ... | [
797,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_nsmul | [] | [
353,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.Integrable.integral_norm_prod_left | [] | [
305,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
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Mathlib/Algebra/Homology/Homology.lean | cyclesMap_comp | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\nC₁ C₂ C₃ : HomologicalComplex V c\nf✝ f : C₁ ⟶ C₂\ng : C₂ ⟶ C₃\ni : ι\n⊢ Subobject.factorThru (cycles C₃ i) (Subobject.arrow (cycles C₁ i) ≫ Hom.f (... | [
223,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Antitone.map_limsup_of_continuousAt | [] | [
363,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.continuousWithinAt | [] | [
734,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.exists_coe | [] | [
270,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
11
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | LinearMap.hasDerivWithinAt | [] | [
99,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
11
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.measure_pos_of_nonempty_interior | [] | [
62,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero | [
{
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303,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/Ray.lean | Module.Ray.map_refl | [] | [
303,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/LinearAlgebra/Determinant.lean | Basis.det_self | [
{
"state_after": "no goals",
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... | [
538,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
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Mathlib/CategoryTheory/FullSubcategory.lean | CategoryTheory.fullSubcategoryInclusion_obj_lift_obj | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
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Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.dest_map | [
{
"state_after": "case mk\nn : ℕ\nP : MvPFunctor (n + 1)\nα β : TypeVec n\ng : α ⟹ β\na : (mp P).A\nf : B (mp P) a ⟹ α\n⊢ dest P (g <$$> { fst := a, snd := f }) = (g ::: fun x => g <$$> x) <$$> dest P { fst := a, snd := f }",
"state_before": "n : ℕ\nP : MvPFunctor (n + 1)\nα β : TypeVec n\ng : α ⟹ β\nx : M ... | [
376,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_top_of_surjective | [
{
"state_after": "G : Type u_1\nG' : Type ?u.282904\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.282913\ninst✝² : AddGroup A\nH K : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.282940\ninst✝ : Group P\nf : G →* N\nh : Surjective ↑f\n⊢ ⊤ ≤ map f ⊤",
"state_before": "G : Type u_1\nG... | [
1573,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.le_card_falling_div_choose | [
{
"state_after": "case zero\n𝕜 : Type u_2\nα : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : DecidableEq α\nk : ℕ\n𝒜 : Finset (Finset α)\ns : Finset α\ninst✝ : Fintype α\nhk✝ : k ≤ Fintype.card α\nh𝒜 : IsAntichain (fun x x_1 => x ⊆ x_1) ↑𝒜\nhk : zero ≤ Fintype.card α\n⊢ ∑ r in range (zero + 1), ↑(card ... | [
203,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.apply_firstDiff_ne | [
{
"state_after": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nh : x ≠ y\n⊢ x (Nat.find (_ : ∃ a, x a ≠ y a)) ≠ y (Nat.find (_ : ∃ a, x a ≠ y a))",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nh : x ≠ y\n⊢ x (firstDiff x y) ≠ y (firstDiff x y)",
"tactic": "rw [firstDiff_def, dif_pos h]"
},
{
... | [
79,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_cellsOfRowLens | [
{
"state_after": "case nil\nc✝ c : ℕ × ℕ\n⊢ c ∈ ∅ ↔ ∃ h, c.snd < List.get [] { val := c.fst, isLt := h }\n\ncase cons\nc✝ : ℕ × ℕ\nw_hd : ℕ\nw_tl : List ℕ\nw_ih : ∀ {c : ℕ × ℕ}, c ∈ YoungDiagram.cellsOfRowLens w_tl ↔ ∃ h, c.snd < List.get w_tl { val := c.fst, isLt := h }\nc : ℕ × ℕ\n⊢ c ∈\n {0} ×ˢ Finset.r... | [
472,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
11
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_sInf | [
{
"state_after": "no goals",
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675,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
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Mathlib/Order/Heyting/Basic.lean | sdiff_inf_distrib | [
{
"state_after": "ι : Type ?u.136551\nα : Type u_1\nβ : Type ?u.136557\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d✝ a b c d : α\n⊢ a \\ d ≤ b ∧ a \\ d ≤ c ↔ a \\ b ≤ d ∧ a \\ c ≤ d",
"state_before": "ι : Type ?u.136551\nα : Type u_1\nβ : Type ?u.136557\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝... | [
650,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Dynamics/Minimal.lean | isMinimal_iff_closed_smul_invariant | [
{
"state_after": "case mp\nM : Type u_1\nG : Type ?u.17773\nα : Type u_2\ninst✝⁵ : Monoid M\ninst✝⁴ : Group G\ninst✝³ : TopologicalSpace α\ninst✝² : MulAction M α\ninst✝¹ : MulAction G α\ninst✝ : ContinuousConstSMul M α\n⊢ IsMinimal M α → ∀ (s : Set α), IsClosed s → (∀ (c : M), c • s ⊆ s) → s = ∅ ∨ s = univ\n\n... | [
129,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.isRoot_of_eval₂_map_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type ?u.1305085\nB' : Type ?u.1305088\na b : R\nn : ℕ\ninst✝⁷ : CommSemiring A'\ninst✝⁶ : Semiring B'\ninst✝⁵ : CommSemiring R\np q : R[X]\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\nB : Type ?u.1305301\ninst✝² : Semiring B\ninst✝¹ : Algebra... | [
371,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sub_nat_mul_two_pi | [] | [
289,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/Order/Concept.lean | Concept.bot_fst | [] | [
322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_toLinearEquiv | [
{
"state_after": "case h\nR₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.1532382\ninst✝²⁴ : Semiring R₁\ninst✝²³ : Semiring R₂\ninst✝²² : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₁ : R₂ →+* R₁\ninst✝²¹ : RingHomInvPair σ₁₂ σ₂₁\ninst✝²⁰ : RingHomInvPair σ₂₁ σ₁₂\nσ₂₃ : R₂ →+* R₃\nσ₃₂ : R₃ →+* R₂\ninst✝¹⁹ : RingHomInvPair σ₂₃ ... | [
1951,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1949,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.toAlgHom_bijective | [
{
"state_after": "case intro\nM : Type u\ninst✝⁹ : Monoid M\nG✝ : Type u\ninst✝⁸ : Group G✝\nF✝ : Type v\ninst✝⁷ : Field F✝\ninst✝⁶ : MulSemiringAction M F✝\ninst✝⁵ : MulSemiringAction G✝ F✝\nm : M\nG : Type u\nF : Type v\ninst✝⁴ : Group G\ninst✝³ : Field F\ninst✝² : Finite G\ninst✝¹ : MulSemiringAction G F\nin... | [
369,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.approxOn_comp | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_mul' | [] | [
273,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.filter_mono | [] | [
4102,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4101,
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] |
Mathlib/Algebra/Ring/Basic.lean | pred_ne_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : NonAssocRing α\ninst✝ : Nontrivial α\na : α\nh : a - 1 = a\n⊢ a + -1 = a + -0",
"tactic": "simp [←sub_eq_add_neg, h]"
}
] | [
148,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/Algebra/ValuedField.lean | Valued.extension_extends | [
{
"state_after": "K : Type u_2\ninst✝¹ : Field K\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : K\n⊢ Tendsto (↑v) (Filter.comap (↑K) (𝓝 (↑K x))) (𝓝 (↑v x))",
"state_before": "K : Type u_2\ninst✝¹ : Field K\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Va... | [
286,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.invOn_invFunOn | [] | [
1261,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
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Mathlib/Topology/Separation.lean | loc_compact_t2_tot_disc_iff_tot_sep | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nH : Type u_1\ninst✝² : TopologicalSpace H\ninst✝¹ : LocallyCompactSpace H\ninst✝ : T2Space H\n⊢ TotallyDisconnectedSpace H → TotallySeparatedSpace H\n\ncase mpr\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nH : Type u_1\nins... | [
2039,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2034,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.fderiv | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.268497\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u... | [
541,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaCurry_smul | [
{
"state_after": "case h.h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.615890\nα : ι → Type u_1\nδ : (i : ι) → α i → Type v\ninst✝² : Monoid γ\ninst✝¹ : (i : ι) → (j : α i) → AddMonoid (δ i j)\ninst✝ : (i : ι) → (j : α i) → DistribMulAction γ (δ ... | [
1503,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1498,
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Mathlib/Data/Set/Basic.lean | Set.singleton_eq_singleton_iff | [] | [
1282,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_nonneg | [
{
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540,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.mul_le_nndist | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2568\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nK : ℝ≥0\nf : α → β\nhf : AntilipschitzWith K f\nx y : α\n⊢ K⁻¹ * nndist x y ≤ nndist (f x) (f y)",
"tactic": "simpa only [div_eq_inv_mul] using NNReal.di... | [
80,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Quot.lean | Trunc.eq | [] | [
514,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
11
] |
Mathlib/Topology/Connected.lean | isPreconnected_range | [] | [
759,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.quotientToQuotientRangePowQuotSucc_mk | [] | [
551,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_self_lt_mul_self | [] | [
1237,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1236,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_periodic | [
{
"state_after": "θ : Angle\n⊢ tan (θ + ↑π) = tan θ",
"state_before": "⊢ Function.Periodic tan ↑π",
"tactic": "intro θ"
},
{
"state_after": "case h\nx✝ : ℝ\n⊢ tan (↑x✝ + ↑π) = tan ↑x✝",
"state_before": "θ : Angle\n⊢ tan (θ + ↑π) = tan θ",
"tactic": "induction θ using Real.Angle.induction... | [
800,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Equitabilise.lean | Finpartition.card_eq_of_mem_parts_equitabilise | [] | [
158,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | IsAssociatedPrime.map_of_injective | [
{
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_X | [
{
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Mathlib/Data/Set/Finite.lean | Set.Subsingleton.finite | [] | [
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47
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980,
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Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.LaxMonoidalFunctor.associativity_inv | [
{
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137,
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Mathlib/Data/PFun.lean | PFun.image_def | [] | [
405,
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404,
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Mathlib/Data/List/Lattice.lean | List.suffix_union_right | [] | [
113,
57
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112,
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Mathlib/Order/Heyting/Hom.lean | CoheytingHom.ext | [] | [
398,
20
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397,
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Mathlib/Data/Finset/Preimage.lean | Finset.sigma_image_fst_preimage_mk | [] | [
139,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Basic.lean | LieEquiv.one_apply | [] | [
591,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
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Mathlib/Algebra/Algebra/Operations.lean | SubMulAction.mem_one' | [
{
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Mathlib/Topology/SubsetProperties.lean | cluster_point_of_compact | [
{
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724,
58
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Mathlib/Data/Fin/Basic.lean | Fin.rev_le_rev | [
{
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] | [
498,
36
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496,
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.div_pow | [
{
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] | [
436,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
11
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.mem_ndunion | [] | [
164,
51
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163,
1
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_conjTranspose | [
{
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395,
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392,
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Mathlib/Analysis/Normed/Group/Basic.lean | squeeze_one_norm | [] | [
1068,
46
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1066,
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.surjective_untrop | [] | [
156,
28
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155,
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Mathlib/Data/Set/Image.lean | Set.range_id' | [] | [
862,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
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Mathlib/Data/Set/Lattice.lean | Set.iInter₂_eq_empty_iff | [
{
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.conjCle_coe | [] | [
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6
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Mathlib/RingTheory/Ideal/AssociatedPrime.lean | LinearEquiv.AssociatedPrimes.eq | [] | [
119,
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116,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_le_add' | [
{
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2019,
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Mathlib/Data/List/Basic.lean | List.set_eq_nil | [
{
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] | [
2316,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Torsion.lean | AddMonoid.IsTorsion.module_of_torsion | [
{
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172,
89
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src/lean/Init/Control/Lawful.lean | ExceptT.seq_eq | [] | [
138,
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.eval_smul | [
{
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301,
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291,
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Mathlib/Data/Set/Basic.lean | Set.subset_def | [] | [
347,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_monomial_of_ne_zero | [
{
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}
] | [
2406,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2405,
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Std/Data/Nat/Lemmas.lean | Nat.le_or_le | [] | [
386,
99
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386,
11
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Mathlib/Logic/Basic.lean | rec_heq_of_heq | [
{
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},
{
"state_a... | [
566,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
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Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.isUnit_toMatrix_iff | [
{
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.disjointed | [] | [
241,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
11
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Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.GCD.induction | [
{
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191,
37
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180,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_refl | [] | [
499,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.addOrderOf_div_of_gcd_eq_one | [
{
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"state_befo... | [
400,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.Equiv.le | [] | [
745,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.abs_exp_ofReal_mul_I | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑abs (exp (↑x * I)) = 1",
"tactic": "rw [exp_mul_I, abs_cos_add_sin_mul_I]"
}
] | [
2037,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2036,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.add_aux_right | [
{
"state_after": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx y1 y2 : ℕ × K\nH : R K p y1 y2\nn : ℕ\ny : K\n⊢ R K p (x.fst + (n, y).fst, (↑(frobenius K p)^[(n, y).fst]) x.snd + (↑(frobenius K p)^[x.fst]) (n, y).snd)\n (x.fst + (n + 1, ↑(frobenius K p) y).fst,\n ... | [
273,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
9
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Mathlib/Data/Nat/Units.lean | Nat.isUnit_iff | [] | [
33,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
11
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Mathlib/Order/Filter/Basic.lean | Filter.eventually_false_iff_eq_bot | [] | [
1107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
] |
Mathlib/Topology/Separation.lean | continuousAt_update_of_ne | [
{
"state_after": "no goals",
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"tactic": "simp only [← continuousWithin... | [
571,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_assoc | [] | [
759,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_le_nadd_iff_left | [] | [
427,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback.mapDesc_comp | [
{
"state_after": "no goals",
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1396,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
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Mathlib/Geometry/Manifold/ChartedSpace.lean | closedUnderRestriction_iff_id_le | [
{
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468,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
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Mathlib/Data/Rat/Cast.lean | map_ratCast | [
{
"state_after": "no goals",
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"tactic": "rw [cast_def, map_div₀, map_intCast, map_natCast, cast_def]"
}
] | [
439,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_Iio | [] | [
220,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.top_toSubring | [] | [
799,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_congr_norm | [] | [
555,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.nonempty_of_pos_sInf | [
{
"state_after": "s : Set ℕ\nh : 0 < sInf s\ncontra : ¬Set.Nonempty s\n⊢ False",
"state_before": "s : Set ℕ\nh : 0 < sInf s\n⊢ Set.Nonempty s",
"tactic": "by_contra contra"
},
{
"state_after": "s : Set ℕ\nh : 0 < sInf s\ncontra : s = ∅\n⊢ False",
"state_before": "s : Set ℕ\nh : 0 < sInf s\nc... | [
95,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.equivOfRoot_aeval | [] | [
374,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_iff_exists_edge_coe | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.72136\n𝕜 : Type ?u.72139\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\n⊢ Adj G a b ↔ ∃ e, ↑e = Quotient.mk (Sym2.Rel.setoid V) (a, b)",
"tactic": "simp only [mem_e... | [
565,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.sup | [] | [
466,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
8
] |
Mathlib/Data/Matrix/Basic.lean | IsSMulRegular.matrix | [] | [
385,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.smul | [
{
"state_after": "case intro.intro\nα : Type u_1\nE : Type u_2\n𝕜 : Type u_3\ninst✝² : NormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\na b : α → 𝕜\nu v : α → E\nl : Filter α\nhab : a ~[l] b\nhuv : u ~[l] v\nφ : α → 𝕜\nhφ : Tendsto φ l (𝓝 1)\nhabφ : a =ᶠ[l] φ * b\n⊢ (fun x => a x • u... | [
277,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Std/Data/List/Init/Lemmas.lean | List.foldl_eq_foldlM | [
{
"state_after": "no goals",
"state_before": "β : Type u_1\nα : Type u_2\nf : β → α → β\nb : β\nl : List α\n⊢ foldl f b l = List.foldlM f b l",
"tactic": "induction l generalizing b <;> simp [*, foldl]"
}
] | [
179,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
177,
1
] |
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