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/Real/ENNReal.lean | ENNReal.iInf_ennreal | [] | [
448,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsRefl.eq_zero | [] | [
862,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_of_le_of_lt | [] | [
283,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
11
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableWithinAt.mul | [] | [
324,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Order/BoundedOrder.lean | bot_lt_iff_ne_bot | [] | [
381,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_dvd_opow | [
{
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}
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215,
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Mathlib/Data/Finset/Sym.lean | Finset.sym_fill_mem | [] | [
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.smul_const | [
{
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105,
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integral_zero | [] | [
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_pair | [
{
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906,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.zero_kronecker | [] | [
297,
51
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Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_mem_fundamentalDomain | [] | [
156,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_mul_conjTranspose_self | [
{
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"tactic": "rw ... | [
201,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_conj | [
{
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"tactic": "rw [norm_eq_mul_conj, star_star, mul_comm, norm_eq_mul_conj]"
}
] | [
573,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.FinMeasAdditive.of_eq_top_imp_eq_top | [] | [
123,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_univ | [
{
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"tacti... | [
544,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith | [
{
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153,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.cons_congr | [
{
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},
{
"state_afte... | [
1117,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.map_inv₂ | [] | [
168,
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166,
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Mathlib/MeasureTheory/Function/EssSup.lean | le_essInf_of_ae_le | [] | [
175,
41
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174,
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.of_isIso_comp_left | [
{
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445,
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442,
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Mathlib/Data/Finset/Basic.lean | Finset.union_subset_union_left | [] | [
1385,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_one_sub_norm | [
{
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"tactic": "simp only... | [
177,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/Order/Lattice.lean | inf_eq_min | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
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Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeft_mul | [
{
"state_after": "case h\nR : Type u_2\nA : Type u_1\ninst✝⁴ : CommSemiring R\ninst✝³ : NonUnitalSemiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : IsScalarTower R A A\na b x✝ : A\n⊢ ↑(mulLeft R (a * b)) x✝ = ↑(comp (mulLeft R a) (mulLeft R b)) x✝",
"state_before": "R : Type u_2\nA : Typ... | [
146,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mul_toGerm | [] | [
652,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_sup | [
{
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"tactic": "simp onl... | [
269,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_orthogonal_vadd | [
{
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647,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.exists_pos_preimage_ball | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.cancel_left_on | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.53167\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.53179\nG : Type ?u.53182\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 : Se... | [
274,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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] |
Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : Preadditive C\nj k : ℕ\nA : IndexSet [j].op\nhA : ¬Mono (IndexSet.e A)\n⊢ ιSummand s A ≫ HomologicalComplex.d K[X] j k ≫ πSummand s (IndexSet.id [k].op) = 0",
"state_before":... | [
164,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/Data/List/Forall2.lean | List.forall₂_cons_right_iff | [] | [
109,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_empty | [
{
"state_after": "case h\nα : Type u_1\nM : Type u_2\nN : Type ?u.86392\nP : Type ?u.86395\nR : Type u_3\nS : Type ?u.86401\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nl : α... | [
273,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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Mathlib/Algebra/Quaternion.lean | Quaternion.one_imJ | [] | [
874,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
9
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | Conformal.differentiable | [] | [
141,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.gc | [
{
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"state_before": ... | [
278,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
11
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essInf_mono_ae | [] | [
164,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Topology/Connected.lean | exists_clopen_of_totally_separated | [
{
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1418,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt_mul_eq_succ | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\nha : a ≠ 0\n⊢ padicValInt p a + padicValInt p ↑p = padicValInt p a + 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\nha : a ≠ 0\n⊢ padicValInt p (a * ↑p) = padicValInt p a + 1",
"tactic": "rw [padicValInt.mul ha (Int.coe_nat_ne_zero.mp... | [
539,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioi_of_Ici | [] | [
192,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.obj | [
{
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"state_before": "C : Type u\ninst✝² : Category C\nD : Type u'\ninst✝¹ : Category D\ninst✝ : HasZeroObject ... | [
236,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/Topology/Order.lean | nhds_discrete | [] | [
297,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.cons_ndunion | [] | [
159,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/CategoryTheory/FullSubcategory.lean | CategoryTheory.FullSubcategory.lift_comp_map | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_rat | [] | [
747,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Data/List/Perm.lean | List.subperm_append_left | [] | [
713,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Data/List/Zip.lean | List.mem_zip_inits_tails | [
{
"state_after": "case nil\nα : Type u\nβ : Type ?u.161184\nγ : Type ?u.161187\nδ : Type ?u.161190\nε : Type ?u.161193\ninit✝ tail✝ init tail : List α\n⊢ (init, tail) ∈ ([], []) :: zip [] [] ↔ init ++ tail = []\n\ncase cons\nα : Type u\nβ : Type ?u.161184\nγ : Type ?u.161187\nδ : Type ?u.161190\nε : Type ?u.161... | [
444,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.lift_comp_mk' | [
{
"state_after": "case h\nM : Type u_1\nN : Type ?u.60480\nP : Type u_2\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nc : Con M\nx y : M\nf : M →* P\nH : c ≤ ker f\nx✝ : M\n⊢ ↑(MonoidHom.comp (lift c f H) (mk' c)) x✝ = ↑f x✝",
"state_before": "M : Type u_1\nN : Type ?u.60480\nP : T... | [
944,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.image_sub_const_Ico | [
{
"state_after": "case a\na b c : ℕ\nh : c ≤ a\nx : ℕ\n⊢ x ∈ image (fun x => x - c) (Ico a b) ↔ x ∈ Ico (a - c) (b - c)",
"state_before": "a b c : ℕ\nh : c ≤ a\n⊢ image (fun x => x - c) (Ico a b) = Ico (a - c) (b - c)",
"tactic": "ext x"
},
{
"state_after": "case a\na b c : ℕ\nh : c ≤ a\nx : ℕ\n... | [
219,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.mapAlgHom_coe_ringHom | [] | [
1411,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
] |
Mathlib/Algebra/Category/Ring/Basic.lean | RingCat.coe_of | [] | [
216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.strictMonoOn_arcsin | [] | [
83,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_fin | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.136300\nβ : Type ?u.136303\nγ : Type ?u.136306\nn : ℕ\ns : Finset ℕ\na : ℕ\nha : a < n\n⊢ { val := a, isLt := ha } ∈ Finset.fin n s ↔ ↑{ val := a, isLt := ha } ∈ s",
"tactic": "simp [Finset.fin, ha, and_comm]"
}
] | [
733,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translate_iterate | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nn : ℕ\n⊢ ↑↑(↑translate (↑Multiplicative.ofAdd x))^[n] = ↑↑(↑translate (↑Multiplicative.ofAdd (↑n * x)))",
"tactic": "rw [← coe_pow, ← Units.val_pow_eq_pow_val, translate_pow]"
}
] | [
322,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_mem_mul | [] | [
448,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.continuousWithinAt_Iio_iff_leftLim_eq | [] | [
357,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.contDiff_sinh | [] | [
120,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.add_one_eq_succ | [] | [
1058,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_div | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.of_cons | [] | [
68,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | StrictAntiOn.strictConcaveOn_of_deriv | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.448822\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.448918\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nh_anti : StrictAntiOn (deriv f) (interior D)\n⊢... | [
1133,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Std/Data/List/Lemmas.lean | List.append_ne_nil_of_ne_nil_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : List α\n⊢ s ≠ [] → s ++ t ≠ []",
"tactic": "simp_all"
}
] | [
113,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
113,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mk_mul_mk | [] | [
692,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.isGLB_sInf | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.92784\nγ : Type ?u.92787\nι : Sort ?u.92790\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set (WithTop α)\nhs : BddBelow s\n⊢ IsGLB s (sInf s)\n\ncase neg\nα : Type u_1\nβ : Type ?u.92784\nγ : Type ?u.92787\nι : Sort ?u.92790\ninst✝ : ConditionallyComp... | [
1211,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.congr_fun | [] | [
215,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
11
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.maximal_of_minimal_image | [] | [
870,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_le_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ -x ≤ 0 ↔ 0 ≤ x",
"tactic": "rw [neg_le_iff, neg_zero]"
}
] | [
1372,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_le_iInf₂ | [] | [
837,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_lt_zero | [] | [
738,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
737,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquivCodomain_apply | [] | [
1368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.range_mulVecLin | [
{
"state_after": "R : Type u_3\ninst✝¹ : CommSemiring R\nk : Type ?u.315479\nl : Type ?u.315482\nm : Type u_1\nn : Type u_2\ninst✝ : Fintype n\nM : Matrix m n R\nthis : DecidableEq n := Classical.decEq n\n⊢ LinearMap.range (mulVecLin M) = span R (Set.range Mᵀ)",
"state_before": "R : Type u_3\ninst✝¹ : CommS... | [
281,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_int_left | [] | [
1171,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.extract_gcd | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.42482\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf✝ f : β → α\nhs : Finset.Nonempty s\nh : ∀ (x : β), x ∈ s → f x = 0\n⊢ ∃ g, (∀ (b : β), b ∈ s → f b = gcd s f * g b) ∧ gcd s g = 1\n\ncase neg\nα : ... | [
283,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_iUnion_le | [
{
"state_after": "α : Type u_2\nβ : Type ?u.285208\nγ : Type ?u.285211\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α → ℝ≥0∞\nι : Type u_1\ninst✝ : Fintype ι\nf : α → ℝ≥0∞\nt : ι → Set α\n⊢ (∑' (x : ↑(⋃ (i : ι), t i)), f ↑x) ≤ ∑' (b : ι) (x : ↑(t b)), f ↑x",
"state_before": "α : ... | [
1018,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_eq_support_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type ?u.25735\nN : Type u_2\nP : Type ?u.25741\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf f₁ f₂ g g₁ g₂ : α →₀ N\n⊢ neLocus f g = (f - g).support",
"tactic": "rw [← neLocus_add_right _ _ (-g), add_right_neg, neLo... | [
148,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_converges_iff | [
{
"state_after": "α : Type u\nu : Ultrafilter (Ultrafilter α)\nx : Ultrafilter α\n⊢ ↑u ≤ 𝓝 x ↔ ↑(joinM u) ≤ ↑x",
"state_before": "α : Type u\nu : Ultrafilter (Ultrafilter α)\nx : Ultrafilter α\n⊢ ↑u ≤ 𝓝 x ↔ x = joinM u",
"tactic": "rw [eq_comm, ← Ultrafilter.coe_le_coe]"
},
{
"state_after": "α... | [
80,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.coe_deleteEdges_le | [
{
"state_after": "ι : Sort ?u.255030\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns : Set (Sym2 V)\nv w : ↑(deleteEdges G' s).verts\n⊢ SimpleGraph.Adj (Subgraph.coe (deleteEdges G' s)) v w → SimpleGraph.Adj (Subgraph.coe G') v w",
"state_before": "ι : Sort ?u.255030\nV : Type u\nW : Type v\n... | [
1112,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Order/Monotone/Basic.lean | List.foldl_monotone | [] | [
722,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.isThreeCycle_isConj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh5 : 5 ≤ card α\nσ τ : { x // x ∈ alternatingGroup α }\nhσ : IsThreeCycle ↑σ\nhτ : IsThreeCycle ↑τ\n⊢ Finset.card (support ↑σ) + 2 ≤ card α",
"tactic": "rwa [hσ.card_support]"
}
] | [
140,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_map | [] | [
504,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.unop_neg | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero | [] | [
406,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_le_of_mem_of_edist_le | [] | [
431,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.bot_smul | [] | [
195,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousAt_of_monotoneOn_of_exists_between | [] | [
254,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_mul | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nhn : n ∈ support (p * q)\n⊢ trailingDegree p + trailingDegree q ≤ ↑n",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ trailingDegree p + trailingDegree q ≤ tr... | [
367,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_comm | [] | [
378,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.IsBounded.union | [] | [
205,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_ofReal_mul | [
{
"state_after": "r : ℝ\nhr : 0 < r\nx : ℂ\nhx : ↑abs x ≠ 0\n⊢ log (↑r * x) = ↑(Real.log r) + log x",
"state_before": "r : ℝ\nhr : 0 < r\nx : ℂ\nhx : x ≠ 0\n⊢ log (↑r * x) = ↑(Real.log r) + log x",
"tactic": "replace hx := Complex.abs.ne_zero_iff.mpr hx"
},
{
"state_after": "no goals",
"stat... | [
85,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | le_mul_of_le_one_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.40562\ninst✝ : OrderedRing α\na b c d : α\nhb : b ≤ 0\nh : a ≤ 1\n⊢ b ≤ a * b",
"tactic": "simpa only [one_mul] using mul_le_mul_of_nonpos_right h hb"
}
] | [
395,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.incidenceFinset_eq_filter | [
{
"state_after": "case a\nι : Sort ?u.277119\n𝕜 : Type ?u.277122\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\ninst✝² : Fintype ↑(neighborSet G v)\ninst✝¹ : DecidableEq V\ninst✝ : Fintype ↑(edgeSet G)\ne : Sym2 V\n⊢ e ∈ incidenceFinset G v ↔ e ∈ filte... | [
1430,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1426,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.source_eq | [] | [
952,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.ext | [] | [
706,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.span_empty | [] | [
661,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Algebra/Star/Module.lean | StarModule.selfAdjointPart_add_skewAdjointPart | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝⁷ : Semiring R\ninst✝⁶ : StarSemigroup R\ninst✝⁵ : TrivialStar R\ninst✝⁴ : AddCommGroup A\ninst✝³ : Module R A\ninst✝² : StarAddMonoid A\ninst✝¹ : StarModule R A\ninst✝ : Invertible 2\nx : A\n⊢ ↑(↑(selfAdjointPart R) x) + ↑(↑(ske... | [
138,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_singleton | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.157791\nγ : Type ?u.157794\nι : Sort ?u.157797\nκ : ι → Sort ?u.157802\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\nx a x✝ : α\n⊢ x✝ ∈ ↑(upperClosure {a}) ↔ x✝ ∈ ↑(UpperSet.Ici a)",
"state_before": "α : Type u_1\nβ : Type ?u.157791\nγ : Type ?u... | [
1403,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Iic_mem_nhds' | [] | [
1465,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1464,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_orthogonalComplement_singleton_eq_neg | [] | [
990,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.zero_ne_bit1 | [] | [
151,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsTrail.rotate | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v : V\nc : Walk G v v\nhc : IsTrail c\nh : u ∈ support c\n⊢ List.Nodup (edges c)",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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