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/FieldTheory/ChevalleyWarning.lean | char_dvd_card_solutions | [
{
"state_after": "K : Type u_2\nσ : Type u_1\nι : Type ?u.638341\ninst✝⁵ : Fintype K\ninst✝⁴ : Field K\ninst✝³ : Fintype σ\ninst✝² : DecidableEq σ\ninst✝¹ : DecidableEq K\np : ℕ\ninst✝ : CharP K p\nf : MvPolynomial σ K\nh : totalDegree f < Fintype.card σ\nF : Unit → MvPolynomial σ K := fun x => f\n⊢ p ∣ Fintype... | [
193,
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185,
1
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.multichoose_zero_right | [
{
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}
] | [
364,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
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Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.restrict_mker | [] | [
1196,
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Mathlib/Analysis/Calculus/MeanValue.lean | Convex.is_const_of_fderivWithin_eq_zero | [
{
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Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_inv | [
{
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1442,
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1426,
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Mathlib/Analysis/Convex/Strict.lean | DirectedOn.strictConvex_sUnion | [
{
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100,
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97,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul'_char | [
{
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"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\n... | [
218,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/Logic/Equiv/Basic.lean | Function.update_comp_equiv | [
{
"state_after": "no goals",
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"tactic": "rw [← update_comp_eq_of_injective _ g.injective, g.apply_symm_app... | [
1921,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1918,
1
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Mathlib/Data/Nat/Factors.lean | Nat.factors_chain | [
{
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"tactic": "match n with\n| 0 => simp\n| 1 => simp\n| k + 2 =>\n intro a h\n let m := minFac (k + 2)\n have : (k + 2) / m < (k + 2) := factor... | [
104,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_source_mem_nhdsWithin' | [] | [
1078,
65
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1076,
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Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousWithinAt.zpow | [] | [
536,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_const | [] | [
1158,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.one | [] | [
193,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.iselect_cons | [
{
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"tactic": "sim... | [
574,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/Data/List/BigOperators/Basic.lean | MonoidHom.map_list_prod | [] | [
704,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
11
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Mathlib/SetTheory/Game/PGame.lean | PGame.leftMoves_mk | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.closure_cycle_coprime_swap | [
{
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"state_before": "ι : Type ?u.29580... | [
1680,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1668,
1
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_eq_norm_of_isMaxOn_of_ball_subset | [] | [
208,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_one_left_iff | [
{
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1346,
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1339,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_inter_Ioc_of_le | [] | [
715,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
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Mathlib/Order/Hom/Bounded.lean | BotHom.coe_copy | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.flip_apply | [] | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_mul | [] | [
254,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Mathlib/MeasureTheory/Group/Arithmetic.lean | Finset.measurable_prod' | [] | [
934,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
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Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.mem_normalizer | [] | [
64,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/Data/Set/Basic.lean | Set.setOf_or | [] | [
306,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
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Mathlib/Algebra/Order/Group/Abs.lean | sub_lt_of_abs_sub_lt_left | [] | [
301,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_eq_of_isRotated | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.774035\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nhd : Nodup l\nn : ℕ\n⊢ formPerm l = formPerm (rotate l n)",
"state_before": "α : Type u_1\nβ : Type ?u.774035\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl l' : List α\nhd : Nodup l\nh : l ... | [
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.findMin_dual | [] | [
591,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
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Mathlib/Order/BoundedOrder.lean | bot_unique | [] | [
369,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/Data/Fin/VecNotation.lean | Matrix.vecHead_vecAlt0 | [] | [
362,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Func.lean | List.Func.get_map | [
{
"state_after": "no goals",
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"tactic": "cases h"
},
{
"state_after": "α : Type u\nβ : Type ... | [
205,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Analysis/Convex/Function.lean | concaveOn_iff_pairwise_pos | [] | [
356,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.measurePreserving_inv | [] | [
390,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/Data/Complex/Exponential.lean | Real.add_one_le_exp | [
{
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"state_before": "x : ℝ\n⊢ x + 1 ≤ exp x",
"tactic": "cases' le_or_lt 0 x with h h"
},
{
"state_after": "no goals",
"state_before": "case inr\nx : ℝ\nh : x < 0\n⊢ x + 1 ≤ exp x",
... | [
1990,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
1
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Mathlib/Algebra/Squarefree.lean | Squarefree.squarefree_of_dvd | [] | [
88,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_mem_subspace_eq_self | [
{
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519,
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Mathlib/Data/Finset/Basic.lean | Finset.pair_eq_singleton | [] | [
1113,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
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Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.isTransitive_iff_sUnion_subset | [
{
"state_after": "case intro.intro\nx y✝ z✝ : ZFSet\nh : IsTransitive x\ny : ZFSet\nhy : y ∈ ⋃₀ x\nz : ZFSet\nhz : z ∈ x\nhz' : y ∈ z\n⊢ y ∈ x",
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"tactic": "rcases mem_sUnion.1 hy with ⟨z, hz, hz'⟩"
},
{
"sta... | [
99,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.MeasurePreserving.set_lintegral_comp_emb | [
{
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
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Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongUniformity.uniformEmbedding_coeFn | [] | [
104,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLeast.csInf_eq | [] | [
569,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Deprecated/Group.lean | RingHom.to_isAddGroupHom | [] | [
391,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/Analysis/Convex/Star.lean | StarConvex.smul_mem | [
{
"state_after": "no goals",
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344,
92
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343,
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Std/Data/List/Lemmas.lean | List.sublist_of_cons_sublist | [] | [
342,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_natDegree | [
{
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81,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Data/Num/Lemmas.lean | ZNum.zneg_zneg | [
{
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"tactic": "cases n <;> rfl"
}
] | [
1079,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.isIso_of_bijective | [] | [
564,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_monomial_zero_mul | [] | [
292,
29
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290,
1
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Mathlib/Data/Nat/Factors.lean | Nat.dvd_of_factors_subperm | [
{
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"state_before": "a b : ℕ\nha : a ≠ 0\nh : factors a <+~ factors b\n⊢ a ∣ b",
"tactic": "rcases b.eq_zero_or_pos with (rfl | hb)"
},
... | [
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Mathlib/Data/Finset/Basic.lean | Finset.toList_cons | [
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Mathlib/Analysis/Normed/Group/Basic.lean | Pi.sum_nnnorm_apply_le_nnnorm' | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.comap_comap | [] | [
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Mathlib/Order/Bounds/Basic.lean | le_of_isLUB_le_isGLB | [] | [
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Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.trans_refl_reparam | [
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Mathlib/Data/Set/Function.lean | Set.restrict_extend_range | [
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.normalize_apply | [] | [
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Mathlib/Topology/Instances/ENNReal.lean | Continuous.ennreal_mul | [] | [
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Mathlib/Algebra/Ring/AddAut.lean | AddAut.mulRight_symm_apply | [] | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.comp_eq_sum_left | [
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_map_left | [] | [
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.linearIndependent_powers_iff_aeval | [
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Mathlib/Data/Complex/Module.lean | Complex.coe_basisOneI_repr | [] | [
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.count_normalizedFactors_eq | [
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.trans' | [] | [
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_eq_iInter_thickening' | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_coe | [] | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_sub | [
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Mathlib/Algebra/GroupPower/Ring.lean | zero_pow_eq | [
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Mathlib/RingTheory/Finiteness.lean | RingHom.Finite.id | [] | [
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_union_le | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.iSup_induction | [
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Mathlib/Order/MinMax.lean | min_lt_of_right_lt | [] | [
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32
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_cons_self | [] | [
2354,
29
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Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_div_unitSphere | [] | [
142,
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Mathlib/Init/Algebra/Order.lean | not_lt | [] | [
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372,
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_nat | [] | [
539,
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.withSeminorms_of_nhds | [
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Mathlib/Topology/Basic.lean | nhds_le_of_le | [
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Mathlib/Data/ULift.lean | ULift.up_inj | [] | [
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.funext | [
{
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Mathlib/Order/Heyting/Basic.lean | PUnit.compl_eq | [] | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.cycleFactorsFinset_eq_singleton | [] | [
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1456,
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_one | [] | [
464,
6
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463,
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Mathlib/Analysis/Convex/StoneSeparation.lean | exists_convex_convex_compl_subset | [
{
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Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.Fin.circulant_isSymm_iff | [
{
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Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.zero_completion | [] | [
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_iUnion | [
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Mathlib/Logic/IsEmpty.lean | isEmpty_pprod | [
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176,
61
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.sub_eq | [
{
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Mathlib/Algebra/Periodic.lean | Multiset.periodic_prod | [] | [
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineEquiv.span_eq_top_iff | [
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.iUnion_left_iff | [
{
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Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.mono | [] | [
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Mathlib/Topology/Algebra/Module/Basic.lean | Module.punctured_nhds_neBot | [
{
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictMonoOn.const_mul' | [] | [
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Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.cancel_right | [] | [
260,
73
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258,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_eq_zero | [
{
"state_after": "α✝ : Type ?u.102030\nβ : Type ?u.102033\nγ : Type ?u.102036\nr✝ : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nα : Type u_1\nr : α → α → Prop\nx✝ : IsWellOrder α r\nh : card (type r) = 0\nthis : IsEmpty { α := α, r := r, wo := x✝ }.α\n⊢ type r = 0",
"state_before": "α✝ ... | [
634,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_two | [
{
"state_after": "case h.h\nm k : ℕ\n⊢ hyperoperation 2 m k = m * k",
"state_before": "⊢ hyperoperation 2 = fun x x_1 => x * x_1",
"tactic": "ext (m k)"
},
{
"state_after": "case h.h.zero\nm : ℕ\n⊢ hyperoperation 2 m Nat.zero = m * Nat.zero\n\ncase h.h.succ\nm bn : ℕ\nbih : hyperoperation 2 m bn... | [
83,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t✝ : Set α\na✝ b✝ : α\ninst✝ : LinearOrder γ\na b : γ\ns t : Set γ\nha : IsLeast s a\nhb : IsLeast t b\n⊢ min a b ∈ s ∪ t",
"tactic": "cases' le_total a b with h h <... | [
461,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
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