file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/FieldTheory/Subfield.lean | Subfield.multiset_sum_mem | [] | [
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21
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11
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_degree_le_one | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.natCast_zero | [] | [
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Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_apply_eq' | [] | [
104,
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Mathlib/RingTheory/Ideal/Basic.lean | mem_nonunits_iff | [] | [
830,
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_finset_sum_index | [
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Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_sub | [
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54
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Mathlib/Data/Seq/Computation.lean | Computation.terminates_of_mem | [] | [
359,
11
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Mathlib/Order/Filter/Basic.lean | Set.EqOn.eventuallyEq_of_mem | [] | [
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61
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.ennreal_tsum | [
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Mathlib/Computability/Primrec.lean | Primrec.fin_val_iff | [
{
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Mathlib/CategoryTheory/DiscreteCategory.lean | CategoryTheory.Discrete.natIso_app | [
{
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}
] | [
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk | [
{
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753,
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Mathlib/Algebra/Hom/Aut.lean | MulAut.inv_apply_self | [] | [
108,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | DirectSum.IsInternal.subordinateOrthonormalBasis_subordinate | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_filter_of_ne | [
{
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241,
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_of_isLUB | [] | [
246,
49
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.mem_bot_iff | [] | [
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504,
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Mathlib/Topology/MetricSpace/Basic.lean | MetricSpace.replaceBornology_eq | [
{
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3030,
6
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Mathlib/Data/List/Perm.lean | List.Perm.join | [
{
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"tactic": "simpa only [join, append_assoc] using perm_append_comm.append_right _"
... | [
1074,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousAt.upperSemicontinuousWithinAt | [] | [
682,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tensorTensorTensorComm_tmul | [] | [
930,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
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Std/Data/Int/DivMod.lean | Int.negSucc_emod | [
{
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"state_before": "m : Nat\nb : Int\nbpos : 0 < b\n⊢ -[m+1] % b = b - 1 - ↑m % b",
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},
{
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Icc_infinite | [] | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimit_of_succ_ne | [] | [
126,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.singleton_inj | [] | [
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29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_last | [
{
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"tactic": "simp [snoc]"
}
] | [
471,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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Mathlib/Order/Hom/Lattice.lean | InfTopHom.coe_id | [] | [
937,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_diff_ball | [
{
"state_after": "no goals",
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"tactic": "rw [← ball_union_sphere, Set.union_diff_cancel_left sphere_disjoint_ball.sy... | [
570,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.comp_continuousLinearMap | [] | [
393,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
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Mathlib/Order/Filter/AtTopBot.lean | OrderIso.comap_atBot | [] | [
408,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
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Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.Reachable.exists_walk_of_dist | [] | [
60,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/Computation.lean | Computation.results_think_iff | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
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Mathlib/Data/Finset/Card.lean | Finset.card_image_of_injOn | [
{
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"tactic": "simp only [card, image_val_of_injOn H, card_map]"
}
] | [
224,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_univ_ne_zero | [] | [
1101,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.leftComm_tmul | [] | [
897,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/LinearAlgebra/Dual.lean | Submodule.mem_dualAnnihilator | [
{
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Mathlib/Topology/Basic.lean | interior_univ | [] | [
334,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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Mathlib/Analysis/Normed/Group/Basic.lean | ULift.nnnorm_down | [] | [
2139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2138,
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.map_of | [] | [
173,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_iUnion | [] | [
250,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Index.lean | Subgroup.nat_card_dvd_of_le | [] | [
308,
70
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Mathlib/Data/Setoid/Partition.lean | Setoid.eqv_classes_disjoint | [] | [
172,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply | [
{
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Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.id_left | [] | [
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Mathlib/Data/PFun.lean | PFun.dom_iff_graph | [] | [
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19
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.mem_closure_iff | [
{
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}
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Basic.lean | nhds_basis_uniformity' | [
{
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Mathlib/Topology/PathConnected.lean | Continuous.path_eval | [] | [
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50
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Mathlib/Algebra/DualQuaternion.lean | Quaternion.fst_imK_dualNumberEquiv_symm | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_mul_le | [
{
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"tactic": "classical\nrepeat' rw ... | [
551,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
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Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_apply' | [
{
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_toL1 | [] | [
1446,
37
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Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_pow_sub_C_unit | [
{
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{
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243,
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227,
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left | [
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157,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.All.imp | [] | [
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63
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454,
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Mathlib/Order/GameAdd.lean | Prod.gameAdd_swap_swap | [
{
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78,
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.mapBiproduct_hom_desc | [
{
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442,
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Mathlib/Algebra/Order/Floor.lean | Nat.lt_one_of_floor_lt_one | [
{
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] | [
153,
92
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153,
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Std/Logic.lean | heq_self_iff_true | [] | [
88,
77
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Mathlib/Data/Nat/Factors.lean | Nat.eq_two_pow_or_exists_odd_prime_and_dvd | [] | [
305,
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299,
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Mathlib/Analysis/Convex/Basic.lean | Set.OrdConnected.convex | [] | [
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50
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577,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.isNilpotent_iff_exists_self_le_ucs | [
{
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439,
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Mathlib/Topology/Algebra/UniformMulAction.lean | UniformSpace.Completion.coe_smul | [] | [
185,
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184,
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Mathlib/Order/UpperLower/LocallyFinite.lean | Set.Finite.lowerClosure | [
{
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34,
43
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Mathlib/AlgebraicTopology/DoldKan/Faces.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero | [
{
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.one_le_maxVar | [
{
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82,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_nonneg | [
{
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580,
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576,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.le_opNorm_of_le | [
{
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254,
62
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253,
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Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.isLittleO_log_re_re | [] | [
111,
57
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Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_sub_left | [
{
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153,
64
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152,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.sub_dvd_eval_sub | [
{
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478,
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475,
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Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff_right | [] | [
666,
44
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665,
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Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousAt.div_const | [] | [
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Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.epi_comp | [
{
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310,
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305,
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Mathlib/Data/List/BigOperators/Lemmas.lean | MulOpposite.op_list_prod | [
{
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148,
89
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144,
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Mathlib/Topology/Order/Basic.lean | isOpen_lt | [
{
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288,
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286,
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Mathlib/Order/Heyting/Regular.lean | Heyting.isRegular_of_decidable | [] | [
266,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.not_isUniform_zero | [
{
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{
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95,
83
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Mathlib/LinearAlgebra/FiniteDimensional.lean | finrank_eq_one_iff_of_nonzero | [
{
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{
"state_after": "case h.e... | [
1256,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_mk' | [] | [
306,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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Mathlib/Order/Monotone/Basic.lean | antitone_lam | [] | [
332,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
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Mathlib/Algebra/GroupPower/Ring.lean | neg_pow_bit1 | [
{
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}
] | [
215,
63
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214,
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Mathlib/RingTheory/FractionalIdeal.lean | IsFractional.map | [
{
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725,
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718,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasDerivAt_right | [] | [
761,
59
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758,
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Mathlib/Order/SupIndep.lean | CompleteLattice.independent_def'' | [
{
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267,
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Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_sup_le_inf_aux_left | [] | [
898,
39
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896,
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Mathlib/Data/Rel.lean | Rel.inv_inv | [
{
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{
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67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Init/Algebra/Classes.lean | asymm_of | [] | [
308,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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Mathlib/Computability/Reduce.lean | reflexive_oneOneReducible | [] | [
122,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_factors_comp_self | [
{
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}
] | [
342,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.mul_right_apply_of_ne | [
{
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193,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/Data/List/Duplicate.lean | List.exists_duplicate_iff_not_nodup | [
{
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138,
40
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137,
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Mathlib/Data/List/Nodup.lean | List.Nodup.pmap | [
{
"state_after": "α : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na b : α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nH : ∀ (a : α), a ∈ l → p a\nhf : ∀ (a : α) (ha : p a) (b : α) (hb : p b), f a ha = f b hb → a = b\nh : Nodup l\n⊢ Nodup (map (fun x => f ↑x (_ : p ↑x)) (List.attach l))",
... | [
291,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | LieSubmodule.lieIdeal_oper_eq_tensor_map_range | [
{
"state_after": "R : Type u\ninst✝⁶ : CommRing R\nL : Type v\nM : Type w\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nI : LieIdeal R L\nN : LieSubmodule R L M\n⊢ Submodule.span R {m | ∃ x n, ⁅↑x, ↑n⁆ = m} =\n ... | [
235,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.ofSet_source | [] | [
653,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.ofIsoLimit_lift | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_bind_modify | [] | [
73,
181
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
73,
9
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_le_neg_one_or_one_le_cast_of_ne_zero | [] | [
188,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Matrix/Basic.lean | LinearEquiv.mapMatrix_refl | [] | [
1502,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1501,
1
] |
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