file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
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Mathlib/Order/Ideal.lean | Order.Ideal.coe_subset_coe | [] | [
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153,
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mul_int | [] | [
157,
23
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156,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.restrictScalars_inj | [] | [
464,
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462,
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.adjoin_gen_eq_top | [
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509,
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_map_neg | [
{
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Mathlib/Data/Set/Function.lean | Set.injOn_of_injective | [] | [
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Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixedPoints_antitone | [] | [
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Mathlib/Topology/Order/Basic.lean | Icc_mem_nhdsWithin_Ici | [] | [
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Mathlib/Data/Nat/Factorial/Cast.lean | Nat.cast_descFactorial | [
{
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"tactic": "rw [← pochhammer_eval_cast,... | [
50,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_comap_le | [] | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_eq_iff_eq_add_of_le | [
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_eq_zero_of_pos_iff | [
{
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.tendsto_set_integral_of_monotone | [
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235,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.b_ne_one | [
{
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48
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.cases_mk | [
{
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446,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.max_aleph_eq | [
{
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... | [
264,
51
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261,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_linearEquivTuple | [] | [
546,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
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src/lean/Init/Data/Nat/Basic.lean | Nat.mul_assoc | [
{
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200,
78
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iUnion_null_iff | [] | [
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64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_nonneg | [] | [
1371,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
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Mathlib/Algebra/GroupPower/Basic.lean | one_pow | [
{
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Mathlib/Algebra/Parity.lean | Even.pow_nonneg | [
{
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_inter' | [] | [
941,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
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Mathlib/Order/Filter/Lift.lean | Filter.map_lift_eq2 | [] | [
134,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_sub_eq_sqrt_iff_real_inner_eq_zero | [
{
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.continuous_coe | [] | [
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43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
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Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.mem_ordConnectedComponent_trans | [] | [
93,
34
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Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.IsInitial.subsingleton_to | [] | [
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22
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Mathlib/Algebra/Order/Pointwise.lean | LinearOrderedField.smul_Ici | [
{
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"tactic": "ext x"
... | [
280,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
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Mathlib/Data/Finset/Pi.lean | Finset.pi_subset | [] | [
131,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
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Mathlib/Analysis/NormedSpace/Star/Mul.lean | mul_isometry | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_injective_of_ping_pong | [
{
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Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.ext_ker | [
{
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78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Rat/Defs.lean | Rat.zero_add | [
{
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"tactic": "rw [← zero_divInt d, add_def'', zero_mul, zero_add, divInt_mul_right] <;> simp [h]"
}
] | [
208,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.self_le_power | [
{
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},
{
"state_af... | [
728,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Lattice.lean | Finset.sup'_le | [
{
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807,
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805,
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.Approx.head_succ' | [
{
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178,
17
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Mathlib/Data/List/Basic.lean | List.take_nil | [] | [
1922,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1921,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_eq_zero | [] | [
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341,
20
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_eq | [] | [
388,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.associator_inv_naturality | [
{
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321,
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Mathlib/FieldTheory/Finite/Basic.lean | Nat.ModEq.pow_totient | [
{
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"tactic": "rw [← ZMod.eq_iff_modEq_nat]"
},
{
"state_after": "K : Type ?u.971204\nR :... | [
382,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
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Mathlib/Data/Int/Parity.lean | Int.not_even_one | [
{
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},
{
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"state_before": "m n : ℤ\n⊢ ¬1 % 2 = 0",
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}
] | [
101,
11
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99,
1
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.subtypePermOfFintype_apply | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.app_inv | [] | [
99,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_st | [] | [
358,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.interedges_biUnion_left | [
{
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108,
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Mathlib/Control/Fold.lean | Traversable.foldr_toList | [
{
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367,
32
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363,
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.defn | [
{
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{
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280,
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265,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.intervalIntegral_pos_of_pos_on | [
{
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1311,
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1302,
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | ContDiffOn.continuousOn_iteratedDerivWithin | [
{
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159,
47
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156,
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Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimit_toDual_iff | [
{
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] | [
260,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.mkOfBound_coe | [] | [
137,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_ite_self_eq | [
{
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126,
38
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122,
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Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_sub_swap | [] | [
795,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memℒp | [
{
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339,
38
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313,
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.mk_coe' | [] | [
849,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_add_Ioi | [] | [
49,
40
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48,
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Mathlib/Analysis/Normed/Ring/Seminorm.lean | MulRingSeminorm.apply_one | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.one_apply | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | NNReal.continuousAt_rpow_const | [
{
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}
] | [
478,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
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Mathlib/Logic/Basic.lean | Or.imp3 | [] | [
350,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
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Mathlib/Order/WithBot.lean | WithTop.map_comm | [] | [
744,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
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Std/Data/Int/Lemmas.lean | Int.subNatNat_add | [
{
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243,
80
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236,
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Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.tmulSymm_apply | [] | [
619,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
9
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Mathlib/Algebra/MonoidAlgebra/Ideal.lean | MonoidAlgebra.mem_ideal_span_of_image | [
{
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63,
82
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26,
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Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.zero_mul_nonneg | [] | [
841,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
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Mathlib/Logic/Unique.lean | Fin.default_eq_zero | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Algebra/GroupPower/Basic.lean | pow_mul_comm' | [] | [
150,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.trans_le | [] | [
1667,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1666,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_nonneg_of_nonneg | [
{
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"state_before": "x : ℝ\nhx : 0 ≤ x\ny : ℝ\n⊢ 0 ≤ x ^ y",
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},
{
"state_after": "no goals",
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146,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.hasSum_inner_mul_inner | [
{
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497,
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493,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_restrict | [
{
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1082,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pellZd_re | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_ofSeq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ (match\n match Option.map (fun a' => (a', Seq.tail (some <$> s))) (Seq.get? (some <$> s) 0) with\n | none => Sum.inl none\n | some (none, s') => Sum.inr s'\n | some (some a, s') => Sum.inl (some (a, s')) with\n | Sum.inl a... | [
1357,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_restrict_apply | [] | [
1604,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1601,
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.mk'_mul | [
{
"state_after": "no goals",
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890,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
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Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.inv_left | [
{
"state_after": "no goals",
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"tactic": "rw [← Comma.comp_left, IsIso.hom_inv_id, id_left]"
}
] | [
207,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.mk_coe | [] | [
178,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.filter_inf | [] | [
273,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.add_eq_max_of_ne' | [] | [
634,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq_lem2 | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\nh : xn a1 n * 2 = xn a1 n * a + Pell.d a1 * yn a1 n\n⊢ a = 2 ∧ n = 0",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\nh : 2 * xn a1 n = xn a1 (n + 1)\n⊢ a = 2 ∧ n = 0",
"tactic": "rw [xn_succ, mul_comm] at h"
},
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\n... | [
667,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_mul | [
{
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278,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
11
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isDetecting_iff_isSeparating | [] | [
193,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.FractionRing.isAlgebraic | [
{
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371,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
9
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_zero | [
{
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1161,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
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Mathlib/Computability/Reduce.lean | OneOneReducible.to_many_one | [] | [
108,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.abs_integral_eq_abs_integral_uIoc | [] | [
540,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Algebra/Lie/Matrix.lean | lieEquivMatrix'_symm_apply | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_right_Icc' | [
{
"state_after": "no goals",
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"tactic": "simp [h, division_def]"
}
] | [
731,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_codRestrict | [] | [
1010,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.eq_top_of_unit_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b x y : α\nhx : x ∈ I\nh : y * x = 1\nz : α\nx✝ : z ∈ ⊤\n⊢ z = z * (y * x)",
"tactic": "simp [h]"
}
] | [
88,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.symm_apply_apply | [] | [
529,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
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Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.Hom.ext | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.4131\ninst✝ : Category C\nX Y : PresheafedSpace C\nα β : Hom X Y\nw : α.base = β.base\n⊢ Functor.op (Opens.map α.base) = Functor.op (Opens.map β.base)",
"tactic": "rw [w]"
},
{
"state_after": "case mk\nC : Type u_1\ninst✝ : Category C\nX ... | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_split | [] | [
1429,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_abs | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nφ : Ultrafilter α\ninst✝ : LinearOrderedAddCommGroup β\nx : β\n⊢ ↑(abs x) = abs ↑x",
"tactic": "rw [abs_def, map_const]"
}
] | [
252,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ico_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n => Ico (↑n) (↑n + 1))",
"tactic": "simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)"
}
] | [
258,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Deprecated/Subring.lean | RingHom.isSubring_image | [] | [
67,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basis_ne_zero | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nv : ι → F\ni j : ι\nhvs : Set.InjOn v ↑s\nhi : i ∈ s\n⊢ ∀ (a : ι), a ≠ i ∧ a ∈ s → ¬basisDivisor (v i) (v a) = 0",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Fi... | [
220,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/List/Basic.lean | List.insertNth_injective | [
{
"state_after": "case zero\nι : Type ?u.128977\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na x : α\n⊢ Injective (insertNth zero x)\n\ncase succ\nι : Type ?u.128977\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na x : α\nn : ℕ\nIH : Injective (insertNth n x)\n⊢ Injective (... | [
1761,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1757,
1
] |
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