url stringclasses 3
values | commit stringclasses 3
values | file_path stringlengths 20 79 | full_name stringlengths 3 115 | start sequence | end sequence | traced_tactics stringlengths 2 997k |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | nndist_nnnorm_nnnorm_le' | [
970,
1
] | [
971,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homeomorph.lean | Homeomorph.quotientMap | [
237,
11
] | [
239,
47
] | [{"tactic": "simp only [self_comp_symm, QuotientMap.id]", "annotated_tactic": ["simp only [<a>self_comp_symm</a>, <a>QuotientMap.id</a>]", [{"full_name": "Homeomorph.self_comp_symm", "def_path": "Mathlib/Topology/Homeomorph.lean", "def_pos": [201, 9], "def_end_pos": [201, 23]}, {"full_name": "QuotientMap.id", "def_path... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Bertrand.lean | Bertrand.real_main_inequality | [
54,
1
] | [
112,
35
] | [{"tactic": "let f : \u211d \u2192 \u211d := fun x => log x + sqrt (2 * x) * log (2 * x) - log 4 / 3 * x", "annotated_tactic": ["let f : \u211d \u2192 \u211d := fun x => <a>log</a> x + <a>sqrt</a> (2 * x) * <a>log</a> (2 * x) - <a>log</a> 4 / 3 * x", [{"full_name": "Real.log", "def_path": "Mathlib/Analysis/SpecialFunct... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ContinuedFractions/Computation/Approximations.lean | GeneralizedContinuedFraction.abs_sub_convergents_le' | [
537,
1
] | [
552,
87
] | [{"tactic": "have not_terminated_at_n : \u00ac(of v).TerminatedAt n := by\n simp [terminatedAt_iff_part_denom_none, nth_part_denom_eq]", "annotated_tactic": ["have not_terminated_at_n : \u00ac(<a>of</a> v).<a>TerminatedAt</a> n := by\n simp [<a>terminatedAt_iff_part_denom_none</a>, nth_part_denom_eq]", [{"full_name... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec | [
663,
1
] | [
665,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.map_nsmul | [
89,
1
] | [
90,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SumIntegralComparisons.lean | MonotoneOn.integral_le_sum | [
165,
1
] | [
168,
31
] | [{"tactic": "rw [\u2190 neg_le_neg_iff, \u2190 Finset.sum_neg_distrib, \u2190 intervalIntegral.integral_neg]", "annotated_tactic": ["rw [\u2190 <a>neg_le_neg_iff</a>, \u2190 <a>Finset.sum_neg_distrib</a>, \u2190 <a>intervalIntegral.integral_neg</a>]", [{"full_name": "neg_le_neg_iff", "def_path": "Mathlib/Algebra/Order/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GCDMonoid/Basic.lean | normUnit_one | [
94,
1
] | [
95,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_mul_X_sub_C | [
532,
1
] | [
533,
89
] | [{"tactic": "simp [mul_sub]", "annotated_tactic": ["simp [<a>mul_sub</a>]", [{"full_name": "mul_sub", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [365, 7], "def_end_pos": [365, 14]}]], "state_before": "R : Type u\nS : Type v\na\u271d b c d : R\nn m : \u2115\ninst\u271d : Ring R\np : R[X]\nr : R\na : \u2115... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Periodic.lean | Function.Periodic.const_inv_mul | [
135,
1
] | [
137,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_eq_zero | [
138,
1
] | [
139,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean | jacobiSym.value_at | [
325,
1
] | [
331,
79
] | [{"tactic": "conv_rhs => rw [\u2190 prod_factors hb.pos.ne', cast_list_prod, \u03c7.map_list_prod]", "annotated_tactic": ["conv_rhs => rw [\u2190 <a>prod_factors</a> hb.pos.ne', <a>cast_list_prod</a>, \u03c7.map_list_prod]", [{"full_name": "Nat.prod_factors", "def_path": "Mathlib/Data/Nat/Factors.lean", "def_pos": [67,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Ico_union_Ico | [
1524,
1
] | [
1525,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/RingHomProperties.lean | RingHom.RespectsIso.cancel_left_isIso | [
50,
1
] | [
54,
89
] | [{"tactic": "convert hP.2 (f \u226b g) (asIso f).symm.commRingCatIsoToRingEquiv H", "annotated_tactic": ["convert hP.2 (f \u226b g) (<a>asIso</a> f).symm.commRingCatIsoToRingEquiv H", [{"full_name": "CategoryTheory.asIso", "def_path": "Mathlib/CategoryTheory/Iso.lean", "def_pos": [307, 19], "def_end_pos": [307, 24]}]],... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_biUnion_iff | [
2522,
1
] | [
2524,
69
] | [{"tactic": "simp_rw [Filter.Eventually, ae_restrict_biUnion_eq s ht, mem_iSup]", "annotated_tactic": ["simp_rw [<a>Filter.Eventually</a>, <a>ae_restrict_biUnion_eq</a> s ht, <a>mem_iSup</a>]", [{"full_name": "Filter.Eventually", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [1072, 15], "def_end_pos": [1072... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.ite_univ | [
2307,
1
] | [
2307,
77
] | [{"tactic": "simp [Set.ite]", "annotated_tactic": ["simp [<a>Set.ite</a>]", [{"full_name": "Set.ite", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [2265, 15], "def_end_pos": [2265, 18]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\n\u03b9 : Sort x\na b : \u03b1\ns\u271d s\u2081 s\u2082... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sInf_eq_boundedBy_sInfGen | [
1141,
1
] | [
1148,
54
] | [{"tactic": "refine' le_antisymm _ _", "annotated_tactic": ["refine' <a>le_antisymm</a> _ _", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}]], "state_before": "\u03b1 : Type u_1\nm : Set (OuterMeasure \u03b1)\n\u22a2 sInf m = boundedBy (sInfGen ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_insert_left | [
900,
1
] | [
901,
47
] | [{"tactic": "rw [insert_eq, union_comm, Ioo_union_left h]", "annotated_tactic": ["rw [<a>insert_eq</a>, <a>union_comm</a>, <a>Ioo_union_left</a> h]", [{"full_name": "Set.insert_eq", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1310, 9], "def_end_pos": [1310, 18]}, {"full_name": "Set.union_comm", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/CliffordAlgebra/Grading.lean | CliffordAlgebra.even_induction | [
232,
1
] | [
243,
13
] | [{"tactic": "refine' evenOdd_induction Q 0 (fun rx => _) (@hadd) h\u03b9\u03b9_mul x hx", "annotated_tactic": ["refine' <a>evenOdd_induction</a> Q 0 (fun rx => _) (@hadd) h\u03b9\u03b9_mul x hx", [{"full_name": "CliffordAlgebra.evenOdd_induction", "def_path": "Mathlib/LinearAlgebra/CliffordAlgebra/Grading.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | clusterPt_principal_iff | [
1121,
1
] | [
1123,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/PEquiv.lean | PEquiv.toMatrix_injective | [
124,
1
] | [
140,
33
] | [{"tactic": "intro f g", "annotated_tactic": ["intro f g", []], "state_before": "k : Type u_1\nl : Type u_2\nm : Type u_3\nn : Type u_4\n\u03b1 : Type v\ninst\u271d\u00b2 : DecidableEq n\ninst\u271d\u00b9 : MonoidWithZero \u03b1\ninst\u271d : Nontrivial \u03b1\n\u22a2 Function.Injective toMatrix", "state_after": "k : T... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Lemmas.lean | Nat.pos_iff_ne_zero | [
204,
11
] | [
204,
94
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_mono | [
289,
1
] | [
290,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | nonneg_of_mul_nonneg_left | [
812,
1
] | [
813,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sigma/Basic.lean | Sigma.mk.inj_iff | [
56,
1
] | [
59,
49
] | [{"tactic": "cases h", "annotated_tactic": ["cases h", []], "state_before": "\u03b1 : Type u_1\n\u03b1\u2081 : Type u_2\n\u03b1\u2082 : Type u_3\n\u03b2 : \u03b1 \u2192 Type u_4\n\u03b2\u2081 : \u03b1\u2081 \u2192 Type u_5\n\u03b2\u2082 : \u03b1\u2082 \u2192 Type u_6\na\u2081 a\u2082 : \u03b1\nb\u2081 : \u03b2 a\u2081\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.le_zero | [
557,
1
] | [
558,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | Filter.Ici_mem_atTop | [
57,
1
] | [
58,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_comp | [
73,
1
] | [
75,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_uIcc | [
437,
1
] | [
438,
72
] | [{"tactic": "simp only [\u2190 Icc_min_max, preimage_neg_Icc, min_neg_neg, max_neg_neg]", "annotated_tactic": ["simp only [\u2190 <a>Icc_min_max</a>, <a>preimage_neg_Icc</a>, <a>min_neg_neg</a>, <a>max_neg_neg</a>]", [{"full_name": "Set.Icc_min_max", "def_path": "Mathlib/Data/Set/Intervals/UnorderedInterval.lean", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LucasLehmer.lean | succ_mersenne | [
59,
1
] | [
61,
45
] | [{"tactic": "rw [mersenne, tsub_add_cancel_of_le]", "annotated_tactic": ["rw [<a>mersenne</a>, <a>tsub_add_cancel_of_le</a>]", [{"full_name": "mersenne", "def_path": "Mathlib/NumberTheory/LucasLehmer.lean", "def_pos": [42, 5], "def_end_pos": [42, 13]}, {"full_name": "tsub_add_cancel_of_le", "def_path": "Mathlib/Algebra... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt | [
215,
1
] | [
219,
75
] | [{"tactic": "intro w", "annotated_tactic": ["intro w", []], "state_before": "R : Type u_1\ninst\u271d : CommRing R\nn \u03bd k : \u2115\n\u22a2 k < n - \u03bd \u2192 eval 1 ((\u2191derivative)^[k] (bernsteinPolynomial R n \u03bd)) = 0", "state_after": "R : Type u_1\ninst\u271d : CommRing R\nn \u03bd k : \u2115\nw : k <... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Iic | [
520,
1
] | [
522,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Units.lean | Units.mk_val | [
164,
1
] | [
165,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sups.lean | Set.infs_inter_subset_right | [
335,
1
] | [
336,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_uniformizer | [
428,
1
] | [
430,
30
] | [{"tactic": "simpa only [one_mul, eq_self_iff_true, Units.val_one, pow_one, forall_true_left, Nat.cast_one]\n using addVal_def \u03d6 1 h\u03d6 1", "annotated_tactic": ["simpa only [<a>one_mul</a>, <a>eq_self_iff_true</a>, <a>Units.val_one</a>, <a>pow_one</a>, <a>forall_true_left</a>, <a>Nat.cast_one</a>]\n using <... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Units.lean | Ideal.closure_ne_top | [
255,
1
] | [
257,
85
] | [{"tactic": "have h := closure_minimal (coe_subset_nonunits hI) nonunits.isClosed", "annotated_tactic": ["have h := <a>closure_minimal</a> (<a>coe_subset_nonunits</a> hI) <a>nonunits.isClosed</a>", [{"full_name": "closure_minimal", "def_path": "Mathlib/Topology/Basic.lean", "def_pos": [443, 9], "def_end_pos": [443, 24]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.apply_mk | [
85,
1
] | [
86,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Defs.lean | MeasurableSet.empty | [
80,
1
] | [
81,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Between.lean | wbtw_or_wbtw_smul_vadd_of_nonneg | [
770,
1
] | [
774,
70
] | [{"tactic": "rcases le_total r\u2081 r\u2082 with (h | h)", "annotated_tactic": ["rcases <a>le_total</a> r\u2081 r\u2082 with (h | h)", [{"full_name": "le_total", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [295, 9], "def_end_pos": [295, 17]}]], "state_before": "R : Type u_1\nV : Type u_2\nV' : Type u_3\nP :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/NAry.lean | Finset.image₂_image₂_image₂_comm | [
396,
1
] | [
403,
43
] | [{"tactic": "push_cast", "annotated_tactic": ["push_cast", []], "state_before": "\u03b1 : Type u_1\n\u03b1' : Type u_2\n\u03b2 : Type u_3\n\u03b2' : Type u_4\n\u03b3\u271d : Type u_5\n\u03b3' : Type u_6\n\u03b4\u271d : Type u_7\n\u03b4' : Type u_8\n\u03b5 : Type u_9\n\u03b5' : Type u_10\n\u03b6 : Type u_11\n\u03b6' : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_smul | [
1115,
1
] | [
1116,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_iff_lt_mul | [
305,
1
] | [
306,
54
] | [{"tactic": "rw [\u2190 mul_lt_mul_iff_right b, inv_mul_cancel_right]", "annotated_tactic": ["rw [\u2190 <a>mul_lt_mul_iff_right</a> b, <a>inv_mul_cancel_right</a>]", [{"full_name": "mul_lt_mul_iff_right", "def_path": "Mathlib/Algebra/Order/Monoid/Lemmas.lean", "def_pos": [113, 9], "def_end_pos": [113, 29]}, {"full_nam... |
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