url stringclasses 3
values | commit stringclasses 3
values | file_path stringlengths 20 79 | full_name stringlengths 3 115 | start list | end list | traced_tactics stringlengths 2 997k |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.isTopologicalBasis_cylinders | [
365,
1
] | [
385,
18
] | [{"tactic": "apply isTopologicalBasis_of_open_of_nhds", "annotated_tactic": ["apply <a>isTopologicalBasis_of_open_of_nhds</a>", [{"full_name": "TopologicalSpace.isTopologicalBasis_of_open_of_nhds", "def_path": "Mathlib/Topology/Bases.lean", "def_pos": [127, 9], "def_end_pos": [127, 43]}]], "state_before": "E : \u2115 \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Basic.lean | DFinsupp.subtypeDomain_neg | [
555,
1
] | [
557,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Bind.lean | Multiset.bind_assoc | [
170,
1
] | [
172,
81
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type v\n\u03b3 : Type u_2\n\u03b4 : Type u_3\na : \u03b1\ns\u271d t : Multiset \u03b1\nf\u271d g\u271d : \u03b1 \u2192 Multiset \u03b2\ns : Multiset \u03b1\nf : \u03b1 \u2192 Multiset \u03b2\ng : \u03b2 \u2192 Multiset \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_union_add_inter | [
1723,
1
] | [
1725,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Function.lean | Function.Semiconj.surjOn_image | [
1662,
1
] | [
1666,
52
] | [{"tactic": "rintro y \u27e8x, hxt, rfl\u27e9", "annotated_tactic": ["rintro y \u27e8x, hxt, rfl\u27e9", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Sort u_4\n\u03c0 : \u03b1 \u2192 Type u_5\nfa : \u03b1 \u2192 \u03b1\nfb : \u03b2 \u2192 \u03b2\nf : \u03b1 \u2192 \u03b2\ng : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/DoubleCoset.lean | Doset.doset_eq_of_mem | [
50,
1
] | [
55,
40
] | [{"tactic": "obtain \u27e8_, k, \u27e8h, a, hh, rfl : _ = _, rfl\u27e9, hk, rfl\u27e9 := hb", "annotated_tactic": ["obtain \u27e8_, k, \u27e8h, a, hh, rfl : _ = _, rfl\u27e9, hk, rfl\u27e9 := hb", []], "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\n\u03b1 : Type u_2\ninst\u271d : Mul \u03b1\nJ : Subgroup G\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/IsROrC/Basic.lean | IsROrC.im_to_real | [
928,
1
] | [
929,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inlCokernelCofork_π | [
1885,
1
] | [
1886,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/CharZero/Lemmas.lean | half_add_self | [
160,
1
] | [
160,
99
] | [{"tactic": "rw [\u2190 mul_two, mul_div_cancel a two_ne_zero]", "annotated_tactic": ["rw [\u2190 <a>mul_two</a>, <a>mul_div_cancel</a> a <a>two_ne_zero</a>]", [{"full_name": "mul_two", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 16]}, {"full_name": "mul_div_cancel", "def_pat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_aux | [
520,
1
] | [
547,
90
] | [{"tactic": "simp only [iSup_eapprox_apply, hf, hg]", "annotated_tactic": ["simp only [<a>iSup_eapprox_apply</a>, hf, hg]", [{"full_name": "MeasureTheory.SimpleFunc.iSup_eapprox_apply", "def_path": "Mathlib/MeasureTheory/Function/SimpleFunc.lean", "def_pos": [896, 9], "def_end_pos": [896, 27]}]], "state_before": "\u03b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Function/Basic.lean | Function.Surjective.exists₂ | [
217,
11
] | [
219,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.nodup_antidiagonal | [
63,
1
] | [
64,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/EditDistance/Defs.lean | levenshtein_nil_nil | [
253,
1
] | [
254,
40
] | [{"tactic": "simp [levenshtein, suffixLevenshtein]", "annotated_tactic": ["simp [<a>levenshtein</a>, <a>suffixLevenshtein</a>]", [{"full_name": "levenshtein", "def_path": "Mathlib/Data/List/EditDistance/Defs.lean", "def_pos": [176, 5], "def_end_pos": [176, 16]}, {"full_name": "suffixLevenshtein", "def_path": "Mathlib/D... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Int.ceil_pos | [
1270,
1
] | [
1270,
65
] | [{"tactic": "rw [lt_ceil, cast_zero]", "annotated_tactic": ["rw [<a>lt_ceil</a>, <a>cast_zero</a>]", [{"full_name": "Int.lt_ceil", "def_path": "Mathlib/Algebra/Order/Floor.lean", "def_pos": [1174, 9], "def_end_pos": [1174, 16]}, {"full_name": "Int.cast_zero", "def_path": "Mathlib/Data/Int/Cast/Basic.lean", "def_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Basic.lean | Finsupp.erase_sub | [
1154,
1
] | [
1155,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.lt_of_nadd_lt_nadd_left | [
425,
1
] | [
426,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.degree_multiset_prod | [
336,
1
] | [
337,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Option/NAry.lean | Option.map_map₂_antidistrib_right | [
195,
1
] | [
197,
50
] | [{"tactic": "cases a <;> cases b <;> simp [h_antidistrib]", "annotated_tactic": ["cases a <;> cases b <;> simp [h_antidistrib]", []], "state_before": "\u03b1 : Type u_4\n\u03b2 : Type u_5\n\u03b3 : Type u_3\nf : \u03b1 \u2192 \u03b2 \u2192 \u03b3\na : Option \u03b1\nb : Option \u03b2\nc : Option \u03b3\n\u03b4 : Type u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Bits.lean | Nat.zero_bits | [
211,
1
] | [
211,
54
] | [{"tactic": "simp [Nat.bits]", "annotated_tactic": ["simp [<a>Nat.bits</a>]", [{"full_name": "Nat.bits", "def_path": "Mathlib/Init/Data/Nat/Bitwise.lean", "def_pos": [248, 5], "def_end_pos": [248, 9]}]], "state_before": "n : \u2115\n\u22a2 bits 0 = []", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.comp_def | [
147,
1
] | [
149,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_prod_self | [
90,
1
] | [
92,
73
] | [{"tactic": "rcases s.eq_empty_or_nonempty with (rfl | hs)", "annotated_tactic": ["rcases s.eq_empty_or_nonempty with (rfl | hs)", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\n\u03c0 : \u03b9 \u2192 Type u_4\ninst\u271d\u00b3 : Fintype \u03b9\ninst\u271d\u00b2 : Bornology \u03b1\ninst\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.localization_away_comap_range | [
837,
1
] | [
847,
39
] | [{"tactic": "rw [localization_comap_range S (Submonoid.powers r)]", "annotated_tactic": ["rw [<a>localization_comap_range</a> S (<a>Submonoid.powers</a> r)]", [{"full_name": "PrimeSpectrum.localization_comap_range", "def_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean", "def_pos": [672, 9], "def_end_pos": [6... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Synonym.lean | OrderDual.exists | [
137,
11
] | [
138,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Notation.lean | ONote.exists_lt_omega_opow' | [
1043,
9
] | [
1047,
76
] | [{"tactic": "obtain \u27e8d, hd, h'\u27e9 := (lt_opow_of_limit (zero_lt_one.trans hb).ne' ho).1 h", "annotated_tactic": ["obtain \u27e8d, hd, h'\u27e9 := (<a>lt_opow_of_limit</a> (zero_lt_one.trans hb).<a>ne'</a> ho).1 h", [{"full_name": "Ordinal.lt_opow_of_limit", "def_path": "Mathlib/SetTheory/Ordinal/Exponential.lea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Complex.lean | MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOn | [
88,
1
] | [
106,
62
] | [{"tactic": "set V := {z \u2208 U | \u2016f z\u2016 = \u2016f c\u2016}", "annotated_tactic": ["set V := {z \u2208 U | \u2016f z\u2016 = \u2016f c\u2016}", []], "state_before": "E : Type u_1\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \u2102 E\nF : Type u_2\ninst\u271d\u2077 : NormedAddCommG... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Divisibility/Prod.lean | prod_dvd_iff | [
16,
1
] | [
20,
59
] | [{"tactic": "cases x", "annotated_tactic": ["cases x", []], "state_before": "G\u2081 : Type u_1\nG\u2082 : Type u_2\ninst\u271d\u00b9 : Semigroup G\u2081\ninst\u271d : Semigroup G\u2082\nx y : G\u2081 \u00d7 G\u2082\n\u22a2 x \u2223 y \u2194 x.1 \u2223 y.1 \u2227 x.2 \u2223 y.2", "state_after": "case mk\nG\u2081 : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.neg_right_iff | [
53,
1
] | [
54,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Card.lean | Finset.card_mk | [
52,
1
] | [
53,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Darboux.lean | Set.OrdConnected.image_deriv | [
103,
1
] | [
105,
78
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_centralBinom_eq_zero_of_two_mul_lt | [
118,
1
] | [
120,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.apply_le_norm | [
236,
1
] | [
237,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime | [
398,
1
] | [
404,
75
] | [{"tactic": "suffices cyclotomic p \u2124 = \u2211 i in range p, X ^ i by\n simpa only [map_cyclotomic_int, Polynomial.map_sum, Polynomial.map_pow, Polynomial.map_X] using\n congr_arg (map (Int.castRingHom R)) this", "annotated_tactic": ["suffices <a>cyclotomic</a> p \u2124 = \u2211 i in <a>range</a> p, <a>X</a> ^ ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.span_le_adjoin | [
196,
1
] | [
197,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/NAry.lean | Filter.map₂_right_identity | [
416,
1
] | [
417,
72
] | [{"tactic": "rw [map\u2082_pure_right, funext h, map_id']", "annotated_tactic": ["rw [<a>map\u2082_pure_right</a>, <a>funext</a> h, <a>map_id'</a>]", [{"full_name": "Filter.map\u2082_pure_right", "def_path": "Mathlib/Order/Filter/NAry.lean", "def_pos": [186, 9], "def_end_pos": [186, 24]}, {"full_name": "funext", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.differentiableAt | [
77,
11
] | [
79,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.gMul_def | [
92,
1
] | [
94,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/Rolle.lean | exists_Ioo_extr_on_Icc | [
39,
1
] | [
57,
57
] | [{"tactic": "have ne : (Icc a b).Nonempty := nonempty_Icc.2 (le_of_lt hab)", "annotated_tactic": ["have ne : (<a>Icc</a> a b).<a>Nonempty</a> := <a>nonempty_Icc</a>.2 (<a>le_of_lt</a> hab)", [{"full_name": "Set.Icc", "def_path": "Mathlib/Data/Set/Intervals/Basic.lean", "def_pos": [59, 5], "def_end_pos": [59, 8]}, {"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Basic.lean | RelIso.ordinal_type_eq | [
212,
1
] | [
214,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Extr.lean | Filter.EventuallyEq.isMaxFilter_iff | [
647,
1
] | [
649,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/FilterBasis.lean | ModuleFilterBasis.smul_right | [
362,
1
] | [
363,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/ENNReal.lean | NNReal.indicator_summable | [
1178,
1
] | [
1183,
20
] | [{"tactic": "refine' NNReal.summable_of_le (fun a => le_trans (le_of_eq (s.indicator_apply f a)) _) hf", "annotated_tactic": ["refine' <a>NNReal.summable_of_le</a> (fun a => <a>le_trans</a> (<a>le_of_eq</a> (s.indicator_apply f a)) _) hf", [{"full_name": "NNReal.summable_of_le", "def_path": "Mathlib/Topology/Instances/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/NNRat.lean | Rat.le_toNNRat_iff_coe_le | [
387,
1
] | [
388,
42
] | [{"tactic": "rw [\u2190 coe_le_coe, Rat.coe_toNNRat p hp]", "annotated_tactic": ["rw [\u2190 <a>coe_le_coe</a>, <a>Rat.coe_toNNRat</a> p hp]", [{"full_name": "NNRat.coe_le_coe", "def_path": "Mathlib/Data/Rat/NNRat.lean", "def_pos": [163, 9], "def_end_pos": [163, 19]}, {"full_name": "Rat.coe_toNNRat", "def_path": "Mathl... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | convex_univ | [
91,
1
] | [
91,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_univ | [
158,
1
] | [
159,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans_tendsto_nhds | [
1394,
1
] | [
1396,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_nonneg | [
128,
1
] | [
129,
88
] | [{"tactic": "apply div_nonneg <;> norm_cast <;> apply zero_le", "annotated_tactic": ["apply <a>div_nonneg</a> <;> norm_cast <;> apply <a>zero_le</a>", [{"full_name": "div_nonneg", "def_path": "Mathlib/Algebra/Order/Field/Basic.lean", "def_pos": [94, 9], "def_end_pos": [94, 19]}, {"full_name": "zero_le", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/CompleteLattice.lean | Set.image_sSup | [
943,
1
] | [
950,
34
] | [{"tactic": "ext b", "annotated_tactic": ["ext b", []], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\n\u03b4 : Type u_5\n\u03b9 : Sort u_6\n\u03ba : \u03b9 \u2192 Sort u_7\nf : \u03b1 \u2192 \u03b2\ns : Set (Set \u03b1)\n\u22a2 f '' sSup s = sSup (image f '' s)", "state_after":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/PGame.lean | SetTheory.PGame.equiv_of_eq | [
787,
1
] | [
787,
73
] | [{"tactic": "subst h", "annotated_tactic": ["subst h", []], "state_before": "x y : PGame\nh : x = y\n\u22a2 x \u2248 y", "state_after": "x : PGame\n\u22a2 x \u2248 x"}, {"tactic": "rfl", "annotated_tactic": ["rfl", []], "state_before": "x : PGame\n\u22a2 x \u2248 x", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_prod_of_mulSupport_subset | [
385,
1
] | [
395,
8
] | [{"tactic": "have A : mulSupport (f \u2218 PLift.down) = Equiv.plift.symm '' mulSupport f := by\n rw [mulSupport_comp_eq_preimage]\n exact (Equiv.plift.symm.image_eq_preimage _).symm", "annotated_tactic": ["have A : <a>mulSupport</a> (f \u2218 <a>PLift.down</a>) = Equiv.plift.symm '' <a>mulSupport</a> f := by\n rw... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Regular/SMul.lean | IsRightRegular.isSMulRegular | [
48,
1
] | [
50,
4
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.mem_insert_coe | [
1117,
1
] | [
1118,
7
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ninst\u271d : DecidableEq \u03b1\ns\u271d t u v : Finset \u03b1\na b : \u03b1\ns : Finset \u03b1\nx y : \u03b1\n\u22a2 x \u2208 insert y s \u2194 x \u2208 insert y \u2191s", "state_after": "no ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.partialSum_eq_rat | [
174,
1
] | [
185,
25
] | [{"tactic": "induction' k with k h", "annotated_tactic": ["induction' k with k h", []], "state_before": "m : \u2115\nhm : 0 < m\nk : \u2115\n\u22a2 \u2203 p, partialSum (\u2191m) k = \u2191p / \u2191(m ^ k !)", "state_after": "case zero\nm : \u2115\nhm : 0 < m\n\u22a2 \u2203 p, partialSum (\u2191m) Nat.zero = \u2191p /... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Filter.map_iSup | [
2256,
1
] | [
2257,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_lt_add_iff_left' | [
119,
9
] | [
120,
47
] | [{"tactic": "rw [\u2190 not_le, \u2190 not_le, add_le_add_iff_left]", "annotated_tactic": ["rw [\u2190 <a>not_le</a>, \u2190 <a>not_le</a>, <a>add_le_add_iff_left</a>]", [{"full_name": "not_le", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [373, 9], "def_end_pos": [373, 15]}, {"full_name": "not_le", "def_path... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.IsFiniteKernel.bound_ne_top | [
137,
1
] | [
139,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.Functor.rightDerived_map_eq | [
105,
1
] | [
124,
56
] | [{"tactic": "dsimp only [Functor.rightDerived, Functor.rightDerivedObjIso]", "annotated_tactic": ["dsimp only [<a>Functor.rightDerived</a>, <a>Functor.rightDerivedObjIso</a>]", [{"full_name": "CategoryTheory.Functor.rightDerived", "def_path": "Mathlib/CategoryTheory/Abelian/RightDerived.lean", "def_pos": [66, 5], "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | continuousOn_piecewise_ite | [
1298,
1
] | [
1302,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/BigOperators.lean | Finset.cast_card | [
51,
1
] | [
52,
45
] | [{"tactic": "rw [Finset.sum_const, Nat.smul_one_eq_coe]", "annotated_tactic": ["rw [<a>Finset.sum_const</a>, <a>Nat.smul_one_eq_coe</a>]", [{"full_name": "Finset.sum_const", "def_path": "Mathlib/Algebra/BigOperators/Basic.lean", "def_pos": [1440, 3], "def_end_pos": [1440, 14]}, {"full_name": "Nat.smul_one_eq_coe", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Tuple/Basic.lean | Fin.repeat_zero | [
383,
1
] | [
385,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/RingQuot.lean | RingQuot.zero_quot | [
233,
1
] | [
234,
35
] | [{"tactic": "rw [zero_def]", "annotated_tactic": ["rw [<a>zero_def</a>]", [{"full_name": "_private.Mathlib.Algebra.RingQuot.0.RingQuot.zero_def", "def_path": "Mathlib/Algebra/RingQuot.lean", "def_pos": [1, 1], "def_end_pos": [1, 1]}]], "state_before": "R : Type uR\ninst\u271d\u00b3 : Semiring R\nS : Type uS\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Bases.lean | Filter.Tendsto.basis_both | [
887,
1
] | [
890,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.le_comap_of_map_le | [
287,
1
] | [
288,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/BoundedOrder.lean | Pi.top_def | [
653,
1
] | [
654,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.matrix_desc | [
246,
1
] | [
250,
19
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "C : Type u\ninst\u271d\u2075 : Category.{v, u} C\ninst\u271d\u2074 : Preadditive C\nJ : Type\ninst\u271d\u00b3 : Fintype J\nf\u271d : J \u2192 C\ninst\u271d\u00b2 : HasBiproduct f\u271d\nK : Type\ninst\u271d\u00b9 : Fintype K\ninst\u271d : HasFiniteBi... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measurePreserving_mul_right | [
143,
1
] | [
145,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.nextCoeff_mul | [
209,
1
] | [
215,
36
] | [{"tactic": "nontriviality", "annotated_tactic": ["nontriviality", []], "state_before": "R : Type u\nS : Type v\na b : R\nm n : \u2115\n\u03b9 : Type y\ninst\u271d : Semiring R\np q r : R[X]\nhp : Monic p\nhq : Monic q\n\u22a2 nextCoeff (p * q) = nextCoeff p + nextCoeff q", "state_after": "R : Type u\nS : Type v\na b :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Sqrt.lean | HasFDerivAt.sqrt | [
116,
1
] | [
118,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.coe_coeEmb | [
464,
1
] | [
465,
6
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Gcd.lean | Nat.Coprime.coprime_mul_left | [
321,
1
] | [
322,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_zero_of_forall_eq_zero | [
280,
1
] | [
282,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/MinMax.lean | List.minimum_not_lt_of_mem | [
326,
1
] | [
327,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_iSup_eq | [
954,
1
] | [
956,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero | [
229,
1
] | [
232,
62
] | [{"tactic": "rw [\u2190 neg_eq_zero, \u2190 inner_neg_right] at h", "annotated_tactic": ["rw [\u2190 <a>neg_eq_zero</a>, \u2190 <a>inner_neg_right</a>] at h", [{"full_name": "neg_eq_zero", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [422, 3], "def_end_pos": [422, 14]}, {"full_name": "inner_neg_right", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toSubMulAction_injective | [
154,
1
] | [
155,
98
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.isLocalization_of_submonoid_le | [
206,
1
] | [
242,
84
] | [{"tactic": "rintro \u27e8_, \u27e8y, hy, rfl\u27e9\u27e9", "annotated_tactic": ["rintro \u27e8_, \u27e8y, hy, rfl\u27e9\u27e9", []], "state_before": "R : Type u_1\ninst\u271d\u2079 : CommRing R\nM\u271d : Submonoid R\nS : Type u_2\ninst\u271d\u2078 : CommRing S\ninst\u271d\u2077 : Algebra R S\nP : Type u_3\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/CharP/Basic.lean | CharZero.charZero_iff_forall_prime_ne_zero | [
744,
1
] | [
753,
36
] | [{"tactic": "refine \u27e8fun h p hp => by simp [hp.ne_zero], fun h => ?_\u27e9", "annotated_tactic": ["refine \u27e8fun h p hp => by simp [hp.ne_zero], fun h => ?_\u27e9", []], "state_before": "R : Type u_1\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : NoZeroDivisors R\ninst\u271d : Nontrivial R\n\u22a2 CharZ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DList/Defs.lean | Std.DList.toList_cons | [
80,
1
] | [
81,
16
] | [{"tactic": "cases l", "annotated_tactic": ["cases l", []], "state_before": "\u03b1 : Type u\nx : \u03b1\nl : DList \u03b1\n\u22a2 toList (cons x l) = x :: toList l", "state_after": "case mk\n\u03b1 : Type u\nx : \u03b1\napply\u271d : List \u03b1 \u2192 List \u03b1\ninvariant\u271d : \u2200 (l : List \u03b1), apply\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/ZFC/Basic.lean | Class.not_empty_hom | [
1466,
1
] | [
1467,
5
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Sigma.lean | List.perm_nodupKeys | [
141,
1
] | [
142,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_inj' | [
137,
1
] | [
140,
30
] | [{"tactic": "simpa [h] using congr_arg length h_eq", "annotated_tactic": ["simpa [h] using <a>congr_arg</a> <a>length</a> h_eq", [{"full_name": "congr_arg", "def_path": "Mathlib/Init/Logic.lean", "def_pos": [43, 7], "def_end_pos": [43, 16]}, {"full_name": "Quiver.Path.length", "def_path": "Mathlib/Combinatorics/Quiver/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_pair_mul_span_pair | [
832,
1
] | [
834,
88
] | [{"tactic": "simp_rw [span_insert, sup_mul, mul_sup, span_singleton_mul_span_singleton, sup_assoc]", "annotated_tactic": ["simp_rw [<a>span_insert</a>, <a>sup_mul</a>, <a>mul_sup</a>, <a>span_singleton_mul_span_singleton</a>, <a>sup_assoc</a>]", [{"full_name": "Ideal.span_insert", "def_path": "Mathlib/RingTheory/Ideal/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/GCD/Basic.lean | Nat.lcm_pos | [
126,
1
] | [
128,
20
] | [{"tactic": "simp_rw [pos_iff_ne_zero]", "annotated_tactic": ["simp_rw [<a>pos_iff_ne_zero</a>]", [{"full_name": "pos_iff_ne_zero", "def_path": "Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean", "def_pos": [243, 3], "def_end_pos": [243, 14]}]], "state_before": "m n : \u2115\n\u22a2 0 < m \u2192 0 < n \u2192 0 < lcm m ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/ZMod/Quotient.lean | MulAction.minimalPeriod_eq_card | [
180,
1
] | [
183,
72
] | [{"tactic": "rw [\u2190 Fintype.ofEquiv_card (orbitZpowersEquiv a b), @ZMod.card _ (_)]", "annotated_tactic": ["rw [\u2190 <a>Fintype.ofEquiv_card</a> (<a>orbitZpowersEquiv</a> a b), @<a>ZMod.card</a> _ (_)]", [{"full_name": "Fintype.ofEquiv_card", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [145, 9], "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/NAry.lean | Filter.map₂_left | [
203,
1
] | [
208,
30
] | [{"tactic": "ext u", "annotated_tactic": ["ext u", []], "state_before": "\u03b1 : Type u_1\n\u03b1' : Type u_2\n\u03b2 : Type u_3\n\u03b2' : Type u_4\n\u03b3 : Type u_5\n\u03b3' : Type u_6\n\u03b4 : Type u_7\n\u03b4' : Type u_8\n\u03b5 : Type u_9\n\u03b5' : Type u_10\nm : \u03b1 \u2192 \u03b2 \u2192 \u03b3\nf f\u2081 f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/ImageToKernel.lean | image_le_kernel | [
41,
1
] | [
42,
57
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b9 : Type u_1\nV : Type u\ninst\u271d\u00b3 : Category.{v, u} V\ninst\u271d\u00b2 : HasZeroMorphisms V\nA B C : V\nf : A \u27f6 B\ninst\u271d\u00b9 : HasImage f\ng : B \u27f6 C\ninst\u271d : HasKernel g\nw : f \u226b g = 0\n\u22a2 kernel.lift g ... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/Lemmas.lean | Std.RBNode.exists_insert_toList_zoom_node | [
555,
1
] | [
559,
55
] | [{"tactic": "refine \u27e8p.listL ++ l.toList, r.toList ++ p.listR, ?_\u27e9", "annotated_tactic": ["refine \u27e8p.listL ++ l.toList, r.toList ++ p.listR, ?_\u27e9", []], "state_before": "\u03b1 : Type u_1\nc : RBColor\nn : Nat\ncmp : \u03b1 \u2192 \u03b1 \u2192 Ordering\nc' : RBColor\nl : RBNode \u03b1\nv' : \u03b1\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Basic.lean | one_le_inv | [
309,
1
] | [
310,
54
] | [{"tactic": "rwa [le_inv (@zero_lt_one \u03b1 _ _ _ _ _) h\u2081, inv_one]", "annotated_tactic": ["rwa [<a>le_inv</a> (@<a>zero_lt_one</a> \u03b1 _ _ _ _ _) h\u2081, <a>inv_one</a>]", [{"full_name": "le_inv", "def_path": "Mathlib/Algebra/Order/Field/Basic.lean", "def_pos": [270, 9], "def_end_pos": [270, 15]}, {"full_na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.tan_eq_zero_iff | [
63,
1
] | [
69,
20
] | [{"tactic": "have h := (sin_two_mul \u03b8).symm", "annotated_tactic": ["have h := (<a>sin_two_mul</a> \u03b8).<a>symm</a>", [{"full_name": "Complex.sin_two_mul", "def_path": "Mathlib/Data/Complex/Exponential.lean", "def_pos": [1039, 9], "def_end_pos": [1039, 20]}, {"full_name": "Eq.symm", "def_path": "lake-packages/le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_tsub_iff_left_of_le_of_le | [
175,
11
] | [
178,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Polynomial/Tower.lean | Subalgebra.aeval_coe | [
86,
1
] | [
87,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_integral_deterministic' | [
419,
1
] | [
423,
63
] | [{"tactic": "rw [kernel.deterministic_apply, set_integral_dirac' hf _ hs]", "annotated_tactic": ["rw [<a>kernel.deterministic_apply</a>, <a>set_integral_dirac'</a> hf _ hs]", [{"full_name": "ProbabilityTheory.kernel.deterministic_apply", "def_path": "Mathlib/Probability/Kernel/Basic.lean", "def_pos": [365, 9], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk_inv | [
171,
1
] | [
172,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_symm_zero | [
148,
1
] | [
149,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedGroup.pos_one | [
162,
1
] | [
163,
11
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Sum/Basic.lean | Sum.isLeft_inr | [
79,
9
] | [
79,
67
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.tailD_eq_tail? | [
524,
9
] | [
525,
18
] | [{"tactic": "cases l <;> rfl", "annotated_tactic": ["cases l <;> rfl", []], "state_before": "\u03b1 : Type u_1\nl l' : List \u03b1\n\u22a2 tailD l l' = Option.getD (tail? l) l'", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.nthHom_zero | [
491,
1
] | [
491,
62
] | [{"tactic": "simp [nthHom]", "annotated_tactic": ["simp [<a>nthHom</a>]", [{"full_name": "PadicInt.nthHom", "def_path": "Mathlib/NumberTheory/Padics/RingHoms.lean", "def_pos": [487, 5], "def_end_pos": [487, 11]}]], "state_before": "p : \u2115\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst\u271d : NonAssocSemiring R... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.apply_symm_apply | [
1094,
1
] | [
1095,
35
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Init/Lemmas.lean | List.map_append | [
91,
9
] | [
92,
49
] | [{"tactic": "intro l\u2081", "annotated_tactic": ["intro l\u2081", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nf : \u03b1 \u2192 \u03b2\n\u22a2 \u2200 (l\u2081 l\u2082 : List \u03b1), map f (l\u2081 ++ l\u2082) = map f l\u2081 ++ map f l\u2082", "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nf : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.pi_mem_of_mulSingle_mem_aux | [
200,
1
] | [
231,
11
] | [{"tactic": "induction' I using Finset.induction_on with i I hnmem ih generalizing x", "annotated_tactic": ["induction' I using <a>Finset.induction_on</a> with i I hnmem ih generalizing x", [{"full_name": "Finset.induction_on", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1251, 19], "def_end_pos": [1251, 3... |
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