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/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_lt_wf | [
50,
1
] | [
51,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/TopologicalSimplex.lean | SimplexCategory.toTopObj.ext | [
46,
1
] | [
47,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/TotallyDisconnected.lean | Continuous.connectedComponentsLift_apply_coe | [
262,
1
] | [
264,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Antilipschitz.lean | antilipschitzWith_iff_le_mul_nndist | [
51,
1
] | [
54,
12
] | [{"tactic": "simp only [AntilipschitzWith, edist_nndist]", "annotated_tactic": ["simp only [<a>AntilipschitzWith</a>, <a>edist_nndist</a>]", [{"full_name": "AntilipschitzWith", "def_path": "Mathlib/Topology/MetricSpace/Antilipschitz.lean", "def_pos": [33, 5], "def_end_pos": [33, 22]}, {"full_name": "edist_nndist", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/JapaneseBracket.lean | closedBall_rpow_sub_one_eq_empty_aux | [
70,
1
] | [
73,
93
] | [{"tactic": "rw [Metric.closedBall_eq_empty, sub_neg]", "annotated_tactic": ["rw [<a>Metric.closedBall_eq_empty</a>, <a>sub_neg</a>]", [{"full_name": "Metric.closedBall_eq_empty", "def_path": "Mathlib/Topology/MetricSpace/Basic.lean", "def_pos": [525, 9], "def_end_pos": [525, 28]}, {"full_name": "sub_neg", "def_path": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Algebraic.lean | isAlgebraic_algebraMap_iff | [
163,
1
] | [
166,
43
] | [{"tactic": "rwa [map_zero, \u2190 aeval_algebraMap_apply]", "annotated_tactic": ["rwa [<a>map_zero</a>, \u2190 <a>aeval_algebraMap_apply</a>]", [{"full_name": "map_zero", "def_path": "Mathlib/Algebra/Hom/Group/Defs.lean", "def_pos": [201, 3], "def_end_pos": [201, 14]}, {"full_name": "Polynomial.aeval_algebraMap_apply"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Exponential.lean | Real.sin_three_mul | [
1337,
8
] | [
1338,
42
] | [{"tactic": "rw [\u2190 ofReal_inj]", "annotated_tactic": ["rw [\u2190 <a>ofReal_inj</a>]", [{"full_name": "Complex.ofReal_inj", "def_path": "Mathlib/Data/Complex/Basic.lean", "def_pos": [106, 9], "def_end_pos": [106, 19]}]], "state_before": "x y : \u211d\n\u22a2 sin (3 * x) = 3 * sin x - 4 * sin x ^ 3", "state_after":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Height.lean | Set.chainHeight_eq_top_iff | [
127,
1
] | [
131,
69
] | [{"tactic": "refine' \u27e8fun h n \u21a6 le_chainHeight_iff.1 (le_top.trans_eq h.symm), fun h \u21a6 _\u27e9", "annotated_tactic": ["refine' \u27e8fun h n \u21a6 <a>le_chainHeight_iff</a>.1 (le_top.trans_eq h.symm), fun h \u21a6 _\u27e9", [{"full_name": "Set.le_chainHeight_iff", "def_path": "Mathlib/Order/Height.lean"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.nth_map | [
416,
1
] | [
424,
8
] | [{"tactic": "refine' l.inductionOn fun l \u21a6 _", "annotated_tactic": ["refine' l.inductionOn fun l \u21a6 _", []], "state_before": "\u0393 : Type u_1\n\u0393' : Type u_2\ninst\u271d\u00b9 : Inhabited \u0393\ninst\u271d : Inhabited \u0393'\nf : PointedMap \u0393 \u0393'\nl : ListBlank \u0393\nn : \u2115\n\u22a2 nth (... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.ker_le_ker_completion | [
165,
1
] | [
168,
42
] | [{"tactic": "rintro _ \u27e8\u27e8g, h\u2080 : f g = 0\u27e9, rfl\u27e9", "annotated_tactic": ["rintro _ \u27e8\u27e8g, h\u2080 : f g = 0\u27e9, rfl\u27e9", []], "state_before": "G : Type u_1\ninst\u271d\u00b2 : SeminormedAddCommGroup G\nH : Type u_2\ninst\u271d\u00b9 : SeminormedAddCommGroup H\nK : Type u_3\ninst\u271... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | Monotone.map_csSup_of_continuousAt | [
2899,
1
] | [
2903,
33
] | [{"tactic": "refine' ((isLUB_csSup (ne.image f) (Mf.map_bddAbove H)).unique _).symm", "annotated_tactic": ["refine' ((<a>isLUB_csSup</a> (ne.image f) (Mf.map_bddAbove H)).<a>unique</a> _).<a>symm</a>", [{"full_name": "isLUB_csSup", "def_path": "Mathlib/Order/ConditionallyCompleteLattice/Basic.lean", "def_pos": [498, 9]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.orderIsoIicCoe_symm_apply_coe | [
1854,
1
] | [
1856,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Integral.lean | ConcaveOn.le_map_integral | [
220,
1
] | [
223,
79
] | [{"tactic": "simpa only [average_eq_integral] using hg.le_map_average hgc hsc hfs hfi hgi", "annotated_tactic": ["simpa only [<a>average_eq_integral</a>] using hg.le_map_average hgc hsc hfs hfi hgi", [{"full_name": "MeasureTheory.average_eq_integral", "def_path": "Mathlib/MeasureTheory/Integral/Average.lean", "def_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.div_const | [
1503,
8
] | [
1505,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/MinMax.lean | min_le_mul_of_one_le_right | [
133,
1
] | [
135,
55
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_inj | [
336,
1
] | [
337,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Multiplicity.lean | pow_two_pow_sub_pow_two_pow | [
255,
1
] | [
262,
11
] | [{"tactic": "induction' n with d hd", "annotated_tactic": ["induction' n with d hd", []], "state_before": "R : Type u_1\nn\u271d : \u2115\ninst\u271d : CommRing R\nx y : R\nn : \u2115\n\u22a2 x ^ 2 ^ n - y ^ 2 ^ n = (\u220f i in range n, (x ^ 2 ^ i + y ^ 2 ^ i)) * (x - y)", "state_after": "case zero\nR : Type u_1\nn : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | ext_inner_left | [
687,
1
] | [
688,
87
] | [{"tactic": "rw [\u2190 sub_eq_zero, \u2190 @inner_self_eq_zero \ud835\udd5c, inner_sub_right, sub_eq_zero, h (x - y)]", "annotated_tactic": ["rw [\u2190 <a>sub_eq_zero</a>, \u2190 @<a>inner_self_eq_zero</a> \ud835\udd5c, <a>inner_sub_right</a>, <a>sub_eq_zero</a>, h (x - y)]", [{"full_name": "sub_eq_zero", "def_path":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.natCast_le | [
1356,
1
] | [
1358,
40
] | [{"tactic": "rw [\u2190 lift_mk_fin, \u2190 lift_mk_fin, lift_le, le_def, Function.Embedding.nonempty_iff_card_le,\n Fintype.card_fin, Fintype.card_fin]", "annotated_tactic": ["rw [\u2190 <a>lift_mk_fin</a>, \u2190 <a>lift_mk_fin</a>, <a>lift_le</a>, <a>le_def</a>, <a>Function.Embedding.nonempty_iff_card_le</a>,\n ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.coe_expMapCircle | [
120,
1
] | [
123,
27
] | [{"tactic": "induction \u03b8 using Real.Angle.induction_on", "annotated_tactic": ["induction \u03b8 using <a>Real.Angle.induction_on</a>", [{"full_name": "Real.Angle.induction_on", "def_path": "Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean", "def_pos": [74, 19], "def_end_pos": [74, 31]}]], "state_before":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/QuadraticChar/Basic.lean | quadraticChar_one_iff_isSquare | [
149,
1
] | [
152,
51
] | [{"tactic": "simp only [quadraticChar_apply, quadraticCharFun, ha, (by decide : (-1 : \u2124) \u2260 1), if_false,\n ite_eq_left_iff, imp_false, Classical.not_not]", "annotated_tactic": ["simp only [<a>quadraticChar_apply</a>, <a>quadraticCharFun</a>, ha, (by decide : (-1 : \u2124) \u2260 1), <a>if_false</a>,\n <a>... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoundedVariation.lean | variationOnFromTo.sub_self_monotoneOn | [
757,
11
] | [
770,
64
] | [{"tactic": "rintro b bs c cs bc", "annotated_tactic": ["rintro b bs c cs bc", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : LinearOrder \u03b1\nE : Type u_2\ninst\u271d : PseudoEMetricSpace E\nf\u271d : \u03b1 \u2192 E\ns\u271d : Set \u03b1\nf : \u03b1 \u2192 \u211d\ns : Set \u03b1\nhf : LocallyBoundedVa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_zero | [
245,
1
] | [
246,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Sum.swap_map_inr | [
141,
1
] | [
142,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Num/Lemmas.lean | Num.zero_add | [
211,
1
] | [
211,
61
] | [{"tactic": "cases n <;> rfl", "annotated_tactic": ["cases n <;> rfl", []], "state_before": "\u03b1 : Type u_1\nn : Num\n\u22a2 0 + n = n", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/OfAssociative.lean | LinearEquiv.lieConj_symm | [
352,
1
] | [
353,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/NhdsSet.lean | principal_le_nhdsSet | [
82,
1
] | [
83,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/NonUnitalSubring/Basic.lean | NonUnitalSubring.coe_toSubsemigroup | [
345,
1
] | [
346,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_add_erase | [
1065,
1
] | [
1066,
49
] | [{"tactic": "rw [\u2190 update_eq_single_add_erase, update_self]", "annotated_tactic": ["rw [\u2190 <a>update_eq_single_add_erase</a>, <a>update_self</a>]", [{"full_name": "Finsupp.update_eq_single_add_erase", "def_path": "Mathlib/Data/Finsupp/Defs.lean", "def_pos": [1047, 9], "def_end_pos": [1047, 35]}, {"full_name": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eqToHom_map | [
299,
1
] | [
300,
72
] | [{"tactic": "cases p", "annotated_tactic": ["cases p", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nD : Type u\u2082\ninst\u271d : Category.{v\u2082, u\u2082} D\nF : C \u2964 D\nX Y : C\np : X = Y\n\u22a2 F.map (eqToHom p) = eqToHom (_ : F.obj X = F.obj Y)", "state_after": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_map_iff_mem_of_injective | [
1546,
1
] | [
1548,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Unique.lean | Unique.eq_default | [
143,
1
] | [
144,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_comap | [
1375,
1
] | [
1376,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_mul | [
1295,
1
] | [
1296,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.as_factorThruImage | [
330,
1
] | [
331,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Martingale/Upcrossing.lean | MeasureTheory.upperCrossingTime_eq_of_bound_le | [
329,
1
] | [
332,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/CrossProduct.lean | cross_apply | [
65,
1
] | [
66,
91
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Spectrum.lean | spectrum.isOpen_resolventSet | [
92,
1
] | [
93,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.setSeq_sub_aux | [
709,
1
] | [
710,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | MonoidWithZeroHom.map_zero | [
926,
11
] | [
927,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basis.lean | Basis.coe_sumCoords_eq_finsum | [
234,
1
] | [
239,
28
] | [{"tactic": "ext m", "annotated_tactic": ["ext m", []], "state_before": "\u03b9 : Type u_1\n\u03b9' : Type u_2\nR : Type u_3\nR\u2082 : Type u_4\nK : Type u_5\nM : Type u_6\nM' : Type u_7\nM'' : Type u_8\nV : Type u\nV' : Type u_9\ninst\u271d\u2074 : Semiring R\ninst\u271d\u00b3 : AddCommMonoid M\ninst\u271d\u00b2 : Mo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Field/InfiniteSum.lean | summable_norm_sum_mul_range_of_summable_norm | [
99,
1
] | [
102,
66
] | [{"tactic": "simp_rw [\u2190 sum_antidiagonal_eq_sum_range_succ fun k l => f k * g l]", "annotated_tactic": ["simp_rw [\u2190 <a>sum_antidiagonal_eq_sum_range_succ</a> fun k l => f k * g l]", [{"full_name": "Finset.Nat.sum_antidiagonal_eq_sum_range_succ", "def_path": "Mathlib/Algebra/BigOperators/NatAntidiagonal.lean",... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Max.lean | IsMin.prod_mk | [
413,
1
] | [
413,
101
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.neg | [
405,
8
] | [
407,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.smul_mem_iff | [
416,
1
] | [
417,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Basic.lean | mul_inv_eq_iff_eq_mul | [
697,
1
] | [
698,
87
] | [{"tactic": "rw [\u2190 h, inv_mul_cancel_right]", "annotated_tactic": ["rw [\u2190 h, <a>inv_mul_cancel_right</a>]", [{"full_name": "inv_mul_cancel_right", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [1165, 9], "def_end_pos": [1165, 29]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nG : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.real_toNNReal | [
1965,
1
] | [
1967,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ENNReal.measurable_of_measurable_nnreal | [
2029,
1
] | [
2032,
70
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Basic.lean | Rat.cast_finsupp_sum | [
421,
1
] | [
423,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotEquivCommₐ | [
910,
1
] | [
911,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Bernoulli.lean | bernoulli_spec' | [
247,
1
] | [
267,
13
] | [{"tactic": "cases' n with n n", "annotated_tactic": ["cases' n with n n", []], "state_before": "A : Type u_1\ninst\u271d\u00b9 : CommRing A\ninst\u271d : Algebra \u211a A\nn : \u2115\n\u22a2 \u2211 k in antidiagonal n, \u2191(Nat.choose (k.1 + k.2) k.2) / (\u2191k.2 + 1) * bernoulli k.1 = if n = 0 then 1 else 0", "sta... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableAt.rpow | [
441,
1
] | [
443,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Products/Bifunctor.lean | CategoryTheory.Bifunctor.diagonal | [
46,
1
] | [
49,
73
] | [{"tactic": "rw [\u2190 Functor.map_comp, prod_comp, Category.id_comp, Category.comp_id]", "annotated_tactic": ["rw [\u2190 <a>Functor.map_comp</a>, <a>prod_comp</a>, <a>Category.id_comp</a>, <a>Category.comp_id</a>]", [{"full_name": "CategoryTheory.Functor.map_comp", "def_path": "Mathlib/CategoryTheory/Functor/Basic.l... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.Sigma.ι_reindex_hom | [
644,
1
] | [
653,
21
] | [{"tactic": "dsimp [Sigma.reindex]", "annotated_tactic": ["dsimp [<a>Sigma.reindex</a>]", [{"full_name": "CategoryTheory.Limits.Sigma.reindex", "def_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean", "def_pos": [639, 5], "def_end_pos": [639, 18]}]], "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_le_infDist_of_subset | [
512,
1
] | [
513,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.equiv_zero_of_val_eq_of_equiv_zero | [
145,
1
] | [
148,
45
] | [{"tactic": "simpa [h] using hi _ hj", "annotated_tactic": ["simpa [h] using hi _ hj", []], "state_before": "p : \u2115\ninst\u271d : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : \u2200 (k : \u2115), padicNorm p (\u2191f k) = padicNorm p (\u2191g k)\nhf : f \u2248 0\n\u03b5 : \u211a\nh\u03b5 : \u03b5 > 0\ni : \u2115\nhi :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homeomorph.lean | Homeomorph.piCongrRight_symm | [
610,
1
] | [
613,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Integration.lean | ProbabilityTheory.indepFun_iff_integral_comp_mul | [
305,
1
] | [
320,
69
] | [{"tactic": "refine' \u27e8fun hfg _ _ h\u03c6 h\u03c8 => IndepFun.integral_mul_of_integrable (hfg.comp h\u03c6 h\u03c8), _\u27e9", "annotated_tactic": ["refine' \u27e8fun hfg _ _ h\u03c6 h\u03c8 => <a>IndepFun.integral_mul_of_integrable</a> (hfg.comp h\u03c6 h\u03c8), _\u27e9", [{"full_name": "ProbabilityTheory.IndepF... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/RelIso/Basic.lean | injective_of_increasing | [
165,
1
] | [
177,
33
] | [{"tactic": "intro x y hxy", "annotated_tactic": ["intro x y hxy", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\nr\u271d : \u03b1 \u2192 \u03b1 \u2192 Prop\ns\u271d : \u03b2 \u2192 \u03b2 \u2192 Prop\nt : \u03b3 \u2192 \u03b3 \u2192 Prop\nu : \u03b4 \u2192 \u03b4 \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.inv' | [
623,
1
] | [
624,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.mono | [
182,
1
] | [
183,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.embDomain_zero | [
847,
1
] | [
848,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.monomorphisms.iff | [
464,
1
] | [
464,
67
] | [{"tactic": "rfl", "annotated_tactic": ["rfl", []], "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nD : Type u_1\ninst\u271d : Category.{?u.70988, u_1} D\nX Y : C\nf : X \u27f6 Y\n\u22a2 monomorphisms C f \u2194 Mono f", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_inf | [
201,
1
] | [
202,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/Basic.lean | Vector.scanl_cons | [
338,
1
] | [
340,
24
] | [{"tactic": "simp only [scanl, toList_cons, List.scanl]", "annotated_tactic": ["simp only [<a>scanl</a>, <a>toList_cons</a>, <a>List.scanl</a>]", [{"full_name": "Vector.scanl", "def_path": "Mathlib/Data/Vector/Basic.lean", "def_pos": [321, 5], "def_end_pos": [321, 10]}, {"full_name": "Vector.toList_cons", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/NeLocus.lean | DFinsupp.neLocus_self_add_right | [
160,
1
] | [
161,
74
] | [{"tactic": "rw [\u2190 neLocus_zero_left, \u2190 @neLocus_add_left \u03b1 N _ _ _ f 0 g, add_zero]", "annotated_tactic": ["rw [\u2190 <a>neLocus_zero_left</a>, \u2190 @<a>neLocus_add_left</a> \u03b1 N _ _ _ f 0 g, <a>add_zero</a>]", [{"full_name": "DFinsupp.neLocus_zero_left", "def_path": "Mathlib/Data/DFinsupp/NeLocu... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.ne_nil_of_mem | [
84,
1
] | [
84,
89
] | [{"tactic": "cases h <;> intro.", "annotated_tactic": ["cases h <;> intro.", []], "state_before": "\u03b1 : Type u_1\na : \u03b1\nl : List \u03b1\nh : a \u2208 l\n\u22a2 l \u2260 []", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimit_iff_succ_lt | [
157,
1
] | [
158,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.commute | [
91,
1
] | [
91,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.le_of_forall_pos_nnreal_lt | [
1729,
1
] | [
1731,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basis.lean | Matrix.matrix_eq_sum_std_basis | [
61,
1
] | [
75,
15
] | [{"tactic": "ext i j", "annotated_tactic": ["ext i j", []], "state_before": "l : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_4\n\u03b1 : Type u_5\ninst\u271d\u2075 : DecidableEq l\ninst\u271d\u2074 : DecidableEq m\ninst\u271d\u00b3 : DecidableEq n\ninst\u271d\u00b2 : Semiring \u03b1\ninst\u271d\u00b9 : Fintype m\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/ENNReal.lean | tsum_comp_le_tsum_of_inj | [
1289,
1
] | [
1293,
86
] | [{"tactic": "lift f to \u03b1 \u2192 \u211d\u22650 using hn", "annotated_tactic": ["lift f to \u03b1 \u2192 \u211d\u22650 using hn", []], "state_before": "\u03b1 : Type u_1\n\u03b2\u271d : Type u_2\n\u03b3 : Type u_3\n\u03b2 : Type u_4\nf : \u03b1 \u2192 \u211d\nhf : Summable f\nhn : \u2200 (a : \u03b1), 0 \u2264 f a\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Multiset.stronglyMeasurable_prod' | [
596,
1
] | [
599,
61
] | [{"tactic": "rcases l with \u27e8l\u27e9", "annotated_tactic": ["rcases l with \u27e8l\u27e9", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\ninst\u271d\u00b3 : Countable \u03b9\nf g : \u03b1 \u2192 \u03b2\nM : Type u_5\ninst\u271d\u00b2 : CommMonoid M\ninst\u271d\u00b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Jacobson.lean | Ideal.isJacobson_iso | [
127,
1
] | [
129,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_concat | [
536,
1
] | [
538,
39
] | [{"tactic": "induction p <;> simp [*, concat_nil]", "annotated_tactic": ["induction p <;> simp [*, <a>concat_nil</a>]", [{"full_name": "SimpleGraph.Walk.concat_nil", "def_path": "Mathlib/Combinatorics/SimpleGraph/Connectivity.lean", "def_pos": [280, 9], "def_end_pos": [280, 19]}]], "state_before": "V : Type u\nV' : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_X | [
139,
1
] | [
141,
35
] | [{"tactic": "rw [\u2190 monomial_one_one_eq_X, hasseDeriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,\n zero_mul, monomial_zero_right]", "annotated_tactic": ["rw [\u2190 <a>monomial_one_one_eq_X</a>, <a>hasseDeriv_monomial</a>, <a>Nat.choose_eq_zero_of_lt</a> hk, <a>Nat.cast_zero</a>,\n <a>zero_mul</a>, <... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_nat_ceil_div_atTop | [
637,
1
] | [
638,
62
] | [{"tactic": "simpa using tendsto_nat_ceil_mul_div_atTop (zero_le_one' R)", "annotated_tactic": ["simpa using <a>tendsto_nat_ceil_mul_div_atTop</a> (<a>zero_le_one'</a> R)", [{"full_name": "tendsto_nat_ceil_mul_div_atTop", "def_path": "Mathlib/Analysis/SpecificLimits/Basic.lean", "def_pos": [623, 9], "def_end_pos": [623... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Prod.lean | Set.prod_diff_prod | [
403,
1
] | [
405,
65
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\ns s\u2081 s\u2082 : Set \u03b1\nt t\u2081 t\u2082 : Set \u03b2\na : \u03b1\nb : \u03b2\n\u22a2 s \u00d7\u02e2 t \\ s\u2081 \u00d7\u02e2 t\u2081 = s \u00d7\u02e2 (t \\ t\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | MonoidHom.ext_iff | [
773,
1
] | [
774,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Num/Lemmas.lean | ZNum.cast_lt | [
1393,
1
] | [
1394,
64
] | [{"tactic": "rw [\u2190 cast_to_int m, \u2190 cast_to_int n, Int.cast_lt, lt_to_int]", "annotated_tactic": ["rw [\u2190 <a>cast_to_int</a> m, \u2190 <a>cast_to_int</a> n, <a>Int.cast_lt</a>, <a>lt_to_int</a>]", [{"full_name": "ZNum.cast_to_int", "def_path": "Mathlib/Data/Num/Lemmas.lean", "def_pos": [1097, 9], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Primrec.lean | Nat.Primrec.sub | [
135,
1
] | [
137,
54
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "p : \u2115\n\u22a2 unpaired (fun z n => Nat.rec (id z) (fun y IH => Nat.pred (unpair (unpair (Nat.pair z (Nat.pair y IH))).2).2) n) p =\n unpaired (fun x x_1 => x - x_1) p", "state_after": "p : \u2115\n\u22a2 Nat.rec (unpair p).1 (fun y IH => Nat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_sum | [
113,
1
] | [
115,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_mono | [
414,
1
] | [
416,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Process/Stopping.lean | MeasureTheory.IsStoppingTime.measurableSet_eq_of_countable_range' | [
519,
11
] | [
523,
61
] | [{"tactic": "exact h\u03c4.measurableSet_eq_of_countable_range h_countable i", "annotated_tactic": ["exact h\u03c4.measurableSet_eq_of_countable_range h_countable i", []], "state_before": "\u03a9 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nm : MeasurableSpace \u03a9\ninst\u271d : LinearOrder \u03b9\nf : Filtratio... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.srange_top_of_surjective | [
900,
1
] | [
902,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/MeanInequalities.lean | Real.geom_mean_le_arith_mean_weighted | [
114,
1
] | [
135,
24
] | [{"tactic": "by_cases A : \u2203 i \u2208 s, z i = 0 \u2227 w i \u2260 0", "annotated_tactic": ["by_cases A : \u2203 i \u2208 s, z i = 0 \u2227 w i \u2260 0", []], "state_before": "\u03b9 : Type u\ns : Finset \u03b9\nw z : \u03b9 \u2192 \u211d\nhw : \u2200 (i : \u03b9), i \u2208 s \u2192 0 \u2264 w i\nhw' : \u2211 i in... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Lemmas.lean | Nat.zero_shiftRight | [
981,
9
] | [
983,
51
] | [{"tactic": "simp [shiftRight]", "annotated_tactic": ["simp [<a>shiftRight</a>]", [{"full_name": "Nat.shiftRight", "def_path": "lake-packages/lean4/src/lean/Init/Data/Nat/Bitwise.lean", "def_pos": [44, 5], "def_end_pos": [44, 15]}]], "state_before": "\u22a2 0 >>> 0 = 0", "state_after": "no goals"}, {"tactic": "simp [sh... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Pairwise.lean | Set.pairwise_of_forall | [
60,
1
] | [
61,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.separatingLeft_toLinearMap₂'_iff | [
695,
1
] | [
698,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.leComap_id_iff | [
294,
1
] | [
295,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.Sublist.antisymm | [
1061,
1
] | [
1062,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/WittVector/Defs.lean | WittVector.coeff_mk | [
93,
1
] | [
94,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_Ioo | [
540,
1
] | [
541,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.sdiff_eq_self_of_disjoint | [
2407,
1
] | [
2408,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WithBot.lean | WithBot.lt_ofDual_iff | [
1064,
1
] | [
1066,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Iterate.lean | Commute.function_commute_mul_right | [
247,
1
] | [
249,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.iSup_Prop | [
1342,
1
] | [
1345,
64
] | [{"tactic": "convert hf", "annotated_tactic": ["convert hf", []], "state_before": "\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b3\u2082 : Type u_4\n\u03b4 : Type u_5\n\u03b9 : Sort y\ns t u : Set \u03b1\u271d\ninst\u271d\u00b9\u00b9 : TopologicalSpace \u03b1\u271d\ninst\u271d\u00b9\u2070 : Measur... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/DualNumber.lean | DualNumber.eps_mul_eps | [
81,
1
] | [
82,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_le_nadd_left | [
255,
1
] | [
258,
17
] | [{"tactic": "rcases lt_or_eq_of_le h with (h | rfl)", "annotated_tactic": ["rcases <a>lt_or_eq_of_le</a> h with (h | rfl)", [{"full_name": "lt_or_eq_of_le", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [228, 9], "def_end_pos": [228, 23]}]], "state_before": "a\u271d b c : Ordinal.{u}\nh : b \u2264 c\na : Ordin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Nat.map_floor | [
1602,
1
] | [
1603,
61
] | [{"tactic": "rw [\u2190 map_natCast f, hf.le_iff_le]", "annotated_tactic": ["rw [\u2190 <a>map_natCast</a> f, hf.le_iff_le]", [{"full_name": "map_natCast", "def_path": "Mathlib/Data/Nat/Cast/Basic.lean", "def_pos": [136, 9], "def_end_pos": [136, 20]}]], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_... |
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