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/Algebra/Group/Commute/Basic.lean | Commute.div_div_div_comm | [
52,
11
] | [
55,
34
] | [{"tactic": "simp_rw [div_eq_mul_inv, mul_inv_rev, inv_inv, hbd.symm.eq, hcd.symm.eq,\n hbc.inv_inv.mul_mul_mul_comm]", "annotated_tactic": ["simp_rw [<a>div_eq_mul_inv</a>, <a>mul_inv_rev</a>, <a>inv_inv</a>, hbd.symm.eq, hcd.symm.eq,\n hbc.inv_inv.mul_mul_mul_comm]", [{"full_name": "div_eq_mul_inv", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | UniformContinuous.dist | [
1823,
11
] | [
1825,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Card.lean | Set.encard_union_le | [
191,
1
] | [
192,
57
] | [{"tactic": "rw [\u2190encard_union_add_encard_inter]", "annotated_tactic": ["rw [\u2190<a>encard_union_add_encard_inter</a>]", [{"full_name": "Set.encard_union_add_encard_inter", "def_path": "Mathlib/Data/Set/Card.lean", "def_pos": [171, 9], "def_end_pos": [171, 38]}]], "state_before": "\u03b1 : Type u_1\ns\u271d t\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Fib.lean | Nat.fib_lt_fib_succ | [
117,
1
] | [
120,
19
] | [{"tactic": "rcases exists_add_of_le hn with \u27e8n, rfl\u27e9", "annotated_tactic": ["rcases <a>exists_add_of_le</a> hn with \u27e8n, rfl\u27e9", [{"full_name": "ExistsAddOfLE.exists_add_of_le", "def_path": "Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean", "def_pos": [37, 3], "def_end_pos": [37, 19]}]], "state_befo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.forget₂_map | [
159,
1
] | [
161,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_of_lt_div' | [
1667,
1
] | [
1668,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_one | [
258,
1
] | [
259,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_sum | [
1334,
1
] | [
1344,
25
] | [{"tactic": "apply (sup_le_iff.2 _).antisymm (max_le_iff.2 \u27e8_, _\u27e9)", "annotated_tactic": ["apply (<a>sup_le_iff</a>.2 _).<a>antisymm</a> (<a>max_le_iff</a>.2 \u27e8_, _\u27e9)", [{"full_name": "Ordinal.sup_le_iff", "def_path": "Mathlib/SetTheory/Ordinal/Arithmetic.lean", "def_pos": [1265, 9], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/NNReal.lean | tendsto_real_toNNReal_atTop | [
131,
1
] | [
133,
59
] | [{"tactic": "rw [\u2190 tendsto_coe_atTop]", "annotated_tactic": ["rw [\u2190 <a>tendsto_coe_atTop</a>]", [{"full_name": "NNReal.tendsto_coe_atTop", "def_path": "Mathlib/Topology/Instances/NNReal.lean", "def_pos": [121, 9], "def_end_pos": [121, 26]}]], "state_before": "\u03b1 : Type u_1\n\u22a2 Tendsto Real.toNNReal at... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_mul_right_closedBall | [
322,
1
] | [
325,
56
] | [{"tactic": "rw [div_eq_mul_inv]", "annotated_tactic": ["rw [<a>div_eq_mul_inv</a>]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}]], "state_before": "M : Type u\nG : Type v\nX : Type w\ninst\u271d\u2075 : PseudoEMetricSpace X\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.one_dotProduct | [
735,
1
] | [
735,
77
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/WF.lean | Acc.ndrec_eq_ndrecC | [
76,
18
] | [
78,
42
] | [{"tactic": "funext \u03b1 r motive intro a t", "annotated_tactic": ["funext \u03b1 r motive intro a t", []], "state_before": "\u22a2 @ndrec = @Acc.ndrecC", "state_after": "case h.h.h.h.h.h\n\u03b1 : Sort u_1\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nmotive : \u03b1 \u2192 Sort u_2\nintro : (x : \u03b1) \u2192 (\u2200 (y ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Derivation.lean | Polynomial.derivation_C | [
39,
1
] | [
40,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Definability.lean | Set.definable_iff_empty_definable_with_params | [
80,
1
] | [
82,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/OfFn.lean | List.ofFn_inj' | [
274,
1
] | [
276,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.inducedOuterMeasure_eq | [
1582,
1
] | [
1584,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Measurable.sub_stronglyMeasurable | [
487,
1
] | [
493,
41
] | [{"tactic": "rw [sub_eq_add_neg]", "annotated_tactic": ["rw [<a>sub_eq_add_neg</a>]", [{"full_name": "sub_eq_add_neg", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [975, 3], "def_end_pos": [975, 14]}]], "state_before": "\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\ninst\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ioo | [
192,
1
] | [
194,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_X | [
57,
1
] | [
58,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.eq_curry_iff | [
221,
1
] | [
222,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.substructureEquivMap_apply | [
962,
1
] | [
964,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/JordanHolder.lean | CompositionSeries.length_toList | [
216,
1
] | [
217,
32
] | [{"tactic": "rw [toList, List.length_ofFn]", "annotated_tactic": ["rw [<a>toList</a>, <a>List.length_ofFn</a>]", [{"full_name": "CompositionSeries.toList", "def_path": "Mathlib/Order/JordanHolder.lean", "def_pos": [200, 5], "def_end_pos": [200, 11]}, {"full_name": "List.length_ofFn", "def_path": "Mathlib/Data/List/OfFn... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Basic.lean | List.take_eq_takeTR | [
138,
10
] | [
146,
54
] | [{"tactic": "funext \u03b1 n l", "annotated_tactic": ["funext \u03b1 n l", []], "state_before": "\u22a2 @take = @takeTR", "state_after": "case h.h.h\n\u03b1 : Type u_1\nn : Nat\nl : List \u03b1\n\u22a2 take n l = takeTR n l"}, {"tactic": "simp [takeTR]", "annotated_tactic": ["simp [<a>takeTR</a>]", [{"full_name": "List... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_le_of_limit | [
67,
1
] | [
68,
77
] | [{"tactic": "rw [opow_limit a0 h, bsup_le_iff]", "annotated_tactic": ["rw [<a>opow_limit</a> a0 h, <a>bsup_le_iff</a>]", [{"full_name": "Ordinal.opow_limit", "def_path": "Mathlib/SetTheory/Ordinal/Exponential.lean", "def_pos": [62, 9], "def_end_pos": [62, 19]}, {"full_name": "Ordinal.bsup_le_iff", "def_path": "Mathlib/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.continuousOn_fderivWithin | [
1210,
1
] | [
1212,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sum_measure_le_measure_univ | [
399,
1
] | [
403,
37
] | [{"tactic": "rw [\u2190 measure_biUnion_finset H h]", "annotated_tactic": ["rw [\u2190 <a>measure_biUnion_finset</a> H h]", [{"full_name": "MeasureTheory.measure_biUnion_finset", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpace.lean", "def_pos": [194, 9], "def_end_pos": [194, 31]}]], "state_before": "\u03b1 : Ty... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_one | [
664,
1
] | [
665,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospan_map_inr | [
238,
1
] | [
239,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Combination.lean | convexHull_basis_eq_stdSimplex | [
495,
1
] | [
503,
34
] | [{"tactic": "refine' Subset.antisymm (convexHull_min _ (convex_stdSimplex R \u03b9)) _", "annotated_tactic": ["refine' <a>Subset.antisymm</a> (<a>convexHull_min</a> _ (<a>convex_stdSimplex</a> R \u03b9)) _", [{"full_name": "Set.Subset.antisymm", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [370, 9], "def_end_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/WittVector/Basic.lean | WittVector.map_injective | [
281,
1
] | [
282,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_splits_id | [
413,
1
] | [
421,
65
] | [{"tactic": "decide", "annotated_tactic": ["decide", []], "state_before": "F : Type u\nK : Type v\nL : Type w\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Field L\ninst\u271d : Field F\ni : K \u2192+* L\nf x\u271d\u00b9 : K[X]\nhu : IsUnit x\u271d\u00b9\nx\u271d : Splits (RingHom.id K) x\u271d\u00b9\n\u22a2 0 \u2264... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.pure_mul_pure | [
197,
1
] | [
198,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Diffeomorph.lean | Diffeomorph.contMDiffAt_transDiffeomorph_left | [
625,
1
] | [
627,
76
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Invertible/Defs.lean | invOf_eq_left_inv | [
152,
1
] | [
153,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sum/Basic.lean | Sum.update_inl_apply_inr | [
142,
1
] | [
144,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Constructions.lean | continuous_pi | [
1203,
1
] | [
1204,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | MeasurableSet.of_union_cover | [
642,
1
] | [
646,
82
] | [{"tactic": "convert (hs.subtype_image hsu).union (ht.subtype_image htu)", "annotated_tactic": ["convert (hs.subtype_image hsu).<a>union</a> (ht.subtype_image htu)", [{"full_name": "MeasurableSet.union", "def_path": "Mathlib/MeasureTheory/MeasurableSpace/Defs.lean", "def_pos": [191, 19], "def_end_pos": [191, 38]}]], "s... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_eq_bot | [
1330,
1
] | [
1331,
38
] | [{"tactic": "rw [\u2190 range_le_bot_iff, le_bot_iff]", "annotated_tactic": ["rw [\u2190 <a>range_le_bot_iff</a>, <a>le_bot_iff</a>]", [{"full_name": "LinearMap.range_le_bot_iff", "def_path": "Mathlib/LinearAlgebra/Basic.lean", "def_pos": [1326, 9], "def_end_pos": [1326, 25]}, {"full_name": "le_bot_iff", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Functor.lean | Set.coe_subset | [
84,
1
] | [
85,
60
] | [{"tactic": "intro _ \u27e8_, \u27e8\u27e8\u27e8_, ha\u27e9, rfl\u27e9, _, \u27e8_, rfl\u27e9, _\u27e9\u27e9", "annotated_tactic": ["intro _ \u27e8_, \u27e8\u27e8\u27e8_, ha\u27e9, <a>rfl</a>\u27e9, _, \u27e8_, <a>rfl</a>\u27e9, _\u27e9\u27e9", [{"full_name": "rfl", "def_path": "lake-packages/lean4/src/lean/Init/Prelud... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_unitBall_of_pos | [
144,
1
] | [
145,
55
] | [{"tactic": "rw [smul_unitBall hr.ne', Real.norm_of_nonneg hr.le]", "annotated_tactic": ["rw [<a>smul_unitBall</a> hr.ne', <a>Real.norm_of_nonneg</a> hr.le]", [{"full_name": "smul_unitBall", "def_path": "Mathlib/Analysis/NormedSpace/Pointwise.lean", "def_pos": [93, 9], "def_end_pos": [93, 22]}, {"full_name": "Real.norm... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basis_empty | [
217,
1
] | [
218,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_right_cancel' | [
173,
11
] | [
174,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_eq | [
377,
1
] | [
378,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/MellinTransform.lean | mellin_differentiableAt_of_isBigO_rpow_exp | [
447,
1
] | [
452,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.smn | [
693,
1
] | [
695,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.not_mem_affineSpan_diff | [
462,
1
] | [
464,
12
] | [{"tactic": "simp [ha]", "annotated_tactic": ["simp [ha]", []], "state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst\u271d\u2074 : Ring k\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module k V\ninst\u271d\u00b9 : AffineSpace V P\n\u03b9 : Type u_4\ninst\u271d : Nontrivial k\np : \u03b9 \u2192 P\nh... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.isGLB_iff_isLeast | [
1799,
1
] | [
1806,
99
] | [{"tactic": "refine' \u27e8fun his => _, IsLeast.isGLB\u27e9", "annotated_tactic": ["refine' \u27e8fun his => _, <a>IsLeast.isGLB</a>\u27e9", [{"full_name": "IsLeast.isGLB", "def_path": "Mathlib/Order/Bounds/Basic.lean", "def_pos": [277, 9], "def_end_pos": [277, 22]}]], "state_before": "F : Type u_1\n\u03b1 : Type u_2\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_E'3 | [
135,
1
] | [
136,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.comp_left | [
69,
1
] | [
71,
82
] | [{"tactic": "simpa using CompClosure.intro (f \u226b x) m\u2081 m\u2082 y h", "annotated_tactic": ["simpa using <a>CompClosure.intro</a> (f \u226b x) m\u2081 m\u2082 y h", [{"full_name": "CategoryTheory.Quotient.CompClosure.intro", "def_path": "Mathlib/CategoryTheory/Quotient.lean", "def_pos": [61, 5], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_const_add_Ioo | [
139,
1
] | [
140,
46
] | [{"tactic": "simp only [add_comm a, image_add_const_Ioo]", "annotated_tactic": ["simp only [<a>add_comm</a> a, <a>image_add_const_Ioo</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"full_name": "Set.image_add_const_Ioo", "def_path": "Mat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Function.lean | Set.apply_piecewise₂ | [
1513,
1
] | [
1517,
39
] | [{"tactic": "by_cases hx : x \u2208 s <;> simp [hx]", "annotated_tactic": ["by_cases hx : x \u2208 s <;> simp [hx]", []], "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\n\u03b4 : \u03b1 \u2192 Sort u_6\ns : Set \u03b1\nf g : (i : \u03b1) \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_ne_top | [
324,
1
] | [
325,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Chain.lean | List.chain_of_chain_pmap | [
105,
1
] | [
110,
81
] | [{"tactic": "induction' l with lh lt l_ih generalizing a", "annotated_tactic": ["induction' l with lh lt l_ih generalizing a", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nR r : \u03b1 \u2192 \u03b1 \u2192 Prop\nl\u271d l\u2081 l\u2082 : List \u03b1\na\u271d b : \u03b1\nS : \u03b2 \u2192 \u03b2 \u2192 Prop\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | PMF.mem_support_uniformOfFinset_iff | [
71,
1
] | [
72,
7
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns : Finset \u03b1\nhs : Finset.Nonempty s\na\u271d a : \u03b1\n\u22a2 a \u2208 support (uniformOfFinset s hs) \u2194 a \u2208 s", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_one | [
328,
1
] | [
329,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | AntilipschitzWith.le_mul_norm' | [
1057,
1
] | [
1059,
58
] | [{"tactic": "simpa only [dist_one_right, hf] using h.le_mul_dist x 1", "annotated_tactic": ["simpa only [<a>dist_one_right</a>, hf] using h.le_mul_dist x 1", [{"full_name": "dist_one_right", "def_path": "Mathlib/Analysis/Normed/Group/Basic.lean", "def_pos": [396, 9], "def_end_pos": [396, 23]}]], "state_before": "\ud835... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Basic.lean | Nat.forall_lt_succ | [
258,
1
] | [
259,
81
] | [{"tactic": "simp only [lt_succ_iff, Decidable.le_iff_eq_or_lt, forall_eq_or_imp, and_comm]", "annotated_tactic": ["simp only [<a>lt_succ_iff</a>, <a>Decidable.le_iff_eq_or_lt</a>, <a>forall_eq_or_imp</a>, <a>and_comm</a>]", [{"full_name": "Nat.lt_succ_iff", "def_path": "Mathlib/Data/Nat/Basic.lean", "def_pos": [207, 9... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atBot_curry | [
1552,
1
] | [
1554,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.aestronglyMeasurable | [
457,
1
] | [
459,
7
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.trunc_c | [
748,
1
] | [
753,
51
] | [{"tactic": "classical\nrw [coeff_trunc, coeff_C, MvPolynomial.coeff_C]\nsplit_ifs with H <;> first |rfl|try simp_all\nexfalso; apply H; subst m; exact Ne.bot_lt hnn", "annotated_tactic": ["classical\n rw [<a>coeff_trunc</a>, <a>coeff_C</a>, <a>MvPolynomial.coeff_C</a>]\n split_ifs with H <;> first |rfl|try simp_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.zero_left | [
111,
1
] | [
112,
59
] | [{"tactic": "rw [\u2190 @zero_smul R _ _ _ _ (0 : M), smul_left, zero_mul]", "annotated_tactic": ["rw [\u2190 @<a>zero_smul</a> R _ _ _ _ (0 : M), <a>smul_left</a>, <a>zero_mul</a>]", [{"full_name": "zero_smul", "def_path": "Mathlib/Algebra/SMulWithZero.lean", "def_pos": [70, 9], "def_end_pos": [70, 18]}, {"full_name":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_sup_left | [
641,
1
] | [
642,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Dirac.lean | MeasureTheory.Measure.map_dirac | [
62,
1
] | [
63,
72
] | [{"tactic": "simp [hs, map_apply hf hs, hf hs, indicator_apply]", "annotated_tactic": ["simp [hs, <a>map_apply</a> hf hs, hf hs, <a>indicator_apply</a>]", [{"full_name": "MeasureTheory.Measure.map_apply", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpace.lean", "def_pos": [1236, 9], "def_end_pos": [1236, 18]}, {"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Erased.lean | Erased.out_proof | [
52,
1
] | [
53,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.cocone_naturality | [
164,
1
] | [
168,
21
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "J : Type u\ninst\u271d : Category.{v, u} J\nF : J \u2964 AddCommGroupCat\nj j' : J\nf : j \u27f6 j'\n\u22a2 F.map f \u226b coconeMorphism F j' = coconeMorphism F j", "state_after": "case w\nJ : Type u\ninst\u271d : Category.{v, u} J\nF : J \u2964 AddC... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Primrec.lean | Primrec.ulower_up | [
1263,
1
] | [
1265,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.face_mono | [
404,
1
] | [
406,
89
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Defs.lean | neg_mul_eq_neg_mul | [
301,
1
] | [
302,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.getD_eq_default | [
4317,
1
] | [
4323,
43
] | [{"tactic": "exact getD_nil _ _", "annotated_tactic": ["exact <a>getD_nil</a> _ _", [{"full_name": "List.getD_nil", "def_path": "Mathlib/Data/List/Basic.lean", "def_pos": [4280, 9], "def_end_pos": [4280, 17]}]], "state_before": "case nil\n\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nl\u2081 l\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.expand_C | [
38,
1
] | [
39,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | LocalHomeomorph.contDiffAt_symm_deriv | [
1880,
1
] | [
1883,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.isSpecial_iff | [
150,
1
] | [
156,
95
] | [{"tactic": "dsimp [IsSpecial, IsSpecial']", "annotated_tactic": ["dsimp [<a>IsSpecial</a>, <a>IsSpecial'</a>]", [{"full_name": "PNat.XgcdType.IsSpecial", "def_path": "Mathlib/Data/PNat/Xgcd.lean", "def_pos": [141, 5], "def_end_pos": [141, 14]}, {"full_name": "PNat.XgcdType.IsSpecial'", "def_path": "Mathlib/Data/PNat/X... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | round_ofNat | [
1429,
1
] | [
1429,
94
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bases.lean | TopologicalSpace.countable_cover_nhdsWithin | [
826,
1
] | [
832,
20
] | [{"tactic": "have : \u2200 x : s, (\u2191) \u207b\u00b9' f x \u2208 \ud835\udcdd x := fun x => preimage_coe_mem_nhds_subtype.2 (hf x x.2)", "annotated_tactic": ["have : \u2200 x : s, (\u2191) \u207b\u00b9' f x \u2208 \ud835\udcdd x := fun x => <a>preimage_coe_mem_nhds_subtype</a>.2 (hf x x.2)", [{"full_name": "preimage... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/LocalExtr/Basic.lean | IsLocalMinOn.fderivWithin_eq_zero | [
178,
1
] | [
183,
71
] | [{"tactic": "rw [fderivWithin_zero_of_not_differentiableWithinAt hf]", "annotated_tactic": ["rw [<a>fderivWithin_zero_of_not_differentiableWithinAt</a> hf]", [{"full_name": "fderivWithin_zero_of_not_differentiableWithinAt", "def_path": "Mathlib/Analysis/Calculus/FDeriv/Basic.lean", "def_pos": [229, 9], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.sSup_coe_toSubmodule | [
490,
1
] | [
492,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_def | [
1100,
1
] | [
1101,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Interval.lean | Interval.exists | [
356,
1
] | [
357,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Ici | [
430,
1
] | [
439,
66
] | [{"tactic": "refine' tendsto_nhds_unique (tendsto_measure_Ico_atTop _ _) _", "annotated_tactic": ["refine' <a>tendsto_nhds_unique</a> (<a>tendsto_measure_Ico_atTop</a> _ _) _", [{"full_name": "tendsto_nhds_unique", "def_path": "Mathlib/Topology/Separation.lean", "def_pos": [994, 9], "def_end_pos": [994, 28]}, {"full_na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | NeZero.of_gt | [
315,
1
] | [
316,
24
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.negSucc_add_ofNat | [
53,
15
] | [
53,
96
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean | Orientation.oangle_sub_right_eq_arccos_of_oangle_eq_pi_div_two | [
268,
1
] | [
274,
55
] | [{"tactic": "have hs : (o.oangle y (y - x)).sign = 1 := by\n rw [oangle_sign_sub_right_swap, h, Real.Angle.sign_coe_pi_div_two]", "annotated_tactic": ["have hs : (o.oangle y (y - x)).<a>sign</a> = 1 := by\n rw [<a>oangle_sign_sub_right_swap</a>, h, <a>Real.Angle.sign_coe_pi_div_two</a>]", [{"full_name": "Real.Angle... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_le | [
475,
1
] | [
476,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.centroid_eq_iff | [
929,
1
] | [
949,
39
] | [{"tactic": "refine' \u27e8fun h => _, @congrArg _ _ fs\u2081 fs\u2082 (fun z => Finset.centroid k z s.points)\u27e9", "annotated_tactic": ["refine' \u27e8fun h => _, @<a>congrArg</a> _ _ fs\u2081 fs\u2082 (fun z => <a>Finset.centroid</a> k z s.points)\u27e9", [{"full_name": "congrArg", "def_path": "lake-packages/lean4... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiff_iff_iteratedDeriv | [
258,
1
] | [
262,
90
] | [{"tactic": "simp only [contDiff_iff_continuous_differentiable, iteratedFDeriv_eq_equiv_comp,\n LinearIsometryEquiv.comp_continuous_iff, LinearIsometryEquiv.comp_differentiable_iff]", "annotated_tactic": ["simp only [<a>contDiff_iff_continuous_differentiable</a>, <a>iteratedFDeriv_eq_equiv_comp</a>,\n <a>LinearIsom... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Lemmas.lean | Nat.cast_pow | [
533,
1
] | [
536,
62
] | [{"tactic": "induction' m with m ih", "annotated_tactic": ["induction' m with m ih", []], "state_before": "\u03b1 : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u\u2081\nS : Type u\u2082\ninst\u271d : Semiring R\nn m : \u2115\n\u22a2 \u2191(n ^ m) = \u2191n ^ m", "state_aft... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_add | [
1742,
1
] | [
1745,
23
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "l : Type u_1\nm : Type u_2\nn : Type u_3\no : Type u_4\nm' : o \u2192 Type u_5\nn' : o \u2192 Type u_6\nR : Type u_7\nS : Type u_8\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type u_9\ninst\u271d\u00b9 : NonUnitalNonAssocSemiring \u03b1\ninst\u271d : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.IsHaarMeasure.smul | [
768,
1
] | [
770,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsCompl_smul | [
266,
1
] | [
269,
37
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R\u271d : Type u_1\ninst\u271d\u00b9\u2074 : Ring R\u271d\nE\u271d : Type u_2\ninst\u271d\u00b9\u00b3 : AddCommGroup E\u271d\ninst\u271d\u00b9\u00b2 : Module R\u271d E\u271d\nF\u271d : Type u_3\ninst\u271d\u00b9\u00b9 : AddCommGroup F\u271d\ninst\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_right_cancel' | [
197,
11
] | [
199,
86
] | [{"tactic": "simp [modEq_iff_dvd, \u2190 sub_mul, mul_dvd_mul_iff_right (by simp [hc] : (c : \u2124) \u2260 0)]", "annotated_tactic": ["simp [<a>modEq_iff_dvd</a>, \u2190 <a>sub_mul</a>, <a>mul_dvd_mul_iff_right</a> (by simp [hc] : (c : \u2124) \u2260 0)]", [{"full_name": "Nat.modEq_iff_dvd", "def_path": "Mathlib/Data/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Nontrivial/Defs.lean | Decidable.exists_ne | [
43,
11
] | [
48,
26
] | [{"tactic": "rcases exists_pair_ne \u03b1 with \u27e8y, y', h\u27e9", "annotated_tactic": ["rcases <a>exists_pair_ne</a> \u03b1 with \u27e8y, y', h\u27e9", [{"full_name": "exists_pair_ne", "def_path": "Mathlib/Logic/Nontrivial/Defs.lean", "def_pos": [38, 9], "def_end_pos": [38, 23]}]], "state_before": "\u03b1 : Type u_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Category/Compactum.lean | Compactum.le_nhds_of_str_eq | [
352,
1
] | [
353,
61
] | [{"tactic": "rwa [h]", "annotated_tactic": ["rwa [h]", []], "state_before": "X : Compactum\nF : Ultrafilter X.A\nx : X.A\nh : str X F = x\ns : Set X.A\nhx : x \u2208 s\nhs : IsOpen s\n\u22a2 str X F \u2208 s", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Partrec.lean | Nat.rfind_dom' | [
93,
1
] | [
98,
24
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Lemmas.lean | Nat.eq_zero_of_zero_dvd | [
875,
11
] | [
876,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.initial.subsingleton_to | [
125,
1
] | [
126,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk | [
407,
1
] | [
412,
10
] | [{"tactic": "simp only [ofMkLE, ofLEMk, ofLE, ofMkLEMk, \u2190 Functor.map_comp_assoc underlying,\n assoc, Iso.hom_inv_id_assoc]", "annotated_tactic": ["simp only [<a>ofMkLE</a>, <a>ofLEMk</a>, <a>ofLE</a>, <a>ofMkLEMk</a>, \u2190 <a>Functor.map_comp_assoc</a> <a>underlying</a>,\n <a>assoc</a>, <a>Iso.hom_inv_id_as... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_monotone | [
215,
1
] | [
215,
87
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.toRealLinearIsometryEquiv_apply | [
133,
1
] | [
135,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/NNReal.lean | NNReal.smul_def | [
247,
1
] | [
248,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.id_right | [
57,
1
] | [
58,
14
] | [] |
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