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/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.sum_integral_congr | [
645,
1
] | [
650,
46
] | [{"tactic": "refine' tendsto_nhds_unique (h.tendsto_integralSum_sum_integral \u03c0\u2081) _", "annotated_tactic": ["refine' <a>tendsto_nhds_unique</a> (h.tendsto_integralSum_sum_integral \u03c0\u2081) _", [{"full_name": "tendsto_nhds_unique", "def_path": "Mathlib/Topology/Separation.lean", "def_pos": [994, 9], "def_en... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basis.lean | Basis.groupSMul_apply | [
1225,
1
] | [
1229,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.coe_toOrthonormalBasis | [
514,
1
] | [
516,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.map_comp_map | [
1799,
1
] | [
1800,
44
] | [{"tactic": "ext l", "annotated_tactic": ["ext l", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nl\u2081 l\u2082 : List \u03b1\ng : \u03b2 \u2192 \u03b3\nf : \u03b1 \u2192 \u03b2\n\u22a2 map g \u2218 map f = map (g \u2218 f)", "state_after": "case h.a.a\n\u03b9 : Type u_1\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Tuple/Basic.lean | Fin.append_assoc | [
338,
1
] | [
350,
27
] | [{"tactic": "ext i", "annotated_tactic": ["ext i", []], "state_before": "m n : \u2115\n\u03b1\u271d : Fin (n + 1) \u2192 Type u\nx : \u03b1\u271d 0\nq : (i : Fin (n + 1)) \u2192 \u03b1\u271d i\np\u271d : (i : Fin n) \u2192 \u03b1\u271d (succ i)\ni : Fin n\ny : \u03b1\u271d (succ i)\nz : \u03b1\u271d 0\np : \u2115\n\u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ZetaFunction.lean | hasMellin_one_div_sqrt_sub_one_div_two_Ioc | [
441,
1
] | [
457,
74
] | [{"tactic": "have step1 :\n HasMellin (indicator (Ioc 0 1) (fun t => 1 - 1 / \u2191(sqrt t) : \u211d \u2192 \u2102)) s\n (1 / s - 1 / (s - 1 / 2)) := by\n have a := hasMellin_one_Ioc (one_half_pos.trans hs)\n have b := hasMellin_one_div_sqrt_Ioc hs\n simpa only [a.2, b.2, \u2190 indicator_sub] using hasMellin_su... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff_left | [
666,
1
] | [
667,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/AList.lean | AList.perm_replace | [
211,
1
] | [
213,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | mdifferentiableWithinAt_inter | [
579,
1
] | [
583,
44
] | [{"tactic": "rw [MDifferentiableWithinAt, MDifferentiableWithinAt, extChartAt_preimage_inter_eq,\n differentiableWithinAt_inter, continuousWithinAt_inter ht]", "annotated_tactic": ["rw [<a>MDifferentiableWithinAt</a>, <a>MDifferentiableWithinAt</a>, <a>extChartAt_preimage_inter_eq</a>,\n <a>differentiableWithinAt_i... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.toSubalgebra_lt_toSubalgebra | [
593,
1
] | [
595,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Basic.lean | Order.succ_eq_succ_iff | [
481,
1
] | [
482,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_two_add_inv_two | [
1771,
1
] | [
1772,
76
] | [{"tactic": "rw [\u2190 two_mul, \u2190 div_eq_mul_inv, ENNReal.div_self two_ne_zero two_ne_top]", "annotated_tactic": ["rw [\u2190 <a>two_mul</a>, \u2190 <a>div_eq_mul_inv</a>, <a>ENNReal.div_self</a> <a>two_ne_zero</a> <a>two_ne_top</a>]", [{"full_name": "two_mul", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_top_right | [
325,
1
] | [
327,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/NhdsSet.lean | nhdsSet_Icc | [
47,
1
] | [
50,
73
] | [{"tactic": "rcases h.eq_or_lt with rfl | hlt", "annotated_tactic": ["rcases h.eq_or_lt with rfl | hlt", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : LinearOrder \u03b1\ninst\u271d\u00b9 : TopologicalSpace \u03b1\ninst\u271d : OrderClosedTopology \u03b1\na b c d : \u03b1\nh : a \u2264 b\n\u22a2 \ud835\ud... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Choose/Basic.lean | Nat.descFactorial_eq_factorial_mul_choose | [
255,
1
] | [
260,
87
] | [{"tactic": "obtain h | h := Nat.lt_or_ge n k", "annotated_tactic": ["obtain h | h := <a>Nat.lt_or_ge</a> n k", [{"full_name": "Nat.lt_or_ge", "def_path": "lake-packages/lean4/src/lean/Init/Prelude.lean", "def_pos": [1644, 19], "def_end_pos": [1644, 31]}]], "state_before": "n k : \u2115\n\u22a2 descFactorial n k = k ! ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | Monoid.coe_mul | [
1322,
1
] | [
1322,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.IsAdjMatrix.apply_ne_one_iff | [
69,
1
] | [
70,
80
] | [{"tactic": "obtain h | h := h.zero_or_one i j <;> simp [h]", "annotated_tactic": ["obtain h | h := h.zero_or_one i j <;> simp [h]", []], "state_before": "V : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nA : Matrix V V \u03b1\ninst\u271d\u00b9 : MulZeroOneClass \u03b1\ninst\u271d : Nontrivial \u03b1\nh : IsAdjMatrix... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_subset | [
248,
1
] | [
249,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.coe_injective | [
830,
1
] | [
831,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_congr_fun | [
316,
1
] | [
320,
28
] | [{"tactic": "rw [lintegral_congr_ae]", "annotated_tactic": ["rw [<a>lintegral_congr_ae</a>]", [{"full_name": "MeasureTheory.lintegral_congr_ae", "def_path": "Mathlib/MeasureTheory/Integral/Lebesgue.lean", "def_pos": [304, 9], "def_end_pos": [304, 27]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Basic.lean | OrderIso.trans_apply | [
902,
1
] | [
903,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | DirectSum.IsInternal.collectedBasis_orthonormal | [
2175,
1
] | [
2180,
90
] | [{"tactic": "simpa only [hV_sum.collectedBasis_coe] using hV.orthonormal_sigma_orthonormal hv_family", "annotated_tactic": ["simpa only [hV_sum.collectedBasis_coe] using hV.orthonormal_sigma_orthonormal hv_family", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u2076 : IsROrC \ud8... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay | [
804,
1
] | [
847,
15
] | [{"tactic": "rcases him with \u27e8C, hC\u27e9", "annotated_tactic": ["rcases him with \u27e8C, hC\u27e9", []], "state_before": "E : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \u2102 E\na b C : \u211d\nf g : \u2102 \u2192 E\nz : \u2102\nhd : DiffContOnCl \u2102 f {z | 0 < z.re}\nhexp : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Card.lean | Set.encard_union_eq | [
113,
1
] | [
116,
82
] | [{"tactic": "classical\nhave e := (Equiv.Set.union (by rwa [subset_empty_iff, \u2190disjoint_iff_inter_eq_empty])).symm\nsimp [encard, \u2190PartENat.card_congr e, PartENat.card_sum, PartENat.withTopEquiv]", "annotated_tactic": ["classical\n have e := (<a>Equiv.Set.union</a> (by rwa [<a>subset_empty_iff</a>, \u2190<a>... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Category/UniformSpace.lean | UniformSpaceCat.extension_comp_coe | [
208,
1
] | [
213,
63
] | [{"tactic": "apply Subtype.eq", "annotated_tactic": ["apply <a>Subtype.eq</a>", [{"full_name": "Subtype.eq", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", "def_pos": [960, 19], "def_end_pos": [960, 21]}]], "state_before": "X : UniformSpaceCat\nY : CpltSepUniformSpace\nf : toUniformSpace (CpltSepUniformSpac... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.nontrivial_of_exists_lt | [
2529,
1
] | [
2532,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Icc' | [
535,
1
] | [
537,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Cover.lean | Covby.of_image | [
354,
1
] | [
355,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Div.lean | Polynomial.sub_dvd_eval_sub | [
514,
1
] | [
517,
24
] | [{"tactic": "suffices X - C b \u2223 p - C (p.eval b) by\n simpa only [coe_evalRingHom, eval_sub, eval_X, eval_C] using (evalRingHom a).map_dvd this", "annotated_tactic": ["suffices <a>X</a> - <a>C</a> b \u2223 p - <a>C</a> (p.eval b) by\n simpa only [<a>coe_evalRingHom</a>, <a>eval_sub</a>, <a>eval_X</a>, <a>eval_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_nonneg' | [
176,
9
] | [
177,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_left_surjective | [
841,
1
] | [
842,
82
] | [{"tactic": "simp_rw [\u2190 rpow_mul, _root_.inv_mul_cancel hx, rpow_one]", "annotated_tactic": ["simp_rw [\u2190 <a>rpow_mul</a>, <a>_root_.inv_mul_cancel</a> hx, <a>rpow_one</a>]", [{"full_name": "ENNReal.rpow_mul", "def_path": "Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean", "def_pos": [532, 9], "def_end_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Icc_union_Ioc | [
1601,
1
] | [
1602,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.RCond.mono | [
432,
1
] | [
434,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.half_le_self | [
1810,
11
] | [
1811,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | MulHom.comp_id | [
1240,
1
] | [
1241,
26
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Option/Lemmas.lean | Option.isSome_none | [
51,
9
] | [
51,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.mem_grade_iff' | [
71,
1
] | [
77,
32
] | [{"tactic": "rw [mem_grade_iff, Finsupp.support_subset_singleton']", "annotated_tactic": ["rw [<a>mem_grade_iff</a>, <a>Finsupp.support_subset_singleton'</a>]", [{"full_name": "AddMonoidAlgebra.mem_grade_iff", "def_path": "Mathlib/Algebra/MonoidAlgebra/Grading.lean", "def_pos": [66, 9], "def_end_pos": [66, 22]}, {"full... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_nonempty_iff | [
218,
1
] | [
219,
77
] | [{"tactic": "simp only [Finsupp.support_eq_empty, Finset.nonempty_iff_ne_empty, Ne.def]", "annotated_tactic": ["simp only [<a>Finsupp.support_eq_empty</a>, <a>Finset.nonempty_iff_ne_empty</a>, <a>Ne.def</a>]", [{"full_name": "Finsupp.support_eq_empty", "def_path": "Mathlib/Data/Finsupp/Defs.lean", "def_pos": [214, 9], ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/MeanValue.lean | lipschitzWith_of_nnnorm_fderiv_le | [
555,
1
] | [
561,
93
] | [{"tactic": "let A : NormedSpace \u211d E := RestrictScalars.normedSpace \u211d \ud835\udd5c E", "annotated_tactic": ["let A : <a>NormedSpace</a> \u211d E := <a>RestrictScalars.normedSpace</a> \u211d \ud835\udd5c E", [{"full_name": "NormedSpace", "def_path": "Mathlib/Analysis/NormedSpace/Basic.lean", "def_pos": [43, 7]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.lift_desc | [
467,
1
] | [
468,
98
] | [{"tactic": "simp [biprod.lift_eq, biprod.desc_eq]", "annotated_tactic": ["simp [<a>biprod.lift_eq</a>, <a>biprod.desc_eq</a>]", [{"full_name": "CategoryTheory.Limits.biprod.lift_eq", "def_path": "Mathlib/CategoryTheory/Preadditive/Biproducts.lean", "def_pos": [458, 9], "def_end_pos": [458, 23]}, {"full_name": "Categor... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | FDerivMeasurableAux.isOpen_A | [
137,
1
] | [
145,
30
] | [{"tactic": "rw [Metric.isOpen_iff]", "annotated_tactic": ["rw [<a>Metric.isOpen_iff</a>]", [{"full_name": "Metric.isOpen_iff", "def_path": "Mathlib/Topology/MetricSpace/Basic.lean", "def_pos": [1013, 9], "def_end_pos": [1013, 19]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_subset_left | [
209,
1
] | [
213,
35
] | [{"tactic": "push_cast", "annotated_tactic": ["push_cast", []], "state_before": "\u03b1 : Type u_1\n\u03b1' : Type u_2\n\u03b2 : Type u_3\n\u03b2' : Type u_4\n\u03b3 : 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\n\u03b6 : Type u_11\n\u03b6' : Type u_12\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Bind.lean | Multiset.mem_bind | [
141,
1
] | [
142,
14
] | [{"tactic": "simp [bind]", "annotated_tactic": ["simp [<a>bind</a>]", [{"full_name": "Multiset.bind", "def_path": "Mathlib/Data/Multiset/Bind.lean", "def_pos": [93, 5], "def_end_pos": [93, 9]}]], "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 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.inf_erase_top | [
431,
1
] | [
432,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Support.lean | Function.support_smul | [
351,
1
] | [
353,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.inter_subset_left | [
965,
1
] | [
965,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.map_obj_hom | [
177,
1
] | [
178,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.coe_ne_infty | [
96,
1
] | [
97,
7
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sups.lean | Set.iUnion_image_inf_right | [
357,
1
] | [
358,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Prepartition.measure_iUnion_toReal | [
85,
1
] | [
89,
82
] | [{"tactic": "erw [\u2190 ENNReal.toReal_sum, \u03c0.iUnion_def, measure_biUnion_finset \u03c0.pairwiseDisjoint]", "annotated_tactic": ["erw [\u2190 <a>ENNReal.toReal_sum</a>, \u03c0.iUnion_def, <a>measure_biUnion_finset</a> \u03c0.pairwiseDisjoint]", [{"full_name": "ENNReal.toReal_sum", "def_path": "Mathlib/Data/Real/E... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_add_measure | [
561,
1
] | [
563,
91
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/MinMax.lean | List.foldr_max_of_ne_nil | [
483,
1
] | [
489,
18
] | [{"tactic": "induction' l with hd tl IH", "annotated_tactic": ["induction' l with hd tl IH", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : OrderBot \u03b1\nl : List \u03b1\nh : l \u2260 []\n\u22a2 \u2191(foldr max \u22a5 l) = maximum l", "state_after": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Star.lean | continuous_selfAdjointPart | [
50,
1
] | [
52,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_comp | [
969,
1
] | [
976,
81
] | [{"tactic": "simp only [map_C, forall_const, C_comp, eq_self_iff_true]", "annotated_tactic": ["simp only [<a>map_C</a>, <a>forall_const</a>, <a>C_comp</a>, <a>eq_self_iff_true</a>]", [{"full_name": "Polynomial.map_C", "def_path": "Mathlib/Data/Polynomial/Eval.lean", "def_pos": [718, 9], "def_end_pos": [718, 14]}, {"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Finite.lean | Set.infinite_smul_set | [
151,
1
] | [
152,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_mul_const | [
456,
1
] | [
458,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.sum | [
339,
1
] | [
344,
26
] | [{"tactic": "induction' s using Finset.induction_on with a s ha ihs", "annotated_tactic": ["induction' s using <a>Finset.induction_on</a> with a s ha ihs", [{"full_name": "Finset.induction_on", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1251, 19], "def_end_pos": [1251, 31]}]], "state_before": "\u03b9 : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAdjointPair_iff_eq_of_nondegenerate | [
1596,
1
] | [
1601,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.denseEmbedding_pureCauchy | [
207,
1
] | [
208,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sigma/Basic.lean | Sigma.subtype_ext_iff | [
91,
1
] | [
93,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_apply_prime_pow | [
948,
1
] | [
950,
97
] | [{"tactic": "rw [cardDistinctFactors_apply, hp.factors_pow, List.replicate_dedup hk, List.length_singleton]", "annotated_tactic": ["rw [<a>cardDistinctFactors_apply</a>, hp.factors_pow, <a>List.replicate_dedup</a> hk, <a>List.length_singleton</a>]", [{"full_name": "Nat.ArithmeticFunction.cardDistinctFactors_apply", "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Divisibility/Basic.lean | MulHom.map_dvd | [
104,
1
] | [
105,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.constr_basisSpanSingleton | [
2027,
1
] | [
2031,
98
] | [{"tactic": "erw [Basis.constr_basis, Function.comp_apply, basisSpanSingleton_apply, LinearMap.mul_apply']", "annotated_tactic": ["erw [<a>Basis.constr_basis</a>, <a>Function.comp_apply</a>, <a>basisSpanSingleton_apply</a>, <a>LinearMap.mul_apply'</a>]", [{"full_name": "Basis.constr_basis", "def_path": "Mathlib/LinearA... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_of_one_lt_sumInv_aux' | [
227,
1
] | [
246,
24
] | [{"tactic": "have hp3 : p < 3 := lt_three hpq hqr H", "annotated_tactic": ["have hp3 : p < 3 := <a>lt_three</a> hpq hqr H", [{"full_name": "ADEInequality.lt_three", "def_path": "Mathlib/NumberTheory/ADEInequality.lean", "def_pos": [173, 9], "def_end_pos": [173, 17]}]], "state_before": "p q r : \u2115+\nhpq : p \u2264 q... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Log.lean | Nat.log_zero_right | [
72,
1
] | [
73,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_top | [
1090,
1
] | [
1091,
53
] | [{"tactic": "simp [mem_prod, MonoidHom.coe_fst]", "annotated_tactic": ["simp [<a>mem_prod</a>, <a>MonoidHom.coe_fst</a>]", [{"full_name": "Subsemiring.mem_prod", "def_path": "Mathlib/RingTheory/Subsemiring/Basic.lean", "def_pos": [1071, 9], "def_end_pos": [1071, 17]}, {"full_name": "MonoidHom.coe_fst", "def_path": "Mat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_left_inj | [
47,
1
] | [
48,
82
] | [{"tactic": "simp_rw [le_antisymm_iff, tsub_le_tsub_iff_right h1, tsub_le_tsub_iff_right h2]", "annotated_tactic": ["simp_rw [<a>le_antisymm_iff</a>, <a>tsub_le_tsub_iff_right</a> h1, <a>tsub_le_tsub_iff_right</a> h2]", [{"full_name": "le_antisymm_iff", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [192, 9], "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measurable_superset_forall_eq | [
219,
1
] | [
222,
93
] | [{"tactic": "simpa only [\u2190 measure_eq_trim] using\n OuterMeasure.exists_measurable_superset_forall_eq_trim (fun i => (\u03bc i).toOuterMeasure) s", "annotated_tactic": ["simpa only [\u2190 <a>measure_eq_trim</a>] using\n <a>OuterMeasure.exists_measurable_superset_forall_eq_trim</a> (fun i => (\u03bc i).toOuter... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Surreal/Basic.lean | SetTheory.PGame.le_of_lf | [
134,
1
] | [
135,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/MeanValue.lean | image_norm_le_of_norm_deriv_right_lt_deriv_boundary | [
291,
1
] | [
296,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Reverse.lean | Polynomial.coeff_reverse | [
255,
1
] | [
256,
30
] | [{"tactic": "rw [reverse, coeff_reflect]", "annotated_tactic": ["rw [<a>reverse</a>, <a>coeff_reflect</a>]", [{"full_name": "Polynomial.reverse", "def_path": "Mathlib/Data/Polynomial/Reverse.lean", "def_pos": [251, 19], "def_end_pos": [251, 26]}, {"full_name": "Polynomial.coeff_reflect", "def_path": "Mathlib/Data/Polyn... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Sentence.realize_cardGe | [
1103,
1
] | [
1118,
19
] | [{"tactic": "rw [\u2190 lift_mk_fin, \u2190 lift_le.{0}, lift_lift, lift_mk_le, Sentence.cardGe, Sentence.Realize,\n BoundedFormula.realize_exs]", "annotated_tactic": ["rw [\u2190 <a>lift_mk_fin</a>, \u2190 <a>lift_le</a>.{0}, <a>lift_lift</a>, <a>lift_mk_le</a>, <a>Sentence.cardGe</a>, <a>Sentence.Realize</a>,\n <... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_zero | [
52,
1
] | [
53,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | closure_Ioi | [
2304,
1
] | [
2305,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Interval.lean | Finsupp.card_Ico | [
112,
1
] | [
113,
46
] | [{"tactic": "rw [card_Ico_eq_card_Icc_sub_one, card_Icc]", "annotated_tactic": ["rw [<a>card_Ico_eq_card_Icc_sub_one</a>, <a>card_Icc</a>]", [{"full_name": "Finset.card_Ico_eq_card_Icc_sub_one", "def_path": "Mathlib/Data/Finset/LocallyFinite.lean", "def_pos": [655, 9], "def_end_pos": [655, 37]}, {"full_name": "Finsupp.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Icc_of_monotone_surjective | [
53,
1
] | [
60,
50
] | [{"tactic": "intro p hp", "annotated_tactic": ["intro p hp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : PartialOrder \u03b2\nf : \u03b1 \u2192 \u03b2\nh_mono : Monotone f\nh_surj : Surjective f\na b : \u03b1\nhab : a \u2264 b\n\u22a2 SurjOn f (Icc a b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Indexes.lean | List.mapIdxMGo_eq_mapIdxMAuxSpec | [
311,
1
] | [
328,
26
] | [{"tactic": "generalize e : as.length = len", "annotated_tactic": ["generalize e : as.length = len", []], "state_before": "\u03b1\u271d : Type u\n\u03b2\u271d : Type v\nm : Type u \u2192 Type v\ninst\u271d\u00b9 : Monad m\ninst\u271d : LawfulMonad m\n\u03b1 : Type u_1\n\u03b2 : Type u\nf : \u2115 \u2192 \u03b1 \u2192 m... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Basic.lean | div_lt_iff | [
169,
1
] | [
170,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv_symm_addEquiv | [
73,
1
] | [
75,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Function.lean | neg_convexOn_iff | [
832,
1
] | [
842,
28
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\n\u03b1 : Type u_4\n\u03b2 : Type u_5\n\u03b9 : Type u_6\ninst\u271d\u2075 : OrderedSemiring \ud835\udd5c\ninst\u271d\u2074 : AddCommMonoid E\ninst\u271d\u00b3 : AddCommMonoid F\ninst... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | tendsto_one_plus_div_pow_exp | [
644,
1
] | [
646,
88
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "t : \u211d\n\u22a2 \u2200 (x : \u2115), ((fun x => (1 + t / x) ^ x) \u2218 Nat.cast) x = (1 + t / \u2191x) ^ \u2191x", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ioc_of_le | [
183,
1
] | [
184,
43
] | [{"tactic": "rw [card_fintype_Ioc, toNat_sub_of_le h]", "annotated_tactic": ["rw [<a>card_fintype_Ioc</a>, <a>toNat_sub_of_le</a> h]", [{"full_name": "Int.card_fintype_Ioc", "def_path": "Mathlib/Data/Int/Interval.lean", "def_pos": [162, 9], "def_end_pos": [162, 25]}, {"full_name": "Int.toNat_sub_of_le", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_tsum_of_hasSum_iff_hasSum | [
593,
1
] | [
595,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/CoprodI.lean | Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul | [
589,
1
] | [
592,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_le_map_iff' | [
3162,
1
] | [
3164,
69
] | [{"tactic": "simp only [map_le_map_iff, sup_le_iff, le_sup_right, and_true_iff]", "annotated_tactic": ["simp only [<a>map_le_map_iff</a>, <a>sup_le_iff</a>, <a>le_sup_right</a>, <a>and_true_iff</a>]", [{"full_name": "Subgroup.map_le_map_iff", "def_path": "Mathlib/GroupTheory/Subgroup/Basic.lean", "def_pos": [3156, 9], ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/PID.lean | Module.torsion_by_prime_power_decomposition | [
170,
1
] | [
230,
16
] | [{"tactic": "obtain \u27e8d, s, hs\u27e9 := @Module.Finite.exists_fin _ _ _ _ _ h'", "annotated_tactic": ["obtain \u27e8d, s, hs\u27e9 := @<a>Module.Finite.exists_fin</a> _ _ _ _ _ h'", [{"full_name": "Module.Finite.exists_fin", "def_path": "Mathlib/RingTheory/Finiteness.lean", "def_pos": [555, 9], "def_end_pos": [555,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/UpperLower/Basic.lean | bddAbove_lowerClosure | [
1600,
1
] | [
1601,
47
] | [{"tactic": "simp_rw [BddAbove, upperBounds_lowerClosure]", "annotated_tactic": ["simp_rw [<a>BddAbove</a>, <a>upperBounds_lowerClosure</a>]", [{"full_name": "BddAbove", "def_path": "Mathlib/Order/Bounds/Basic.lean", "def_pos": [56, 5], "def_end_pos": [56, 13]}, {"full_name": "upperBounds_lowerClosure", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | Continuous.limUnder_eq | [
1097,
1
] | [
1099,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_cancel' | [
953,
1
] | [
954,
72
] | [{"tactic": "rw [Submonoid.smul_def, \u2190 mk'_smul, \u2190 Submonoid.smul_def, mk'_cancel]", "annotated_tactic": ["rw [<a>Submonoid.smul_def</a>, \u2190 <a>mk'_smul</a>, \u2190 <a>Submonoid.smul_def</a>, <a>mk'_cancel</a>]", [{"full_name": "Submonoid.smul_def", "def_path": "Mathlib/GroupTheory/Submonoid/Operations.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | iInf_eq_dif | [
1187,
1
] | [
1189,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_eq_nil_of_not_periodic_pt | [
511,
1
] | [
513,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/VectorBundle/FiberwiseLinear.lean | mem_aux | [
226,
9
] | [
236,
39
] | [{"tactic": "simp only [mem_iUnion, mem_setOf_eq]", "annotated_tactic": ["simp only [<a>mem_iUnion</a>, <a>mem_setOf_eq</a>]", [{"full_name": "Set.mem_iUnion", "def_path": "Mathlib/Data/Set/Lattice.lean", "def_pos": [201, 9], "def_end_pos": [201, 19]}, {"full_name": "Set.mem_setOf_eq", "def_path": "Mathlib/Data/Set/Bas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Icc_of_Icc | [
254,
1
] | [
256,
80
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/PGame.lean | SetTheory.PGame.lf_iff_sub_zero_lf | [
1840,
1
] | [
1848,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasColimit_of_created | [
197,
1
] | [
201,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | ContinuousLinearMap.fpowerSeries_apply_add_two | [
378,
1
] | [
379,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_of_subsingleton | [
1196,
1
] | [
1199,
40
] | [{"tactic": "rw [\u2190 hasFDerivWithinAt_univ, subsingleton_univ.eq_singleton_of_mem (mem_univ x)]", "annotated_tactic": ["rw [\u2190 <a>hasFDerivWithinAt_univ</a>, subsingleton_univ.eq_singleton_of_mem (<a>mem_univ</a> x)]", [{"full_name": "hasFDerivWithinAt_univ", "def_path": "Mathlib/Analysis/Calculus/FDeriv/Basic.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_iInter_cthickening | [
1338,
1
] | [
1342,
40
] | [{"tactic": "apply cthickening_eq_iInter_cthickening' (Ioi \u03b4) rfl.subset", "annotated_tactic": ["apply <a>cthickening_eq_iInter_cthickening'</a> (<a>Ioi</a> \u03b4) rfl.subset", [{"full_name": "Metric.cthickening_eq_iInter_cthickening'", "def_path": "Mathlib/Topology/MetricSpace/HausdorffDistance.lean", "def_pos":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_toReal | [
236,
9
] | [
236,
68
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.ofIsoColimit_desc | [
687,
1
] | [
689,
6
] | [] |
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