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/Finite/Card.lean | Nat.card_eq | [
49,
1
] | [
54,
85
] | [{"tactic": "cases finite_or_infinite \u03b1", "annotated_tactic": ["cases <a>finite_or_infinite</a> \u03b1", [{"full_name": "finite_or_infinite", "def_path": "Mathlib/Data/Finite/Defs.lean", "def_pos": [120, 9], "def_end_pos": [120, 27]}]], "state_before": "\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_δ' | [
489,
1
] | [
494,
67
] | [{"tactic": "simp only [hj, Fin.not_lt_zero] at H", "annotated_tactic": ["simp only [hj, <a>Fin.not_lt_zero</a>] at H", [{"full_name": "Fin.not_lt_zero", "def_path": "lake-packages/std/Std/Data/Fin/Lemmas.lean", "def_pos": [113, 17], "def_end_pos": [113, 28]}]], "state_before": "C : Type u\ninst\u271d : Category.{v, u}... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_zero | [
185,
1
] | [
186,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.subsingleton_isTop | [
2416,
1
] | [
2417,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_of_lt_one' | [
648,
1
] | [
651,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Sphere.lean | Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius | [
290,
1
] | [
295,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.CliqueFree.mono | [
216,
1
] | [
219,
40
] | [{"tactic": "intro hG s hs", "annotated_tactic": ["intro hG s hs", []], "state_before": "\u03b1 : Type u_1\nG H : SimpleGraph \u03b1\nm n : \u2115\ns : Finset \u03b1\nh : m \u2264 n\n\u22a2 CliqueFree G m \u2192 CliqueFree G n", "state_after": "\u03b1 : Type u_1\nG H : SimpleGraph \u03b1\nm n : \u2115\ns\u271d : Finset... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_one | [
544,
11
] | [
545,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Function.Injective.hasSum_iff | [
133,
1
] | [
135,
73
] | [{"tactic": "simp only [HasSum, Tendsto, comp_apply, hg.map_atTop_finset_sum_eq hf]", "annotated_tactic": ["simp only [<a>HasSum</a>, <a>Tendsto</a>, <a>comp_apply</a>, hg.map_atTop_finset_sum_eq hf]", [{"full_name": "HasSum", "def_path": "Mathlib/Topology/Algebra/InfiniteSum/Basic.lean", "def_pos": [57, 5], "def_end_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.mem_map | [
234,
1
] | [
235,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Seminorm.lean | Seminorm.le_def | [
272,
1
] | [
273,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean | PowerBasis.ofGenMemAdjoin'_gen | [
204,
1
] | [
207,
36
] | [{"tactic": "simp [PowerBasis.ofGenMemAdjoin']", "annotated_tactic": ["simp [<a>PowerBasis.ofGenMemAdjoin'</a>]", [{"full_name": "PowerBasis.ofGenMemAdjoin'", "def_path": "Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean", "def_pos": [190, 19], "def_end_pos": [190, 52]}]], "state_before": "R : Type u_1\nS : Type u_2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.sZMod_eq_s | [
120,
1
] | [
124,
34
] | [{"tactic": "induction' i with i ih", "annotated_tactic": ["induction' i with i ih", []], "state_before": "p' i : \u2115\n\u22a2 sZMod (p' + 2) i = \u2191(s i)", "state_after": "case zero\np' : \u2115\n\u22a2 sZMod (p' + 2) zero = \u2191(s zero)\n\ncase succ\np' i : \u2115\nih : sZMod (p' + 2) i = \u2191(s i)\n\u22a2 s... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.toCocone_ι_app_left | [
1200,
1
] | [
1201,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_singleton | [
1501,
1
] | [
1502,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Lift.lean | Filter.principal_le_lift' | [
333,
1
] | [
334,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.yonedaEvaluation_map_down | [
314,
1
] | [
317,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Basic.lean | Nat.mul_ne_mul_right | [
362,
1
] | [
363,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_add_le | [
338,
1
] | [
339,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.mk | [
1077,
1
] | [
1081,
33
] | [{"tactic": "intro s hs", "annotated_tactic": ["intro s hs", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nm : MeasurableSpace \u03b1\nL : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u2075 : AddCommMonoid L\ninst\u271d\u2074 : TopologicalSpace L\ninst\u271d\u00b3 : AddCommMonoid M\ninst\u271d\u00b2 :... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/String/Lemmas.lean | Substring.Valid.nextn | [
1020,
1
] | [
1024,
52
] | [{"tactic": "let \u27e8l, m, r, h\u27e9 := h.validFor", "annotated_tactic": ["let \u27e8l, m, r, h\u27e9 := h.validFor", []], "state_before": "m\u2081 m\u2082 : List Char\nx\u271d : Substring\nh : Valid x\u271d\ne : (toString x\u271d).data = m\u2081 ++ m\u2082\n\u22a2 \u2200 (n : Nat), Substring.nextn x\u271d n { byteI... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/ProdLp.lean | WithLp.norm_equiv_symm_fst | [
694,
1
] | [
695,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq | [
401,
1
] | [
419,
21
] | [{"tactic": "have hg : g \u2248 0 := equiv_zero_of_val_eq_of_equiv_zero h hf", "annotated_tactic": ["have hg : g \u2248 0 := <a>equiv_zero_of_val_eq_of_equiv_zero</a> h hf", [{"full_name": "PadicSeq.equiv_zero_of_val_eq_of_equiv_zero", "def_path": "Mathlib/NumberTheory/Padics/PadicNumbers.lean", "def_pos": [145, 9], "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries_isDescendingCentralSeries | [
324,
1
] | [
328,
50
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\nH : Subgroup G\ninst\u271d : Normal H\n\u22a2 IsDescendingCentralSeries (lowerCentralSeries G)", "state_after": "case left\nG : Type u_1\ninst\u271d\u00b9 : Group G\nH : Subgroup G\ninst\u271d ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.lift_mapBiprod | [
453,
1
] | [
455,
85
] | [{"tactic": "rw [\u2190 biprod.map_lift_mapBiprod, Category.assoc, Iso.hom_inv_id, Category.comp_id]", "annotated_tactic": ["rw [\u2190 <a>biprod.map_lift_mapBiprod</a>, <a>Category.assoc</a>, <a>Iso.hom_inv_id</a>, <a>Category.comp_id</a>]", [{"full_name": "CategoryTheory.Limits.biprod.map_lift_mapBiprod", "def_path":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.coe_sup | [
87,
1
] | [
88,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean | NonUnitalSubalgebra.toNonUnitalSubring_inj | [
164,
1
] | [
166,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.changeOriginSeries_summable_aux₃ | [
1358,
1
] | [
1363,
69
] | [{"tactic": "refine' NNReal.summable_of_le\n (fun n => _) (NNReal.summable_sigma.1 <| p.changeOriginSeries_summable_aux\u2082 hr k).2", "annotated_tactic": ["refine' <a>NNReal.summable_of_le</a>\n (fun n => _) (<a>NNReal.summable_sigma</a>.1 <| p.changeOriginSeries_summable_aux\u2082 hr k).2", [{"full_name": "NNRea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Martingale/Basic.lean | MeasureTheory.Submartingale.ae_le_condexp | [
223,
1
] | [
225,
17
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.le_add_of_sub_right_le | [
993,
11
] | [
995,
32
] | [{"tactic": "have h := Int.add_le_add_right h c", "annotated_tactic": ["have h := <a>Int.add_le_add_right</a> h c", [{"full_name": "Int.add_le_add_right", "def_path": "lake-packages/std/Std/Data/Int/Lemmas.lean", "def_pos": [758, 19], "def_end_pos": [758, 35]}]], "state_before": "a b c : Int\nh : a - c \u2264 b\n\u22a2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | diff_subset_closure_iff | [
483,
1
] | [
484,
68
] | [{"tactic": "rw [diff_subset_iff, union_eq_self_of_subset_left subset_closure]", "annotated_tactic": ["rw [<a>diff_subset_iff</a>, <a>union_eq_self_of_subset_left</a> <a>subset_closure</a>]", [{"full_name": "Set.diff_subset_iff", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1948, 9], "def_end_pos": [1948, 24]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | MeasureTheory.condexp_nonpos | [
367,
1
] | [
372,
29
] | [{"tactic": "by_cases hfint : Integrable f \u03bc", "annotated_tactic": ["by_cases hfint : <a>Integrable</a> f \u03bc", [{"full_name": "MeasureTheory.Integrable", "def_path": "Mathlib/MeasureTheory/Function/L1Space.lean", "def_pos": [442, 5], "def_end_pos": [442, 15]}]], "state_before": "\u03b1 : Type u_1\nF : Type u_2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.prod | [
534,
1
] | [
537,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_trivChange_source | [
475,
1
] | [
478,
7
] | [{"tactic": "erw [mem_prod]", "annotated_tactic": ["erw [<a>mem_prod</a>]", [{"full_name": "Set.mem_prod", "def_path": "Mathlib/Data/Set/Prod.lean", "def_pos": [56, 9], "def_end_pos": [56, 17]}]], "state_before": "\u03b9 : Type u_1\nB : Type u_2\nF : Type u_3\nX : Type u_4\ninst\u271d\u00b2 : TopologicalSpace X\ninst\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Abs.lean | dist_bdd_within_interval | [
362,
1
] | [
364,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp | [
1204,
1
] | [
1218,
77
] | [{"tactic": "ext1", "annotated_tactic": ["ext1", []], "state_before": "\u03b1 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nm m0 : MeasurableSpace \u03b1\np : \u211d\u22650\u221e\nq : \u211d\n\u03bc \u03bd : Measure \u03b1\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsLimit.pos | [
284,
1
] | [
285,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/LiminfLimsup.lean | Filter.le_limsInf_of_le | [
498,
1
] | [
501,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom | [
426,
1
] | [
427,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.coeff_coe_units_zero_ne_zero | [
1097,
1
] | [
1100,
24
] | [{"tactic": "conv in 0 => rw [\u2190 natDegree_coe_units u]", "annotated_tactic": ["conv in 0 => rw [\u2190 <a>natDegree_coe_units</a> u]", [{"full_name": "Polynomial.natDegree_coe_units", "def_path": "Mathlib/Data/Polynomial/RingDivision.lean", "def_pos": [880, 9], "def_end_pos": [880, 28]}]], "state_before": "R : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/PartENat.lean | PartENat.add_left_cancel_iff | [
538,
11
] | [
539,
64
] | [{"tactic": "rw [add_comm a, add_comm a, PartENat.add_right_cancel_iff ha]", "annotated_tactic": ["rw [<a>add_comm</a> a, <a>add_comm</a> a, <a>PartENat.add_right_cancel_iff</a> ha]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"full_name": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ModularLattice.lean | inf_covby_of_covby_sup_right | [
180,
1
] | [
182,
36
] | [{"tactic": "rw [inf_comm, sup_comm]", "annotated_tactic": ["rw [<a>inf_comm</a>, <a>sup_comm</a>]", [{"full_name": "inf_comm", "def_path": "Mathlib/Order/Lattice.lean", "def_pos": [500, 9], "def_end_pos": [500, 17]}, {"full_name": "sup_comm", "def_path": "Mathlib/Order/Lattice.lean", "def_pos": [250, 9], "def_end_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.sum_hom | [
204,
1
] | [
206,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_hom_add_index | [
413,
1
] | [
415,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_apply_of_ne_of_ne | [
1650,
1
] | [
1651,
59
] | [{"tactic": "simp (config := { contextual := true }) [swap_apply_def]", "annotated_tactic": ["simp (config := { contextual := <a>true</a> }) [<a>swap_apply_def</a>]", [{"full_name": "Bool.true", "def_path": "lake-packages/lean4/src/lean/Init/Prelude.lean", "def_pos": [549, 5], "def_end_pos": [549, 9]}, {"full_name": "E... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Measurable.aestronglyMeasurable | [
1285,
1
] | [
1288,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.lsmul_apply | [
1232,
1
] | [
1233,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.rangeSRestrict_surjective | [
1195,
1
] | [
1198,
22
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.subset_append_right | [
298,
9
] | [
298,
100
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_eq_of_two_zsmul_eq | [
822,
1
] | [
824,
33
] | [{"tactic": "exact tan_eq_of_two_nsmul_eq h", "annotated_tactic": ["exact <a>tan_eq_of_two_nsmul_eq</a> h", [{"full_name": "Real.Angle.tan_eq_of_two_nsmul_eq", "def_path": "Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean", "def_pos": [815, 9], "def_end_pos": [815, 31]}]], "state_before": "\u03b8 \u03c8 : Ang... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_eq_of_le | [
433,
1
] | [
434,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Periodic.lean | Function.Periodic.exists_mem_Ico | [
292,
1
] | [
295,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Fintype.card_pos | [
558,
1
] | [
559,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.sub_le_iff_le_add | [
1659,
11
] | [
1662,
39
] | [{"tactic": "revert s", "annotated_tactic": ["revert s", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type v\n\u03b3 : Type u_2\ninst\u271d : DecidableEq \u03b1\ns t u : Multiset \u03b1\na b : \u03b1\n\u22a2 s - t \u2264 u \u2194 s \u2264 u + t", "state_after": "\u03b1 : Type u_1\n\u03b2 : Type v\n\u03b3 : Type u_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_target_iso_zero' | [
400,
1
] | [
401,
46
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.dvd_iff_emod_eq_zero | [
688,
1
] | [
689,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.power_nat_eq | [
962,
1
] | [
963,
53
] | [{"tactic": "exact_mod_cast h2", "annotated_tactic": ["exact_mod_cast h2", []], "state_before": "c : Cardinal.{u}\nn : \u2115\nh1 : \u2135\u2080 \u2264 c\nh2 : 1 \u2264 n\n\u22a2 1 \u2264 \u2191n", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_univ | [
1014,
1
] | [
1015,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_smul | [
370,
1
] | [
372,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Data/Nat/Bitwise.lean | Nat.binaryRec_eq | [
319,
1
] | [
343,
16
] | [{"tactic": "rw [binaryRec]", "annotated_tactic": ["rw [<a>binaryRec</a>]", [{"full_name": "Nat.binaryRec", "def_path": "Mathlib/Init/Data/Nat/Bitwise.lean", "def_pos": [227, 5], "def_end_pos": [227, 14]}]], "state_before": "C : \u2115 \u2192 Sort u\nz : C 0\nf : (b : Bool) \u2192 (n : \u2115) \u2192 C n \u2192 C (bit ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Between.lean | Wbtw.left_ne_right_of_ne_right | [
327,
1
] | [
330,
14
] | [{"tactic": "rintro rfl", "annotated_tactic": ["rintro rfl", []], "state_before": "R : Type u_1\nV : Type u_2\nV' : Type u_3\nP : Type u_4\nP' : Type u_5\ninst\u271d\u2076 : OrderedRing R\ninst\u271d\u2075 : AddCommGroup V\ninst\u271d\u2074 : Module R V\ninst\u271d\u00b3 : AddTorsor V P\ninst\u271d\u00b2 : AddCommGroup... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_eq_equivFun | [
346,
1
] | [
347,
40
] | [{"tactic": "rw [b.equivFun_apply, toDual_eq_repr]", "annotated_tactic": ["rw [b.equivFun_apply, <a>toDual_eq_repr</a>]", [{"full_name": "Basis.toDual_eq_repr", "def_path": "Mathlib/LinearAlgebra/Dual.lean", "def_pos": [342, 9], "def_end_pos": [342, 23]}]], "state_before": "R : Type uR\nM : Type uM\nK : Type uK\nV : Ty... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_limit | [
275,
1
] | [
285,
45
] | [{"tactic": "apply le_antisymm _ (ciSup_le' _)", "annotated_tactic": ["apply <a>le_antisymm</a> _ (<a>ciSup_le'</a> _)", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}, {"full_name": "ciSup_le'", "def_path": "Mathlib/Order/ConditionallyCompleteLa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Cyclotomic/PrimitiveRoots.lean | IsCyclotomicExtension.norm_zeta_eq_one | [
500,
1
] | [
502,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | differentiableWithinAt_inverse | [
530,
1
] | [
532,
55
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_one_add_X_pow | [
337,
1
] | [
338,
90
] | [{"tactic": "rw [add_comm _ X, coeff_X_add_one_pow]", "annotated_tactic": ["rw [<a>add_comm</a> _ <a>X</a>, <a>coeff_X_add_one_pow</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"full_name": "Polynomial.X", "def_path": "Mathlib/Data/Poly... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_pos_of_nonneg | [
218,
1
] | [
220,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableAtFilter.filter_mono | [
428,
1
] | [
431,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Disjoint.lean | Disjoint.mono_left | [
70,
1
] | [
71,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Analytic.lean | HasFPowerSeriesOnBall.fderiv | [
88,
1
] | [
115,
8
] | [{"tactic": "suffices A :\n HasFPowerSeriesOnBall\n (fun z => continuousMultilinearCurryFin1 \ud835\udd5c E F (p.changeOrigin (z - x) 1))\n ((continuousMultilinearCurryFin1 \ud835\udd5c E F :\n (E[\u00d71]\u2192L[\ud835\udd5c] F) \u2192L[\ud835\udd5c] E \u2192L[\ud835\udd5c] F).compFormalMultilinearSeri... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.nontrivial_of_three_le_card | [
216,
1
] | [
221,
47
] | [{"tactic": "haveI := Fintype.one_lt_card_iff_nontrivial.1 (lt_trans (by decide) h3)", "annotated_tactic": ["haveI := <a>Fintype.one_lt_card_iff_nontrivial</a>.1 (<a>lt_trans</a> (by decide) h3)", [{"full_name": "Fintype.one_lt_card_iff_nontrivial", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [588, 9], "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/CompactOpen.lean | ContinuousMap.compactOpen_eq_sInf_induced | [
246,
1
] | [
261,
7
] | [{"tactic": "refine' le_antisymm _ _", "annotated_tactic": ["refine' <a>le_antisymm</a> _ _", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ninst\u271d\u00b2 : Topologic... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | MDifferentiableWithinAt.mul | [
1708,
1
] | [
1711,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.rename_psum | [
305,
1
] | [
306,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_pow | [
267,
11
] | [
268,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/VectorBundle/Hom.lean | hom_trivializationAt_apply | [
310,
1
] | [
314,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Power.lean | zpow_le_one_of_nonpos | [
40,
1
] | [
41,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_ne_zero | [
1008,
1
] | [
1009,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_append | [
1520,
1
] | [
1531,
27
] | [{"tactic": "apply\n Computation.eq_of_bisim\n (fun c1 c2 =>\n \u2203 s t, c1 = destruct (append s t) \u2227 c2 = (destruct s).bind (destruct_append.aux t))\n _ \u27e8s, t, rfl, rfl\u27e9", "annotated_tactic": ["apply\n <a>Computation.eq_of_bisim</a>\n (fun c1 c2 =>\n \u2203 s t, c1 = <a>dest... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.isClosed_fiber | [
72,
1
] | [
73,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.not_mem_range_self | [
3065,
1
] | [
3066,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_sub_lt_descFactorial' | [
447,
1
] | [
460,
36
] | [{"tactic": "rw [descFactorial_succ, pow_succ, pow_one, descFactorial_one]", "annotated_tactic": ["rw [<a>descFactorial_succ</a>, <a>pow_succ</a>, <a>pow_one</a>, <a>descFactorial_one</a>]", [{"full_name": "Nat.descFactorial_succ", "def_path": "Mathlib/Data/Nat/Factorial/Basic.lean", "def_pos": [353, 9], "def_end_pos":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isClassified_of_isPrimitiveClassified | [
207,
1
] | [
212,
16
] | [{"tactic": "obtain \u27e8m, n, H\u27e9 := hp", "annotated_tactic": ["obtain \u27e8m, n, H\u27e9 := hp", []], "state_before": "x y z : \u2124\nh : PythagoreanTriple x y z\nhp : IsPrimitiveClassified h\n\u22a2 IsClassified h", "state_after": "case intro.intro\nx y z : \u2124\nh : PythagoreanTriple x y z\nm n : \u2124\nH... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Order.lean | one_lt_pow_iff_of_nonneg | [
571,
1
] | [
572,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_sin | [
1027,
1
] | [
1029,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_monotone | [
460,
1
] | [
464,
30
] | [{"tactic": "induction' L with _ _ hi", "annotated_tactic": ["induction' L with _ _ hi", []], "state_before": "n p q : \u2115\nL : List \u2115\nh : p \u2264 q\n\u22a2 ofDigits p L \u2264 ofDigits q L", "state_after": "case nil\nn p q : \u2115\nh : p \u2264 q\n\u22a2 ofDigits p [] \u2264 ofDigits q []\n\ncase cons\nn p ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.mem_uniformity | [
245,
9
] | [
259,
38
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "X : Type u\nY : Type v\nZ : Type w\ninst\u271d\u00b9 : MetricSpace X\ninst\u271d : MetricSpace Y\ns : Set ((X \u2295 Y) \u00d7 (X \u2295 Y))\n\u22a2 s \u2208 \ud835\udce4 (X \u2295 Y) \u2194 \u2203 \u03b5, \u03b5 > 0 \u2227 \u2200 (a b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.weak_right | [
919,
1
] | [
921,
56
] | [{"tactic": "cases o\u2081 <;> trivial", "annotated_tactic": ["cases o\u2081 <;> trivial", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : Preorder \u03b1\no\u2081 : WithBot \u03b1\no\u2082 : WithTop \u03b1\nh : Bounded nil o\u2081 o\u2082\n\u22a2 Bounded nil o\u2081 \u22a4", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_restrict_of_zero | [
751,
1
] | [
755,
53
] | [{"tactic": "simp [hs, Set.indicator_comp_of_zero hg]", "annotated_tactic": ["simp [hs, <a>Set.indicator_comp_of_zero</a> hg]", [{"full_name": "Set.indicator_comp_of_zero", "def_path": "Mathlib/Algebra/IndicatorFunction.lean", "def_pos": [260, 3], "def_end_pos": [260, 14]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Monotone/Basic.lean | Function.update_mono | [
1226,
1
] | [
1226,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/QuotientOperations.lean | RingHom.quotientKerEquivOfRightInverse.Symm.apply | [
81,
1
] | [
83,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.cos_angle_add_of_inner_eq_zero | [
136,
1
] | [
143,
51
] | [{"tactic": "rw [angle_add_eq_arccos_of_inner_eq_zero h,\n Real.cos_arccos (le_trans (by norm_num) (div_nonneg (norm_nonneg _) (norm_nonneg _)))\n (div_le_one_of_le _ (norm_nonneg _))]", "annotated_tactic": ["rw [<a>angle_add_eq_arccos_of_inner_eq_zero</a> h,\n <a>Real.cos_arccos</a> (<a>le_trans</a> (by norm_nu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Finite.lean | PartENat.card_le_one_iff_subsingleton | [
230,
1
] | [
234,
42
] | [{"tactic": "rw [\u2190 le_one_iff_subsingleton]", "annotated_tactic": ["rw [\u2190 <a>le_one_iff_subsingleton</a>]", [{"full_name": "Cardinal.le_one_iff_subsingleton", "def_path": "Mathlib/SetTheory/Cardinal/Basic.lean", "def_pos": [421, 9], "def_end_pos": [421, 32]}]], "state_before": "\u03b1\u271d : Type u_1\n\u03b2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.left_mem_Icc | [
114,
1
] | [
115,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Order/Defs.lean | eq_or_lt_of_not_lt | [
386,
1
] | [
387,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.symm_symm | [
229,
1
] | [
231,
7
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "F\u271d : Type u_1\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst\u271d\u00b3 : TopologicalSpace X\ninst\u271d\u00b2 : TopologicalSpace Y\ninst\u271d\u00b9 : TopologicalSpace Z\ninst\u271d : TopologicalSpace Z'\nf\u2080 f\u2081 : C(X, Y)\nF : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Field/Basic.lean | norm_inv | [
572,
1
] | [
573,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Congruence.lean | RingCon.trans | [
105,
11
] | [
106,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/MinMax.lean | List.not_lt_maximum_of_mem | [
322,
1
] | [
323,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.addHaar_closedBall_center | [
432,
1
] | [
436,
34
] | [{"tactic": "rw [this, measure_preimage_add]", "annotated_tactic": ["rw [this, <a>measure_preimage_add</a>]", [{"full_name": "MeasureTheory.measure_preimage_add", "def_path": "Mathlib/MeasureTheory/Group/Measure.lean", "def_pos": [317, 3], "def_end_pos": [317, 14]}]], "state_before": "E\u271d : Type u_1\ninst\u271d\u00... |
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