url stringclasses 3
values | commit stringclasses 3
values | file_path stringlengths 20 79 | full_name stringlengths 3 115 | start list | end list | traced_tactics stringlengths 2 997k |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Category/Profinite/EffectiveEpi.lean | Profinite.effectiveEpiFamily_of_jointly_surjective | [
215,
1
] | [
220,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_left_Ioo | [
1121,
1
] | [
1124,
38
] | [{"tactic": "rw [\u2190 coe_inj, coe_map, coe_Ioo, coe_Ioo]", "annotated_tactic": ["rw [\u2190 <a>coe_inj</a>, <a>coe_map</a>, <a>coe_Ioo</a>, <a>coe_Ioo</a>]", [{"full_name": "Finset.coe_inj", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [244, 9], "def_end_pos": [244, 16]}, {"full_name": "Finset.coe_map", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Icc | [
131,
1
] | [
132,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.absorbs_self | [
276,
1
] | [
281,
22
] | [{"tactic": "refine' \u27e81, zero_lt_one, fun a ha x hx => _\u27e9", "annotated_tactic": ["refine' \u27e81, <a>zero_lt_one</a>, fun a ha x hx => _\u27e9", [{"full_name": "zero_lt_one", "def_path": "Mathlib/Algebra/Order/ZeroLEOne.lean", "def_pos": [39, 15], "def_end_pos": [39, 26]}]], "state_before": "\ud835\udd5c : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Func.lean | List.Func.length_neg | [
267,
1
] | [
268,
30
] | [{"tactic": "simp only [neg, length_map]", "annotated_tactic": ["simp only [<a>neg</a>, <a>length_map</a>]", [{"full_name": "List.Func.neg", "def_path": "Mathlib/Data/List/Func.lean", "def_pos": [45, 5], "def_end_pos": [45, 8]}, {"full_name": "List.length_map", "def_path": "lake-packages/lean4/src/lean/Init/Data/List/B... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Interval.lean | NonemptyInterval.coe_pure_interval | [
631,
1
] | [
632,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.even_odd_of_coprime | [
130,
1
] | [
158,
28
] | [{"tactic": "cases' Int.emod_two_eq_zero_or_one x with hx hx <;>\n cases' Int.emod_two_eq_zero_or_one y with hy hy", "annotated_tactic": ["cases' <a>Int.emod_two_eq_zero_or_one</a> x with hx hx <;>\n cases' <a>Int.emod_two_eq_zero_or_one</a> y with hy hy", [{"full_name": "Int.emod_two_eq_zero_or_one", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Basic.lean | Real.ofCauchy_mul | [
133,
1
] | [
134,
21
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_id | [
1158,
1
] | [
1159,
9
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_distribMulActionHom_mk | [
224,
1
] | [
226,
6
] | [{"tactic": "rfl", "annotated_tactic": ["rfl", []], "state_before": "R : Type u\nA : Type v\nB : Type w\nC : Type w\u2081\ninst\u271d\u2076 : Monoid R\ninst\u271d\u2075 : NonUnitalNonAssocSemiring A\ninst\u271d\u2074 : DistribMulAction R A\ninst\u271d\u00b3 : NonUnitalNonAssocSemiring B\ninst\u271d\u00b2 : DistribMulAc... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_add | [
1074,
1
] | [
1077,
67
] | [{"tactic": "ext s", "annotated_tactic": ["ext s", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\nM : Type u_5\nM' : Type u_6\nN : Type u_7\nP : Type u_8\nG : Type u_9\nH : Type u_10\nR : Type u_11\nS : Type u_12\ninst\u271d : AddZeroClass M\na : \u03b1\nf f' : \u03b1 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/ZFC/Basic.lean | Class.iota_ex | [
1721,
1
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1725,
91
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_map_equiv | [
240,
1
] | [
242,
67
] | [{"tactic": "simp only [IntegrableOn, e.restrict_map, integrable_map_equiv e]", "annotated_tactic": ["simp only [<a>IntegrableOn</a>, e.restrict_map, <a>integrable_map_equiv</a> e]", [{"full_name": "MeasureTheory.IntegrableOn", "def_path": "Mathlib/MeasureTheory/Integral/IntegrableOn.lean", "def_pos": [90, 5], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Analysis/Topology.lean | Ctop.ofEquiv_val | [
79,
1
] | [
80,
15
] | [{"tactic": "cases F", "annotated_tactic": ["cases F", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03c3 : Type u_3\n\u03c4 : Type u_4\nF\u271d : Ctop \u03b1 \u03c3\nE : \u03c3 \u2243 \u03c4\nF : Ctop \u03b1 \u03c3\na : \u03c4\n\u22a2 f (ofEquiv E F) a = f F (\u2191E.symm a)", "state_after": "case mk\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo | [
431,
1
] | [
432,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsPrime.mem_or_mem_of_mul_eq_zero | [
255,
1
] | [
257,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | Function.LeftInverse.closedEmbedding | [
1275,
1
] | [
1277,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_pow_dvd_iff | [
763,
1
] | [
814,
43
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "\u03c3 : Type u_1\nR : Type u_2\ninst\u271d : Semiring R\ns : \u03c3\nn : \u2115\n\u03c6 : MvPowerSeries \u03c3 R\n\u22a2 X s ^ n \u2223 \u03c6 \u2194 \u2200 (m : \u03c3 \u2192\u2080 \u2115), \u2191m s < n \u2192 \u2191(coeff R m) \u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Filter.singleton_mem_pure | [
2671,
1
] | [
2672,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/MulAction.lean | edist_smul₀ | [
119,
1
] | [
120,
89
] | [{"tactic": "simp only [edist_nndist, nndist_smul\u2080, ENNReal.coe_mul, ENNReal.smul_def, smul_eq_mul]", "annotated_tactic": ["simp only [<a>edist_nndist</a>, <a>nndist_smul\u2080</a>, <a>ENNReal.coe_mul</a>, <a>ENNReal.smul_def</a>, <a>smul_eq_mul</a>]", [{"full_name": "edist_nndist", "def_path": "Mathlib/Topology/M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.sub | [
488,
8
] | [
490,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/NormNum/Ineq.lean | Mathlib.Meta.NormNum.isInt_lt_true | [
87,
1
] | [
89,
72
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.length_pos_iff_exists_mem | [
44,
1
] | [
45,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Subsingleton.lean | Filter.Subsingleton.map | [
35,
1
] | [
36,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/LiminfLimsup.lean | Filter.CompleteLatticeHom.apply_limsup_iterate | [
933,
1
] | [
942,
52
] | [{"tactic": "rw [limsup_eq_iInf_iSup_of_nat', map_iInf]", "annotated_tactic": ["rw [<a>limsup_eq_iInf_iSup_of_nat'</a>, <a>map_iInf</a>]", [{"full_name": "Filter.limsup_eq_iInf_iSup_of_nat'", "def_path": "Mathlib/Order/LiminfLimsup.lean", "def_pos": [800, 9], "def_end_pos": [800, 36]}, {"full_name": "map_iInf", "def_pa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Nat.floor_lt' | [
206,
1
] | [
207,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOf.ext | [
116,
1
] | [
123,
43
] | [{"tactic": "rcases a with \u27e8a, a_le, e1\u27e9", "annotated_tactic": ["rcases a with \u27e8a, a_le, e1\u27e9", []], "state_before": "R : Type u\ninst\u271d\u2076 : Ring R\nQ : TypeMax\ninst\u271d\u2075 : AddCommGroup Q\ninst\u271d\u2074 : Module R Q\nM N : Type (max u v)\ninst\u271d\u00b3 : AddCommGroup M\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/WithDensity.lean | MeasureTheory.set_lintegral_withDensity_eq_set_lintegral_mul | [
288,
1
] | [
291,
79
] | [{"tactic": "rw [restrict_withDensity hs, lintegral_withDensity_eq_lintegral_mul _ hf hg]", "annotated_tactic": ["rw [<a>restrict_withDensity</a> hs, <a>lintegral_withDensity_eq_lintegral_mul</a> _ hf hg]", [{"full_name": "MeasureTheory.restrict_withDensity", "def_path": "Mathlib/MeasureTheory/Measure/WithDensity.lean"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | isClosedMap_inv | [
346,
1
] | [
347,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_sum | [
769,
1
] | [
771,
96
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_target | [
975,
1
] | [
976,
94
] | [{"tactic": "simp_rw [extend, LocalEquiv.trans_target, I.target_eq, I.toLocalEquiv_coe_symm, inter_comm]", "annotated_tactic": ["simp_rw [<a>extend</a>, <a>LocalEquiv.trans_target</a>, I.target_eq, I.toLocalEquiv_coe_symm, <a>inter_comm</a>]", [{"full_name": "LocalHomeomorph.extend", "def_path": "Mathlib/Geometry/Manif... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Derivation/Basic.lean | Derivation.neg_apply | [
434,
1
] | [
435,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconvexOn.convex_lt | [
146,
1
] | [
150,
48
] | [{"tactic": "refine' fun x hx y hy a b ha hb hab => _", "annotated_tactic": ["refine' fun x hx y hy a b ha hb hab => _", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\n\u03b2 : Type u_4\ninst\u271d\u2074 : OrderedSemiring \ud835\udd5c\ninst\u271d\u00b3 : AddCommMonoid E\ninst\u271d\u00b2 : A... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_add_C | [
65,
1
] | [
67,
28
] | [{"tactic": "rw [separable_def, derivative_add, derivative_X, derivative_C, add_zero]", "annotated_tactic": ["rw [<a>separable_def</a>, <a>derivative_add</a>, <a>derivative_X</a>, <a>derivative_C</a>, <a>add_zero</a>]", [{"full_name": "Polynomial.separable_def", "def_path": "Mathlib/FieldTheory/Separable.lean", "def_po... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.indep_limsup_atTop_self | [
131,
1
] | [
143,
31
] | [{"tactic": "let ns : \u03b9 \u2192 Set \u03b9 := Set.Iic", "annotated_tactic": ["let ns : \u03b9 \u2192 <a>Set</a> \u03b9 := <a>Set.Iic</a>", [{"full_name": "Set", "def_path": "Mathlib/Init/Set.lean", "def_pos": [38, 5], "def_end_pos": [38, 8]}, {"full_name": "Set.Iic", "def_path": "Mathlib/Data/Set/Intervals/Basic.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_lt_self_iff | [
1217,
11
] | [
1218,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | exists_lt_of_csInf_lt | [
1014,
1
] | [
1015,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.supp_eq | [
235,
1
] | [
246,
10
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "P : PFunctor.{u}\n\u03b1 : Type u\na : P.A\nf : B P a \u2192 \u03b1\n\u22a2 supp { fst := a, snd := f } = f '' univ", "state_after": "case h\nP : PFunctor.{u}\n\u03b1 : Type u\na : P.A\nf : B P a \u2192 \u03b1\nx : \u03b1\n\u22a2 x \u2208 supp { f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.prod_left_snd | [
1070,
1
] | [
1071,
41
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.zero_mod | [
248,
9
] | [
248,
78
] | [{"tactic": "cases b <;> simp [mod]", "annotated_tactic": ["cases b <;> simp [<a>mod</a>]", [{"full_name": "Int.mod", "def_path": "lake-packages/lean4/src/lean/Init/Data/Int/Basic.lean", "def_pos": [315, 5], "def_end_pos": [315, 8]}]], "state_before": "b : Int\n\u22a2 mod 0 b = 0", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.adjoint_inner_left | [
398,
1
] | [
402,
53
] | [{"tactic": "haveI := FiniteDimensional.complete \ud835\udd5c E", "annotated_tactic": ["haveI := <a>FiniteDimensional.complete</a> \ud835\udd5c E", [{"full_name": "FiniteDimensional.complete", "def_path": "Mathlib/Topology/Algebra/Module/FiniteDimension.lean", "def_pos": [516, 9], "def_end_pos": [516, 35]}]], "state_be... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Maps.lean | IsOpenMap.preimage_closure_eq_closure_preimage | [
426,
1
] | [
428,
87
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_compl | [
295,
1
] | [
296,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/PathConnected.lean | Path.reparam_id | [
720,
1
] | [
722,
6
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "X : Type u_1\nY : Type u_2\ninst\u271d\u00b9 : TopologicalSpace X\ninst\u271d : TopologicalSpace Y\nx y z : X\n\u03b9 : Type u_3\n\u03b3\u271d \u03b3 : Path x y\n\u22a2 reparam \u03b3 id (_ : Continuous id) (_ : id 0 = id 0) (_ : id 1 = id 1) = \u03b3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | subset_Icc_csInf_csSup | [
591,
1
] | [
592,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_union' | [
2783,
1
] | [
2785,
31
] | [{"tactic": "rcases h with \u27e8x, \u27e8xs, xt\u27e9\u27e9", "annotated_tactic": ["rcases h with \u27e8x, \u27e8xs, xt\u27e9\u27e9", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nX : Type u_1\n\u03b9 : Type u_2\ninst\u271d : PseudoMetricSpace \u03b1\ns : Set \u03b1\nx y z : \u03b1\nt : Set \u03b1\nh : Set.N... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean | Orientation.rotation_pi | [
148,
1
] | [
150,
18
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "V : Type u_1\nV' : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup V\ninst\u271d\u2074 : NormedAddCommGroup V'\ninst\u271d\u00b3 : InnerProductSpace \u211d V\ninst\u271d\u00b2 : InnerProductSpace \u211d V'\ninst\u271d\u00b9 : Fact (finrank \u211d ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_bot_iff | [
258,
1
] | [
275,
35
] | [{"tactic": "cases' isEmpty_or_nonempty \u03b1 with h\u03b1 h\u03b1", "annotated_tactic": ["cases' <a>isEmpty_or_nonempty</a> \u03b1 with h\u03b1 h\u03b1", [{"full_name": "isEmpty_or_nonempty", "def_path": "Mathlib/Logic/IsEmpty.lean", "def_pos": [207, 9], "def_end_pos": [207, 28]}]], "state_before": "\u03b1 : Type u_1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/Basic.lean | Vector.get_append_cons_zero | [
782,
1
] | [
783,
6
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type ?u.91721\nm n : \u2115\nxs : Vector \u03b1 n\nys : Vector \u03b1 m\nx : \u03b1\n\u22a2 0 < Nat.succ n + m", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Eval.lean | Polynomial.evalRingHom_zero | [
1088,
1
] | [
1089,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/Order.lean | Rat.nonneg_iff_zero_le | [
236,
1
] | [
239,
7
] | [{"tactic": "rw [Rat.le_iff_Nonneg]", "annotated_tactic": ["rw [<a>Rat.le_iff_Nonneg</a>]", [{"full_name": "Rat.le_iff_Nonneg", "def_path": "Mathlib/Data/Rat/Order.lean", "def_pos": [109, 19], "def_end_pos": [109, 32]}]], "state_before": "a\u271d b c a : \u211a\n\u22a2 Rat.Nonneg a \u2194 0 \u2264 a", "state_after": "a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Compactness/Compact.lean | LocallyFinite.finite_nonempty_of_compact | [
781,
1
] | [
783,
80
] | [{"tactic": "simpa only [inter_univ] using hf.finite_nonempty_inter_compact isCompact_univ", "annotated_tactic": ["simpa only [<a>inter_univ</a>] using hf.finite_nonempty_inter_compact <a>isCompact_univ</a>", [{"full_name": "Set.inter_univ", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1012, 9], "def_end_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub | [
191,
1
] | [
193,
84
] | [{"tactic": "rw [sum_smul_vsub_eq_weightedVSubOfPoint_sub, weightedVSubOfPoint_apply_const]", "annotated_tactic": ["rw [<a>sum_smul_vsub_eq_weightedVSubOfPoint_sub</a>, <a>weightedVSubOfPoint_apply_const</a>]", [{"full_name": "Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub", "def_path": "Mathlib/LinearAlgebra/AffineSp... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | Dense.diff_finite | [
743,
1
] | [
746,
37
] | [{"tactic": "convert hs.diff_finset ht.toFinset", "annotated_tactic": ["convert hs.diff_finset ht.toFinset", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : TopologicalSpace \u03b1\ninst\u271d\u00b9 : T1Space \u03b1\ninst\u271d : \u2200 (x : \u03b1), NeBot (\ud835\udcdd[{x}\u1d9c] x)\ns : Set... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_of_support_subset | [
60,
1
] | [
63,
33
] | [{"tactic": "refine Finset.prod_subset hs fun x hxs hx => h x hxs \u25b8 (congr_arg (g x) ?_)", "annotated_tactic": ["refine <a>Finset.prod_subset</a> hs fun x hxs hx => h x hxs \u25b8 (<a>congr_arg</a> (g x) ?_)", [{"full_name": "Finset.prod_subset", "def_path": "Mathlib/Algebra/BigOperators/Basic.lean", "def_pos": [7... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ioc | [
589,
1
] | [
590,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.sdiff_adj | [
310,
1
] | [
311,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Count.lean | MeasureTheory.Measure.count_apply_infinite | [
74,
1
] | [
81,
35
] | [{"tactic": "refine' top_unique (le_of_tendsto' ENNReal.tendsto_nat_nhds_top fun n => _)", "annotated_tactic": ["refine' <a>top_unique</a> (<a>le_of_tendsto'</a> <a>ENNReal.tendsto_nat_nhds_top</a> fun n => _)", [{"full_name": "top_unique", "def_path": "Mathlib/Order/BoundedOrder.lean", "def_pos": [161, 9], "def_end_po... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.midpoint_fixed | [
45,
1
] | [
84,
35
] | [{"tactic": "set z := midpoint \u211d x y", "annotated_tactic": ["set z := <a>midpoint</a> \u211d x y", [{"full_name": "midpoint", "def_path": "Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean", "def_pos": [43, 5], "def_end_pos": [43, 13]}]], "state_before": "E : Type u_1\nPE : Type u_2\nF : Type u_3\nPF : Type u_4\nins... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.IsUniversal.hom_desc | [
672,
1
] | [
675,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/FilterBasis.lean | RingFilterBasis.mul_right | [
295,
1
] | [
296,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.rpow_logb | [
134,
1
] | [
136,
22
] | [{"tactic": "rw [rpow_logb_eq_abs b_pos b_ne_one hx.ne']", "annotated_tactic": ["rw [<a>rpow_logb_eq_abs</a> b_pos b_ne_one hx.ne']", [{"full_name": "Real.rpow_logb_eq_abs", "def_path": "Mathlib/Analysis/SpecialFunctions/Log/Base.lean", "def_pos": [124, 9], "def_end_pos": [124, 25]}]], "state_before": "b x y : \u211d\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bases.lean | TopologicalSpace.isOpen_of_mem_countableBasis | [
719,
1
] | [
721,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_comp | [
1055,
1
] | [
1056,
64
] | [{"tactic": "rw [comp, p.as_sum_range]", "annotated_tactic": ["rw [<a>comp</a>, p.as_sum_range]", [{"full_name": "Polynomial.comp", "def_path": "Mathlib/Data/Polynomial/Eval.lean", "def_pos": [539, 5], "def_end_pos": [539, 9]}]], "state_before": "R : Type u\nS : Type v\nT : Type w\n\u03b9 : Type y\na b : R\nm n : \u211... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subring/Basic.lean | Subring.comap_comap | [
581,
1
] | [
583,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.natCast_def | [
173,
1
] | [
173,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.Approx.truncate_eq_of_agree | [
101,
1
] | [
115,
13
] | [{"tactic": "induction n <;> cases x <;> cases y", "annotated_tactic": ["induction n <;> cases x <;> cases y", []], "state_before": "F : PFunctor.{u}\nn : \u2115\nx : CofixA F n\ny : CofixA F (succ n)\nh : Agree x y\n\u22a2 truncate y = x", "state_after": "case zero.continue.intro\nF : PFunctor.{u}\na\u271d\u00b9 : F.A... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.lt_tsub_of_add_lt_right | [
324,
11
] | [
327,
31
] | [{"tactic": "rintro rfl", "annotated_tactic": ["rintro rfl", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : PartialOrder \u03b1\ninst\u271d\u00b2 : AddCommSemigroup \u03b1\ninst\u271d\u00b9 : Sub \u03b1\ninst\u271d : OrderedSub \u03b1\na b c d : \u03b1\nhc : AddLECancellable c\nh : a + c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Ideal.lean | Order.Ideal.directed | [
133,
11
] | [
134,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean | expNegInvGlue.zero_of_nonpos | [
51,
1
] | [
51,
97
] | [{"tactic": "simp [expNegInvGlue, hx]", "annotated_tactic": ["simp [<a>expNegInvGlue</a>, hx]", [{"full_name": "expNegInvGlue", "def_path": "Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean", "def_pos": [44, 5], "def_end_pos": [44, 18]}]], "state_before": "x : \u211d\nhx : x \u2264 0\n\u22a2 expNegInvGlue x = 0"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_smul_span_singleton | [
134,
1
] | [
143,
85
] | [{"tactic": "rw [add_smul, hy1, hy2]", "annotated_tactic": ["rw [<a>add_smul</a>, hy1, hy2]", [{"full_name": "add_smul", "def_path": "Mathlib/Algebra/Module/Basic.lean", "def_pos": [91, 9], "def_end_pos": [91, 17]}]], "state_before": "R : Type u\nM : Type v\nF : Type u_1\nG : Type u_2\ninst\u271d\u00b2 : CommSemiring R... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero | [
270,
1
] | [
274,
54
] | [{"tactic": "rw [\u2190 neg_eq_zero, \u2190 inner_neg_right] at h", "annotated_tactic": ["rw [\u2190 <a>neg_eq_zero</a>, \u2190 <a>inner_neg_right</a>] at h", [{"full_name": "neg_eq_zero", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [422, 3], "def_end_pos": [422, 14]}, {"full_name": "inner_neg_right", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_left | [
554,
1
] | [
563,
80
] | [{"tactic": "refine' le_antisymm _ (le_lintegral_add _ _)", "annotated_tactic": ["refine' <a>le_antisymm</a> _ (<a>le_lintegral_add</a> _ _)", [{"full_name": "le_antisymm", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [188, 9], "def_end_pos": [188, 20]}, {"full_name": "MeasureTheory.le_lintegral_add", "def_pa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_top | [
873,
1
] | [
874,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_inj | [
1000,
1
] | [
1001,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_compl | [
567,
1
] | [
568,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Basic.lean | WithTop.pred_coe | [
1109,
1
] | [
1110,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_zero | [
215,
20
] | [
215,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.nonempty_biUnion | [
839,
1
] | [
840,
65
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Sort u_4\n\u03b9' : Sort u_5\n\u03b9\u2082 : Sort u_6\n\u03ba : \u03b9 \u2192 Sort u_7\n\u03ba\u2081 : \u03b9 \u2192 Sort u_8\n\u03ba\u2082 : \u03b9 \u2192 Sort u_9\n\u03ba' : \u03b9'... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_zero' | [
749,
1
] | [
750,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_zero | [
168,
1
] | [
169,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_zero_eq_zero | [
103,
1
] | [
104,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_periodic | [
1359,
1
] | [
1360,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.unbounded_of_unbounded_iUnion | [
794,
1
] | [
799,
15
] | [{"tactic": "rw [\u2190 sUnion_range] at h\u2081", "annotated_tactic": ["rw [\u2190 <a>sUnion_range</a>] at h\u2081", [{"full_name": "Set.sUnion_range", "def_path": "Mathlib/Data/Set/Lattice.lean", "def_pos": [1317, 9], "def_end_pos": [1317, 21]}]], "state_before": "\u03b1\u271d : Type u_1\nr\u271d : \u03b1\u271d \u219... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.exists_eq_add_translationNumber | [
928,
1
] | [
935,
79
] | [{"tactic": "obtain \u27e8a, ha\u27e9 : \u2203 x, f x \u2264 x + \u03c4 f := by\n by_contra' H\n exact lt_irrefl _ (f.lt_translationNumber_of_forall_add_lt hf H)", "annotated_tactic": ["obtain \u27e8a, ha\u27e9 : \u2203 x, f x \u2264 x + \u03c4 f := by\n by_contra' H\n exact <a>lt_irrefl</a> _ (f.lt_translation... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.initial.hom_ext | [
121,
1
] | [
122,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sq_pi_over_two_pow | [
755,
1
] | [
757,
35
] | [{"tactic": "rw [sin_sq, cos_pi_over_two_pow]", "annotated_tactic": ["rw [<a>sin_sq</a>, <a>cos_pi_over_two_pow</a>]", [{"full_name": "Real.sin_sq", "def_path": "Mathlib/Data/Complex/Exponential.lean", "def_pos": [1302, 9], "def_end_pos": [1302, 15]}, {"full_name": "Real.cos_pi_over_two_pow", "def_path": "Mathlib/Analy... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.mapsTo_iUnion₂ | [
1571,
1
] | [
1573,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Interval.lean | Interval.dual_map | [
425,
1
] | [
428,
33
] | [{"tactic": "cases s", "annotated_tactic": ["cases s", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort u_5\n\u03ba : \u03b9 \u2192 Sort u_6\ninst\u271d\u00b2 : Preorder \u03b1\ninst\u271d\u00b9 : Preorder \u03b2\ninst\u271d : Preorder \u03b3\nf : \u03b1 \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.ι_map_apply' | [
447,
1
] | [
449,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Gauge.lean | gauge_smul_of_nonneg | [
260,
1
] | [
282,
31
] | [{"tactic": "obtain rfl | ha' := ha.eq_or_lt", "annotated_tactic": ["obtain rfl | ha' := ha.eq_or_lt", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u2076 : AddCommGroup E\ninst\u271d\u2075 : Module \u211d E\ns\u271d t : Set E\na\u271d : \u211d\n\u03b1 : Type u_4\ninst\u271d\u207... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Rotate.lean | List.rotate'_mod | [
100,
1
] | [
105,
80
] | [{"tactic": "rw [rotate'_length_mul]", "annotated_tactic": ["rw [<a>rotate'_length_mul</a>]", [{"full_name": "List.rotate'_length_mul", "def_path": "Mathlib/Data/List/Rotate.lean", "def_pos": [90, 9], "def_end_pos": [90, 27]}]], "state_before": "\u03b1 : Type u\nl : List \u03b1\nn : \u2115\n\u22a2 rotate' l (n % length... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/RelClasses.lean | subset_antisymm_iff | [
673,
1
] | [
674,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | le_sSup | [
196,
1
] | [
197,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/GaloisConnection.lean | sInf_image2_eq_sInf_sSup | [
422,
1
] | [
425,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Relation.lean | Relation.TransGen.to_reflTransGen | [
351,
1
] | [
354,
32
] | [{"tactic": "induction' h with b h b c _ bc ab", "annotated_tactic": ["induction' h with b h b c _ bc ab", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\na\u271d b\u271d c d a b : \u03b1\nh : TransGen r a b\n\u22a2 ReflTransGen r a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_comp_ofLE | [
228,
1
] | [
229,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.inf_mem | [
460,
1
] | [
462,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.coe_zpow | [
992,
1
] | [
996,
42
] | [{"tactic": "refine' (coe_inv _).trans _", "annotated_tactic": ["refine' (<a>coe_inv</a> _).<a>trans</a> _", [{"full_name": "Finset.coe_inv", "def_path": "Mathlib/Data/Finset/Pointwise.lean", "def_pos": [269, 9], "def_end_pos": [269, 16]}, {"full_name": "Eq.trans", "def_path": "lake-packages/lean4/src/lean/Init/Prelude... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.iterate | [
81,
11
] | [
85,
34
] | [{"tactic": "induction n with\n| zero => exact LeftOrdContinuous.id \u03b1\n| succ n ihn => exact ihn.comp hf", "annotated_tactic": ["induction n with\n| <a>zero</a> => exact <a>LeftOrdContinuous.id</a> \u03b1\n| <a>succ</a> n ihn => exact ihn.comp hf", [{"full_name": "Nat.zero", "def_path": "lake-packages/lean4/src/le... |
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