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/LinearAlgebra/Matrix/IsDiag.lean | Matrix.isDiag_conjTranspose_iff | [
131,
1
] | [
135,
32
] | [{"tactic": "convert ha.conjTranspose", "annotated_tactic": ["convert ha.conjTranspose", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nR : Type u_3\nn : Type u_4\nm : Type u_5\ninst\u271d\u00b9 : Semiring \u03b1\ninst\u271d : StarRing \u03b1\nA : Matrix n n \u03b1\nha : IsDiag A\u1d34\n\u22a2 IsDiag A", "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_succ | [
329,
1
] | [
329,
98
] | [{"tactic": "rw [\u2190 nadd_one (a \u266f b), nadd_assoc, nadd_one]", "annotated_tactic": ["rw [\u2190 <a>nadd_one</a> (a \u266f b), <a>nadd_assoc</a>, <a>nadd_one</a>]", [{"full_name": "Ordinal.nadd_one", "def_path": "Mathlib/SetTheory/Ordinal/NaturalOps.lean", "def_pos": [318, 9], "def_end_pos": [318, 17]}, {"full_n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.toEquiv_injective | [
1051,
1
] | [
1056,
20
] | [{"tactic": "rintro \u27e8\u27e8\u27e8\u27e8f, -\u27e9, -\u27e9, -\u27e9, f_inv\u27e9 \u27e8\u27e8\u27e8\u27e8g, -\u27e9, -\u27e9, -\u27e9, g_inv\u27e9", "annotated_tactic": ["rintro \u27e8\u27e8\u27e8\u27e8f, -\u27e9, -\u27e9, -\u27e9, f_inv\u27e9 \u27e8\u27e8\u27e8\u27e8g, -\u27e9, -\u27e9, -\u27e9, g_inv\u27e9", []]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_mul_sqrt_lt_succ' | [
183,
1
] | [
184,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.snd_univ | [
965,
1
] | [
965,
94
] | [{"tactic": "rw [snd_apply MeasurableSet.univ, preimage_univ]", "annotated_tactic": ["rw [<a>snd_apply</a> <a>MeasurableSet.univ</a>, <a>preimage_univ</a>]", [{"full_name": "MeasureTheory.Measure.snd_apply", "def_path": "Mathlib/MeasureTheory/Constructions/Prod/Basic.lean", "def_pos": [961, 9], "def_end_pos": [961, 18]... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Init/Lemmas.lean | List.map_id | [
94,
9
] | [
94,
82
] | [{"tactic": "induction l <;> simp_all", "annotated_tactic": ["induction l <;> simp_all", []], "state_before": "\u03b1 : Type u_1\nl : List \u03b1\n\u22a2 map id l = l", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | closure_eq_self_union_frontier | [
800,
1
] | [
801,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_def_of_pos | [
54,
1
] | [
55,
62
] | [{"tactic": "rw [rpow_def_of_nonneg (le_of_lt hx), if_neg (ne_of_gt hx)]", "annotated_tactic": ["rw [<a>rpow_def_of_nonneg</a> (<a>le_of_lt</a> hx), <a>if_neg</a> (<a>ne_of_gt</a> hx)]", [{"full_name": "Real.rpow_def_of_nonneg", "def_path": "Mathlib/Analysis/SpecialFunctions/Pow/Real.lean", "def_pos": [47, 9], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Ico_iff_left | [
65,
1
] | [
66,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Prod.lean | Finset.offDiag_union | [
402,
1
] | [
406,
47
] | [{"tactic": "push_cast", "annotated_tactic": ["push_cast", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ninst\u271d : DecidableEq \u03b1\ns t : Finset \u03b1\nx : \u03b1 \u00d7 \u03b1\nh : _root_.Disjoint s t\n\u22a2 \u2191(offDiag (s \u222a t)) = \u2191(offDiag s \u222a offDiag t \u222... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/Homology.lean | cyclesMap_id | [
214,
1
] | [
216,
7
] | [{"tactic": "dsimp only [cyclesMap]", "annotated_tactic": ["dsimp only [<a>cyclesMap</a>]", [{"full_name": "cyclesMap", "def_path": "Mathlib/Algebra/Homology/Homology.lean", "def_pos": [200, 8], "def_end_pos": [200, 17]}]], "state_before": "\u03b9 : Type u_1\nV : Type u\ninst\u271d\u00b2 : Category.{v, u} V\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_preimage | [
300,
1
] | [
305,
43
] | [{"tactic": "refine' inducedOuterMeasure_preimage _ \u03bc.innerContent_iUnion_nat \u03bc.innerContent_mono _\n (fun _ => f.isOpen_preimage) _", "annotated_tactic": ["refine' <a>inducedOuterMeasure_preimage</a> _ \u03bc.innerContent_iUnion_nat \u03bc.innerContent_mono _\n (fun _ => f.isOpen_preimage) _", [{"full_na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_right_pointReflection | [
240,
9
] | [
242,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_lt | [
451,
1
] | [
452,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Basic.lean | div_le_one_of_le | [
242,
1
] | [
243,
64
] | [{"tactic": "rwa [one_mul]", "annotated_tactic": ["rwa [<a>one_mul</a>]", [{"full_name": "one_mul", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [464, 9], "def_end_pos": [464, 16]}]], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\ninst\u271d : LinearOrderedSemifield \u03b1\na b c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Analysis/Topology.lean | Ctop.coe_mk | [
64,
1
] | [
64,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.eq_empty_or_nonempty | [
635,
1
] | [
636,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.embDomain_succ_smul_powers | [
1777,
1
] | [
1788,
63
] | [{"tactic": "apply SummableFamily.ext", "annotated_tactic": ["apply <a>SummableFamily.ext</a>", [{"full_name": "HahnSeries.SummableFamily.ext", "def_path": "Mathlib/RingTheory/HahnSeries.lean", "def_pos": [1419, 9], "def_end_pos": [1419, 12]}]], "state_before": "\u0393 : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : Linea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.eq_of_length_eq_zero | [
421,
1
] | [
422,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Log.lean | Nat.log_of_left_le_one | [
48,
1
] | [
49,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Concept.lean | intentClosure_union | [
93,
1
] | [
95,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_add | [
614,
1
] | [
616,
80
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_sum | [
976,
1
] | [
979,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.ne_zero | [
151,
1
] | [
153,
52
] | [{"tactic": "rintro rfl", "annotated_tactic": ["rintro rfl", []], "state_before": "p q : \u2124[X]\nhp : IsUnitTrinomial p\n\u22a2 p \u2260 0", "state_after": "q : \u2124[X]\nhp : IsUnitTrinomial 0\n\u22a2 False"}, {"tactic": "exact Nat.zero_ne_bit1 1 hp.card_support_eq_three", "annotated_tactic": ["exact <a>Nat.zero_n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Order/Lattice.lean | norm_inf_sub_inf_le_add_norm | [
118,
1
] | [
129,
43
] | [{"tactic": "rw [\u2190 norm_abs_eq_norm (a - c), \u2190 norm_abs_eq_norm (b - d)]", "annotated_tactic": ["rw [\u2190 <a>norm_abs_eq_norm</a> (a - c), \u2190 <a>norm_abs_eq_norm</a> (b - d)]", [{"full_name": "norm_abs_eq_norm", "def_path": "Mathlib/Analysis/Normed/Order/Lattice.lean", "def_pos": [114, 9], "def_end_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioc.le_one | [
283,
1
] | [
284,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.hasFDerivAtFilter_iff | [
913,
1
] | [
916,
47
] | [{"tactic": "simp only [hy, h\u2081, hx]", "annotated_tactic": ["simp only [hy, h\u2081, hx]", []], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2078 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_withDensity_iff_integrable_smul₀ | [
950,
1
] | [
952,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.clm_comp | [
886,
1
] | [
889,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SymmDiff.lean | symmDiff_eq_right | [
549,
1
] | [
549,
89
] | [{"tactic": "rw [symmDiff_comm, symmDiff_eq_left]", "annotated_tactic": ["rw [<a>symmDiff_comm</a>, <a>symmDiff_eq_left</a>]", [{"full_name": "symmDiff_comm", "def_path": "Mathlib/Order/SymmDiff.lean", "def_pos": [113, 9], "def_end_pos": [113, 22]}, {"full_name": "symmDiff_eq_left", "def_path": "Mathlib/Order/SymmDiff.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Weights/Basic.lean | LieModule.zero_weightSpace_eq_top_of_nilpotent' | [
183,
1
] | [
186,
36
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "R : Type u_1\nL : Type u_2\nM : Type u_3\ninst\u271d\u2078 : CommRing R\ninst\u271d\u2077 : LieRing L\ninst\u271d\u2076 : LieAlgebra R L\ninst\u271d\u2075 : LieAlgebra.IsNilpotent R L\ninst\u271d\u2074 : AddCommGroup M\ninst\u271d\u00b3 : Module R M\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.QuasiMeasurePreserving.prod_of_left | [
770,
1
] | [
778,
59
] | [{"tactic": "convert (QuasiMeasurePreserving.prod_of_right (hf.comp measurable_swap) h2f).comp\n ((measurable_swap.measurePreserving (\u03bd.prod \u03bc)).symm\n MeasurableEquiv.prodComm).quasiMeasurePreserving", "annotated_tactic": ["convert (<a>QuasiMeasurePreserving.prod_of_right</a> (hf.comp <a>measurable... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.leftMulMatrix_injective | [
912,
1
] | [
916,
25
] | [{"tactic": "rw [(LinearMap.toMatrix b b).injective h]", "annotated_tactic": ["rw [(<a>LinearMap.toMatrix</a> b b).<a>injective</a> h]", [{"full_name": "LinearMap.toMatrix", "def_path": "Mathlib/LinearAlgebra/Matrix/ToLin.lean", "def_pos": [527, 5], "def_end_pos": [527, 23]}, {"full_name": "LinearEquiv.injective", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/LDL.lean | LDL.lowerInv_orthogonal | [
79,
1
] | [
81,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_left | [
880,
1
] | [
882,
82
] | [{"tactic": "rw [\u2190 Icc_diff_left, diff_union_self,\n union_eq_self_of_subset_right (singleton_subset_iff.2 <| left_mem_Icc.2 hab)]", "annotated_tactic": ["rw [\u2190 <a>Icc_diff_left</a>, <a>diff_union_self</a>,\n <a>union_eq_self_of_subset_right</a> (<a>singleton_subset_iff</a>.2 <| <a>left_mem_Icc</a>.2 hab)... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Finite.wellFounded_of_trans_of_irrefl | [
918,
1
] | [
931,
49
] | [{"tactic": "classical\ncases nonempty_fintype \u03b1\nhave :\n \u2200 x y, r x y \u2192 (univ.filter fun z => r z x).card < (univ.filter fun z => r z y).card :=\n fun x y hxy =>\n Finset.card_lt_card <| by\n simp only [Finset.lt_iff_ssubset.symm, lt_iff_le_not_le, Finset.le_iff_subset,\n Finset.subset_iff... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Alternating/Basic.lean | MultilinearMap.alternatization_apply | [
925,
1
] | [
927,
57
] | [{"tactic": "simp only [alternatization_def, smul_apply, sum_apply]", "annotated_tactic": ["simp only [<a>alternatization_def</a>, <a>smul_apply</a>, <a>sum_apply</a>]", [{"full_name": "MultilinearMap.alternatization_def", "def_path": "Mathlib/LinearAlgebra/Alternating/Basic.lean", "def_pos": [915, 9], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_of_frequently_le | [
1244,
1
] | [
1248,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_set' | [
208,
1
] | [
210,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Lattice.lean | inf_lt_left | [
464,
1
] | [
465,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.star_subset_adjoin | [
453,
1
] | [
454,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_arrow_factors_left | [
425,
1
] | [
426,
68
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\nX\u271d Y\u271d Z : C\nD : Type u\u2082\ninst\u271d\u00b9 : Category.{v\u2082, u\u2082} D\ninst\u271d : HasPullbacks C\nB : C\nX Y : Subobject B\n\u22a2 ofLE (X \u2293 Y) X (_ : (in... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Function.Injective.exists_unique_of_mem_range | [
1352,
1
] | [
1354,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/NumberField/CanonicalEmbedding.lean | NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt | [
415,
1
] | [
428,
35
] | [{"tactic": "have : @IsAddHaarMeasure (E K) _ _ _ volume := prod.instIsAddHaarMeasure volume volume", "annotated_tactic": ["have : @<a>IsAddHaarMeasure</a> (E K) _ _ _ <a>volume</a> := <a>prod.instIsAddHaarMeasure</a> <a>volume</a> <a>volume</a>", [{"full_name": "MeasureTheory.Measure.IsAddHaarMeasure", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongMono_comp | [
107,
1
] | [
111,
23
] | [{"tactic": "intros", "annotated_tactic": ["intros", []], "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono f\ninst\u271d : StrongMono g\n\u22a2 \u2200 \u2983X Y : C\u2984 (z : X \u27f6 Y) [inst : Epi z], HasLiftingProperty z (f \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PFun.lean | PFun.res_univ | [
193,
1
] | [
194,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/FreeGroup/Basic.lean | FreeGroup.reduce.idem | [
1202,
1
] | [
1203,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.piecewise_insert_of_ne | [
2528,
1
] | [
2529,
93
] | [{"tactic": "simp [piecewise, h]", "annotated_tactic": ["simp [<a>piecewise</a>, h]", [{"full_name": "Finset.piecewise", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [2485, 5], "def_end_pos": [2485, 14]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : \u03b1 \u2192 Sort... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_apply | [
599,
1
] | [
602,
53
] | [{"tactic": "rw [Matrix.toLin'_apply, v\u2082.equivFun_symm_apply]", "annotated_tactic": ["rw [<a>Matrix.toLin'_apply</a>, v\u2082.equivFun_symm_apply]", [{"full_name": "Matrix.toLin'_apply", "def_path": "Mathlib/LinearAlgebra/Matrix/ToLin.lean", "def_pos": [349, 9], "def_end_pos": [349, 28]}]], "state_before": "R : Ty... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | nhds_def' | [
867,
1
] | [
868,
66
] | [{"tactic": "simp only [nhds_def, mem_setOf_eq, @and_comm (a \u2208 _), iInf_and]", "annotated_tactic": ["simp only [<a>nhds_def</a>, <a>mem_setOf_eq</a>, @<a>and_comm</a> (a \u2208 _), <a>iInf_and</a>]", [{"full_name": "nhds_def", "def_path": "Mathlib/Topology/Basic.lean", "def_pos": [1, 1], "def_end_pos": [1, 1]}, {"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.liftPropWithinAt_self | [
222,
1
] | [
223,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finite/Set.lean | Finite.Set.finite_of_finite_image | [
27,
1
] | [
29,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/VecNotation.lean | Matrix.head_add | [
481,
1
] | [
482,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Subtype.coe_image | [
1396,
1
] | [
1399,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.desc_comp_inl_comp_inr | [
888,
1
] | [
891,
31
] | [{"tactic": "rw [\u2190 coprod.map_desc]", "annotated_tactic": ["rw [\u2190 <a>coprod.map_desc</a>]", [{"full_name": "CategoryTheory.Limits.coprod.map_desc", "def_path": "Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean", "def_pos": [880, 9], "def_end_pos": [880, 24]}]], "state_before": "C : Type u\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SymmDiff.lean | bihimp_le_iff_left | [
613,
1
] | [
614,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/MinMax.lean | lt_or_le_of_mul_le_mul | [
99,
1
] | [
103,
48
] | [{"tactic": "contrapose!", "annotated_tactic": ["contrapose!", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : LinearOrder \u03b1\ninst\u271d\u00b2 : Mul \u03b1\ninst\u271d\u00b9 : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst\u271d : CovariantClass \u03b1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Types/Symmetric.lean | CategoryTheory.braiding_hom_apply | [
29,
1
] | [
31,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.lipschitzWith_equiv_aux | [
367,
1
] | [
382,
94
] | [{"tactic": "intro x y", "annotated_tactic": ["intro x y", []], "state_before": "p : \u211d\u22650\u221e\n\ud835\udd5c : Type u_1\n\ud835\udd5c' : Type u_2\n\u03b9 : Type u_3\n\u03b1 : \u03b9 \u2192 Type u_4\n\u03b2 : \u03b9 \u2192 Type u_5\ninst\u271d\u00b3 : Fact (1 \u2264 p)\ninst\u271d\u00b2 : (i : \u03b9) \u2192 P... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Trace.lean | trace_eq_sum_embeddings | [
384,
1
] | [
396,
36
] | [{"tactic": "have hx := IsSeparable.isIntegral K x", "annotated_tactic": ["have hx := <a>IsSeparable.isIntegral</a> K x", [{"full_name": "IsSeparable.isIntegral", "def_path": "Mathlib/FieldTheory/Separable.lean", "def_pos": [502, 9], "def_end_pos": [502, 31]}]], "state_before": "R : Type u_1\nS : Type u_2\nT : Type u_3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Atoms.lean | GaloisCoinsertion.isCoatom_of_l_top | [
854,
1
] | [
856,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_six | [
896,
1
] | [
899,
7
] | [{"tactic": "rw [\u2190 cos_pi_div_two_sub, \u2190 cos_pi_div_three]", "annotated_tactic": ["rw [\u2190 <a>cos_pi_div_two_sub</a>, \u2190 <a>cos_pi_div_three</a>]", [{"full_name": "Real.cos_pi_div_two_sub", "def_path": "Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean", "def_pos": [469, 9], "def_end_pos": [46... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.smul_leftMulMatrix_algebraMap | [
938,
1
] | [
942,
51
] | [{"tactic": "ext \u27e8i, k\u27e9 \u27e8j, k'\u27e9", "annotated_tactic": ["ext \u27e8i, k\u27e9 \u27e8j, k'\u27e9", []], "state_before": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst\u271d\u00b9\u2070 : CommRing R\ninst\u271d\u2079 : CommRing S\ninst\u271d\u2078 : Ring T\ninst\u271d\u2077 : Algebra R S\ninst\u271d\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Commute.lean | Commute.add_right | [
34,
1
] | [
35,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean | ContinuousMap.Homotopy.end_path | [
101,
9
] | [
101,
87
] | [{"tactic": "convert hfg 1 <;> simp only [Path.target]", "annotated_tactic": ["convert hfg 1 <;> simp only [<a>Path.target</a>]", [{"full_name": "Path.target", "def_path": "Mathlib/Topology/Connected/PathConnected.lean", "def_pos": [124, 19], "def_end_pos": [124, 25]}]], "state_before": "X\u2081 X\u2082 Y : TopCat\nf :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | Filter.Tendsto.max_left | [
748,
11
] | [
751,
20
] | [{"tactic": "simp_rw [max_comm _ a]", "annotated_tactic": ["simp_rw [<a>max_comm</a> _ a]", [{"full_name": "max_comm", "def_path": "Mathlib/Init/Order/LinearOrder.lean", "def_pos": [113, 9], "def_end_pos": [113, 17]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u00b2 : TopologicalSp... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Regular/Basic.lean | not_isLeftRegular_zero | [
260,
1
] | [
261,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.differentiableWithinAt | [
278,
11
] | [
279,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/DerivationBundle.lean | PointedSmoothMap.smul_def | [
84,
1
] | [
85,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_mk | [
335,
1
] | [
336,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.join_replicate_nil | [
465,
9
] | [
466,
68
] | [{"tactic": "induction n <;> [rfl; simp only [*, replicate, join, append_nil]]", "annotated_tactic": ["induction n <;> [rfl; simp only [*, <a>replicate</a>, <a>join</a>, <a>append_nil</a>]]", [{"full_name": "List.replicate", "def_path": "lake-packages/lean4/src/lean/Init/Data/List/Basic.lean", "def_pos": [736, 13], "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.neg_mem_iff | [
309,
1
] | [
311,
37
] | [{"tactic": "convert hs.mem_smul_iff (x := x) (norm_neg 1) using 0", "annotated_tactic": ["convert hs.mem_smul_iff (x := x) (<a>norm_neg</a> 1) using 0", [{"full_name": "norm_neg", "def_path": "Mathlib/Analysis/Normed/Group/Basic.lean", "def_pos": [437, 30], "def_end_pos": [437, 38]}]], "state_before": "\ud835\udd5c : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Iterate.lean | Function.Commute.iterate_pos_lt_of_map_lt | [
180,
1
] | [
185,
56
] | [{"tactic": "apply hf.seq_pos_lt_seq_of_le_of_lt hn", "annotated_tactic": ["apply hf.seq_pos_lt_seq_of_le_of_lt hn", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : Preorder \u03b1\nf g : \u03b1 \u2192 \u03b1\nh : Commute f g\nhf : Monotone f\nhg : StrictMono g\nx : \u03b1\nhx : f x < g x\nn : \u2115\nhn : 0 < n\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/QuadraticDiscriminant.lean | discrim_le_zero | [
118,
1
] | [
138,
9
] | [{"tactic": "rw [discrim, sq]", "annotated_tactic": ["rw [<a>discrim</a>, <a>sq</a>]", [{"full_name": "discrim", "def_path": "Mathlib/Algebra/QuadraticDiscriminant.lean", "def_pos": [45, 5], "def_end_pos": [45, 12]}, {"full_name": "sq", "def_path": "Mathlib/Algebra/GroupPower/Basic.lean", "def_pos": [106, 7], "def_end_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftLeft_succ | [
208,
1
] | [
209,
84
] | [{"tactic": "simp only [shiftLeft_eq, Nat.pow_add, Nat.pow_one, \u2190 Nat.mul_assoc, Nat.mul_comm]", "annotated_tactic": ["simp only [<a>shiftLeft_eq</a>, <a>Nat.pow_add</a>, <a>Nat.pow_one</a>, \u2190 <a>Nat.mul_assoc</a>, <a>Nat.mul_comm</a>]", [{"full_name": "Nat.shiftLeft_eq", "def_path": "lake-packages/std/Std/Da... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_npowRec | [
1270,
1
] | [
1272,
65
] | [{"tactic": "rw [npowRec, pow_zero, coe_one]", "annotated_tactic": ["rw [<a>npowRec</a>, <a>pow_zero</a>, <a>coe_one</a>]", [{"full_name": "npowRec", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [485, 5], "def_end_pos": [485, 12]}, {"full_name": "pow_zero", "def_path": "Mathlib/Algebra/Group/Defs.lean", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Basic.lean | Nat.dvd_add_right | [
756,
11
] | [
757,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Reduce.lean | ManyOneEquiv.le_congr_left | [
240,
1
] | [
242,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.comap_incl_eq_top | [
844,
1
] | [
846,
97
] | [{"tactic": "rw [\u2190 LieSubmodule.coe_toSubmodule_eq_iff, LieSubmodule.coeSubmodule_comap, LieSubmodule.incl_coe,\n LieSubmodule.top_coeSubmodule, Submodule.comap_subtype_eq_top, coeSubmodule_le_coeSubmodule]", "annotated_tactic": ["rw [\u2190 <a>LieSubmodule.coe_toSubmodule_eq_iff</a>, <a>LieSubmodule.coeSubmodule... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Basic.lean | Complex.one_im | [
170,
1
] | [
171,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/IsAlgClosed/Basic.lean | Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly | [
560,
1
] | [
579,
58
] | [{"tactic": "have hFK := Algebra.isAlgebraic_iff_isIntegral.1 hK", "annotated_tactic": ["have hFK := <a>Algebra.isAlgebraic_iff_isIntegral</a>.1 hK", [{"full_name": "Algebra.isAlgebraic_iff_isIntegral", "def_path": "Mathlib/RingTheory/Algebraic.lean", "def_pos": [195, 19], "def_end_pos": [195, 53]}]], "state_before": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_cons | [
94,
1
] | [
96,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_monoidHom_refl | [
492,
1
] | [
492,
91
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right | [
663,
1
] | [
672,
63
] | [{"tactic": "cases' eq_zero_or_pos a with ha ha", "annotated_tactic": ["cases' <a>eq_zero_or_pos</a> a with ha ha", [{"full_name": "Ordinal.eq_zero_or_pos", "def_path": "Mathlib/SetTheory/Ordinal/Basic.lean", "def_pos": [411, 9], "def_end_pos": [411, 23]}]], "state_before": "a b : Ordinal.{u}\nhab : a * b = b\n\u22a2 b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Extr.lean | IsMinFilter.tendsto_principal_Ici | [
147,
1
] | [
148,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nmul_lt_nmul_of_pos_left | [
597,
1
] | [
598,
40
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "a b c d : Ordinal.{u}\nh\u2081 : a < b\nh\u2082 : 0 < c\n\u22a2 c \u2a33 a \u266f 0 \u2a33 a \u2264 0 \u2a33 b \u266f c \u2a33 a", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Image.lean | Finset.image_inter | [
510,
1
] | [
512,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Fold.lean | Multiset.coe_fold_l | [
45,
1
] | [
46,
55
] | [{"tactic": "simp [hc.comm]", "annotated_tactic": ["simp [hc.comm]", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nop : \u03b1 \u2192 \u03b1 \u2192 \u03b1\nhc : IsCommutative \u03b1 op\nha : IsAssociative \u03b1 op\nb : \u03b1\nl : List \u03b1\n\u22a2 List.foldl (fun x y => op y x) b l = List.foldl op b l... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Algebra/Classes.lean | trans | [
308,
1
] | [
309,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.set_integral_dirac' | [
1676,
1
] | [
1682,
34
] | [{"tactic": "rw [restrict_dirac' hs]", "annotated_tactic": ["rw [<a>restrict_dirac'</a> hs]", [{"full_name": "MeasureTheory.restrict_dirac'", "def_path": "Mathlib/MeasureTheory/Measure/Dirac.lean", "def_pos": [136, 9], "def_end_pos": [136, 24]}]], "state_before": "\u03b1 : Type u_1\nE : Type u_2\nF : Type u_3\n\ud835\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_add | [
2025,
1
] | [
2028,
29
] | [{"tactic": "rw [ENNReal.ofReal, ENNReal.ofReal, ENNReal.ofReal, \u2190 coe_add, coe_eq_coe,\n Real.toNNReal_add hp hq]", "annotated_tactic": ["rw [<a>ENNReal.ofReal</a>, <a>ENNReal.ofReal</a>, <a>ENNReal.ofReal</a>, \u2190 <a>coe_add</a>, <a>coe_eq_coe</a>,\n <a>Real.toNNReal_add</a> hp hq]", [{"full_name": "ENNRe... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | Monotone.convex_lt | [
419,
1
] | [
420,
68
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Pointwise.lean | Filter.principal_one | [
100,
1
] | [
101,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.mem_orthogonal_singleton_iff_inner_left | [
85,
1
] | [
86,
68
] | [{"tactic": "rw [mem_orthogonal_singleton_iff_inner_right, inner_eq_zero_symm]", "annotated_tactic": ["rw [<a>mem_orthogonal_singleton_iff_inner_right</a>, <a>inner_eq_zero_symm</a>]", [{"full_name": "Submodule.mem_orthogonal_singleton_iff_inner_right", "def_path": "Mathlib/Analysis/InnerProductSpace/Orthogonal.lean", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/EventuallyConst.lean | Filter.eventuallyConst_id | [
78,
9
] | [
78,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_lintegral_restrict | [
526,
1
] | [
528,
53
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.Integrable.neg | [
1282,
1
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1283,
87
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Lift.lean | Filter.lift'_cong | [
287,
1
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289,
57
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Bimod.lean | Bimod.TensorBimod.middle_assoc' | [
359,
1
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374,
12
] | [{"tactic": "refine' (cancel_epi ((tensorLeft _ \u22d9 tensorRight _).map (coequalizer.\u03c0 _ _))).1 _", "annotated_tactic": ["refine' (<a>cancel_epi</a> ((<a>tensorLeft</a> _ \u22d9 <a>tensorRight</a> _).<a>map</a> (<a>coequalizer.\u03c0</a> _ _))).1 _", [{"full_name": "CategoryTheory.cancel_epi", "def_path": "Mathl... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.mem_zpowers | [
32,
1
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33,
18
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