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/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_injective | [
1156,
1
] | [
1157,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sum/Interval.lean | Sum.Ico_inr_inl | [
180,
1
] | [
181,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_monotone | [
370,
1
] | [
371,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Unitization.lean | Unitization.antilipschitzWith_addEquiv | [
169,
1
] | [
182,
91
] | [{"tactic": "refine AddMonoidHomClass.antilipschitz_of_bound (addEquiv \ud835\udd5c A) fun x => ?_", "annotated_tactic": ["refine <a>AddMonoidHomClass.antilipschitz_of_bound</a> (<a>addEquiv</a> \ud835\udd5c A) fun x => ?_", [{"full_name": "AddMonoidHomClass.antilipschitz_of_bound", "def_path": "Mathlib/Analysis/Normed... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.imp | [
509,
11
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514,
67
] | [{"tactic": "simp_rw [SemanticallyEquivalent, ModelsBoundedFormula, BoundedFormula.realize_iff,\n BoundedFormula.realize_imp]", "annotated_tactic": ["simp_rw [<a>SemanticallyEquivalent</a>, <a>ModelsBoundedFormula</a>, <a>BoundedFormula.realize_iff</a>,\n <a>BoundedFormula.realize_imp</a>]", [{"full_name": "FirstOr... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Partrec.lean | Partrec.vector_mOfFn | [
605,
1
] | [
614,
65
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_bound₂ | [
598,
1
] | [
600,
96
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basis.lean | Basis.map_equivFun | [
925,
1
] | [
926,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | QuotientGroup.isClosedMap_coe | [
1455,
1
] | [
1462,
6
] | [{"tactic": "intro t ht", "annotated_tactic": ["intro t ht", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nG : Type w\nH\u271d : Type x\ninst\u271d\u00b2 : TopologicalSpace \u03b1\ninst\u271d\u00b9 : Group \u03b1\ninst\u271d : TopologicalGroup \u03b1\ns t : Set \u03b1\nH : Subgroup \u03b1\nhH : IsCompact \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.zero_apply | [
260,
1
] | [
261,
6
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/LeftExact.lean | CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj_fac | [
153,
1
] | [
176,
6
] | [{"tactic": "dsimp only [liftToPlusObjLimitObj]", "annotated_tactic": ["dsimp only [<a>liftToPlusObjLimitObj</a>]", [{"full_name": "CategoryTheory.GrothendieckTopology.liftToPlusObjLimitObj", "def_path": "Mathlib/CategoryTheory/Sites/LeftExact.lean", "def_pos": [123, 5], "def_end_pos": [123, 26]}]], "state_before": "C ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Abs.lean | le_abs_self | [
57,
1
] | [
58,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_univ | [
184,
1
] | [
185,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Composition.lean | CompositionAsSet.boundary_length | [
921,
1
] | [
923,
71
] | [{"tactic": "convert Finset.orderEmbOfFin_last rfl c.card_boundaries_pos", "annotated_tactic": ["convert <a>Finset.orderEmbOfFin_last</a> <a>rfl</a> c.card_boundaries_pos", [{"full_name": "Finset.orderEmbOfFin_last", "def_path": "Mathlib/Data/Finset/Sort.lean", "def_pos": [198, 9], "def_end_pos": [198, 27]}, {"full_nam... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_periodic | [
242,
1
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243,
28
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Subfield.lean | Subfield.closure_mono | [
729,
1
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730,
52
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.symm_apply_apply | [
599,
1
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601,
30
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https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteProducts.associator_inv | [
111,
1
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114,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Induction.lean | Polynomial.induction_on | [
39,
11
] | [
55,
22
] | [{"tactic": "rw [\u2190 sum_C_mul_X_pow_eq p, Polynomial.sum]", "annotated_tactic": ["rw [\u2190 <a>sum_C_mul_X_pow_eq</a> p, <a>Polynomial.sum</a>]", [{"full_name": "Polynomial.sum_C_mul_X_pow_eq", "def_path": "Mathlib/Data/Polynomial/Basic.lean", "def_pos": [1046, 9], "def_end_pos": [1046, 27]}, {"full_name": "Polyno... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean | NonUnitalAlgHom.range_comp | [
428,
1
] | [
430,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableOn.prod | [
106,
1
] | [
108,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.bddAbove_of_small | [
975,
1
] | [
976,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/InformationTheory/Hamming.lean | hammingNorm_nonneg | [
176,
1
] | [
177,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.sup'_biUnion | [
829,
1
] | [
832,
58
] | [{"tactic": "simp [@forall_swap _ \u03b2]", "annotated_tactic": ["simp [@<a>forall_swap</a> _ \u03b2]", [{"full_name": "forall_swap", "def_path": "Mathlib/Logic/Basic.lean", "def_pos": [667, 9], "def_end_pos": [667, 20]}]], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\n\u03b9 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_nat_iff_finset | [
2200,
1
] | [
2202,
46
] | [{"tactic": "rw [\u2190 mk_univ, mk_set_eq_nat_iff_finset]", "annotated_tactic": ["rw [\u2190 <a>mk_univ</a>, <a>mk_set_eq_nat_iff_finset</a>]", [{"full_name": "Cardinal.mk_univ", "def_path": "Mathlib/SetTheory/Cardinal/Basic.lean", "def_pos": [2113, 9], "def_end_pos": [2113, 16]}, {"full_name": "Cardinal.mk_set_eq_nat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | re_inner_le_norm | [
1100,
1
] | [
1101,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Data/List/Lemmas.lean | List.not_bex_nil | [
76,
1
] | [
76,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.units_smul_resolvent | [
151,
1
] | [
165,
74
] | [{"tactic": "by_cases h : s \u2208 spectrum R a", "annotated_tactic": ["by_cases h : s \u2208 <a>spectrum</a> R a", [{"full_name": "spectrum", "def_path": "Mathlib/Algebra/Algebra/Spectrum.lean", "def_pos": [69, 5], "def_end_pos": [69, 13]}]], "state_before": "R : Type u\nA : Type v\ninst\u271d\u00b2 : CommSemiring R\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.mem_range_self | [
839,
1
] | [
840,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Basic.lean | one_div_zpow | [
367,
1
] | [
367,
99
] | [{"tactic": "simp only [one_div, inv_zpow]", "annotated_tactic": ["simp only [<a>one_div</a>, <a>inv_zpow</a>]", [{"full_name": "one_div", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [318, 9], "def_end_pos": [318, 16]}, {"full_name": "inv_zpow", "def_path": "Mathlib/Algebra/GroupPower/Basic.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.map_toSubmodule | [
498,
1
] | [
500,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.coe_sinOrderIso_apply | [
926,
1
] | [
927,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/KummerDedekind.lean | comap_map_eq_map_adjoin_of_coprime_conductor | [
130,
1
] | [
164,
29
] | [{"tactic": "apply le_antisymm", "annotated_tactic": ["apply <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": "R : Type u_1\nS : Type u_2\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : CommRing S\ninst\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Fintype.card_compl_set | [
302,
1
] | [
304,
99
] | [{"tactic": "classical rw [\u2190 Set.toFinset_card, \u2190 Set.toFinset_card, \u2190 Finset.card_compl, Set.toFinset_compl]", "annotated_tactic": ["classical rw [\u2190 <a>Set.toFinset_card</a>, \u2190 <a>Set.toFinset_card</a>, \u2190 <a>Finset.card_compl</a>, <a>Set.toFinset_compl</a>]", [{"full_name": "Set.toFinset_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.pairwise_disjoint_on_Ioo_succ | [
70,
1
] | [
72,
100
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_bot | [
151,
1
] | [
152,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.toGroupSeminorm_eq_coe | [
764,
1
] | [
765,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.smul_def | [
111,
1
] | [
114,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/GoldenRatio.lean | goldConj_ne_zero | [
124,
1
] | [
125,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.C_inv | [
2279,
1
] | [
2280,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sigma/Interval.lean | Sigma.card_Icc | [
60,
1
] | [
61,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.continuousWithinAt_Ioi_iff_rightLim_eq | [
213,
1
] | [
215,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factors.lean | Nat.mem_factors_mul_right | [
288,
1
] | [
291,
36
] | [{"tactic": "rw [mul_comm]", "annotated_tactic": ["rw [<a>mul_comm</a>]", [{"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [302, 9], "def_end_pos": [302, 17]}]], "state_before": "p a b : \u2115\nhpb : p \u2208 factors b\nha : a \u2260 0\n\u22a2 p \u2208 factors (a * b)", "state_after... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Exponential.lean | Complex.isCauSeq_abs_exp | [
351,
1
] | [
360,
40
] | [{"tactic": "rwa [div_lt_iff hn0, one_mul]", "annotated_tactic": ["rwa [<a>div_lt_iff</a> hn0, <a>one_mul</a>]", [{"full_name": "div_lt_iff", "def_path": "Mathlib/Algebra/Order/Field/Basic.lean", "def_pos": [169, 9], "def_end_pos": [169, 19]}, {"full_name": "one_mul", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/EditDistance/Defs.lean | suffixLevenshtein_nil' | [
192,
1
] | [
194,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.nth_succ | [
305,
1
] | [
308,
49
] | [{"tactic": "conv => lhs; rw [\u2190 ListBlank.cons_head_tail l]", "annotated_tactic": ["conv => lhs; rw [\u2190 <a>ListBlank.cons_head_tail</a> l]", [{"full_name": "Turing.ListBlank.cons_head_tail", "def_path": "Mathlib/Computability/TuringMachine.lean", "def_pos": [265, 9], "def_end_pos": [265, 33]}]], "state_before"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/Group.lean | Commute.smul_left_iff | [
138,
1
] | [
140,
66
] | [{"tactic": "rw [Commute.symm_iff, Commute.smul_right_iff, Commute.symm_iff]", "annotated_tactic": ["rw [<a>Commute.symm_iff</a>, <a>Commute.smul_right_iff</a>, <a>Commute.symm_iff</a>]", [{"full_name": "Commute.symm_iff", "def_path": "Mathlib/Algebra/Group/Commute/Defs.lean", "def_pos": [73, 19], "def_end_pos": [73, 2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | isCobounded_le_nhds | [
90,
1
] | [
91,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Basic.lean | Set.one_nonempty | [
118,
1
] | [
119,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Alternating/Basic.lean | AlternatingMap.coe_multilinearMap_mk | [
170,
1
] | [
173,
10
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R : Type u_1\ninst\u271d\u00b9\u2070 : Semiring R\nM : Type u_2\ninst\u271d\u2079 : AddCommMonoid M\ninst\u271d\u2078 : Module R M\nN : Type u_3\ninst\u271d\u2077 : AddCommMonoid N\ninst\u271d\u2076 : Module R N\nP : Type u_4\ninst\u271d\u2075 : Add... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ne_zero_of_mk'_ne_zero | [
353,
1
] | [
355,
40
] | [{"tactic": "rintro rfl", "annotated_tactic": ["rintro rfl", []], "state_before": "R : Type u_1\ninst\u271d\u2074 : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst\u271d\u00b3 : CommSemiring S\ninst\u271d\u00b2 : Algebra R S\nP : Type u_3\ninst\u271d\u00b9 : CommSemiring P\ninst\u271d : IsLocalization M S\nx : R\ny... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Tuple/Basic.lean | Fin.find_min | [
897,
1
] | [
913,
77
] | [{"tactic": "rw [find] at hi", "annotated_tactic": ["rw [<a>find</a>] at hi", [{"full_name": "Fin.find", "def_path": "Mathlib/Data/Fin/Tuple/Basic.lean", "def_pos": [842, 5], "def_end_pos": [842, 9]}]], "state_before": "m n\u271d n : \u2115\np : Fin (n + 1) \u2192 Prop\nx\u271d : DecidablePred p\ni : Fin (n + 1)\nhi : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.finiteType_iff_group_fg | [
701,
1
] | [
703,
57
] | [{"tactic": "simpa [Group.fg_iff_monoid_fg] using finiteType_iff_fg", "annotated_tactic": ["simpa [<a>Group.fg_iff_monoid_fg</a>] using <a>finiteType_iff_fg</a>", [{"full_name": "Group.fg_iff_monoid_fg", "def_path": "Mathlib/GroupTheory/Finiteness.lean", "def_pos": [319, 9], "def_end_pos": [319, 31]}, {"full_name": "Mo... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.get_set | [
961,
1
] | [
963,
48
] | [{"tactic": "if h : m = n then subst m; simp else simp [h]", "annotated_tactic": ["if h : m = n then subst m; simp else simp [h]", []], "state_before": "\u03b1 : Type u_1\na : \u03b1\nm n : Nat\nl : List \u03b1\nh : n < length (set l m a)\n\u22a2 get (set l m a) { val := n, isLt := h } = if m = n then a else get l { va... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Basic.lean | Int.succ_pred | [
164,
1
] | [
164,
68
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_δ | [
214,
1
] | [
221,
41
] | [{"tactic": "ext k", "annotated_tactic": ["ext k", []], "state_before": "n : \u2115\ni j : Fin (n + 2)\nH : i \u2264 j\n\u22a2 \u03b4 i \u226b \u03b4 (Fin.succ j) = \u03b4 j \u226b \u03b4 (Fin.castSucc i)", "state_after": "case a.h.h.h\nn : \u2115\ni j : Fin (n + 2)\nH : i \u2264 j\nk : Fin (len [n] + 1)\n\u22a2 \u2191... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.subset_hom | [
182,
1
] | [
184,
35
] | [{"tactic": "rintro c \u27e8cL, rfl\u27e9", "annotated_tactic": ["rintro c \u27e8cL, rfl\u27e9", []], "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\nh : K \u2286 L\n\u22a2 \u2191C \u2286 \u2191(hom h C)", "state_after": "case intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Se... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.count_replicate_self | [
2439,
1
] | [
2441,
33
] | [{"tactic": "convert List.count_replicate_self a n", "annotated_tactic": ["convert <a>List.count_replicate_self</a> a n", [{"full_name": "List.count_replicate_self", "def_path": "lake-packages/std/Std/Data/List/Count.lean", "def_pos": [185, 17], "def_end_pos": [185, 37]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Finite.lean | Set.Finite.fin_embedding | [
1089,
1
] | [
1092,
97
] | [{"tactic": "simp only [Finset.coe_sort_coe, Equiv.asEmbedding_range, Finite.coe_toFinset, setOf_mem_eq]", "annotated_tactic": ["simp only [<a>Finset.coe_sort_coe</a>, <a>Equiv.asEmbedding_range</a>, <a>Finite.coe_toFinset</a>, <a>setOf_mem_eq</a>]", [{"full_name": "Finset.coe_sort_coe", "def_path": "Mathlib/Data/Finse... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/LinearIndependent.lean | exists_maximal_independent | [
955,
1
] | [
987,
99
] | [{"tactic": "rcases exists_maximal_independent' R s with \u27e8I, hIlinind, hImaximal\u27e9", "annotated_tactic": ["rcases <a>exists_maximal_independent'</a> R s with \u27e8I, hIlinind, hImaximal\u27e9", [{"full_name": "exists_maximal_independent'", "def_path": "Mathlib/LinearAlgebra/LinearIndependent.lean", "def_pos":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PNat/Prime.lean | PNat.gcd_one | [
233,
1
] | [
235,
16
] | [{"tactic": "rw [gcd_comm]", "annotated_tactic": ["rw [<a>gcd_comm</a>]", [{"full_name": "PNat.gcd_comm", "def_path": "Mathlib/Data/PNat/Prime.lean", "def_pos": [186, 9], "def_end_pos": [186, 17]}]], "state_before": "n : \u2115+\n\u22a2 gcd n 1 = 1", "state_after": "n : \u2115+\n\u22a2 gcd 1 n = 1"}, {"tactic": "apply ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/RingHom/Finite.lean | RingHom.finite_stableUnderComposition | [
23,
1
] | [
25,
19
] | [{"tactic": "introv R hf hg", "annotated_tactic": ["introv R hf hg", []], "state_before": "\u22a2 StableUnderComposition @Finite", "state_after": "R S T : Type u_1\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : CommRing S\ninst\u271d : CommRing T\nf : R \u2192+* S\ng : S \u2192+* T\nhf : Finite f\nhg : Finite g\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsLittleO.trans_isTheta | [
111,
1
] | [
113,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_add | [
115,
1
] | [
116,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsRegular.aleph0_le | [
953,
1
] | [
954,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean | AlgebraicGeometry.quasiCompact_iff_affineProperty | [
113,
1
] | [
119,
44
] | [{"tactic": "rw [quasiCompact_iff_forall_affine]", "annotated_tactic": ["rw [<a>quasiCompact_iff_forall_affine</a>]", [{"full_name": "AlgebraicGeometry.quasiCompact_iff_forall_affine", "def_path": "Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean", "def_pos": [96, 9], "def_end_pos": [96, 39]}]], "state_before": "X... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoundedVariation.lean | LipschitzOnWith.comp_locallyBoundedVariationOn | [
823,
1
] | [
827,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_comp_exp_atTop | [
313,
1
] | [
315,
70
] | [{"tactic": "simp_rw [\u2190comp_apply (g := exp), \u2190 tendsto_map'_iff, map_exp_atTop]", "annotated_tactic": ["simp_rw [\u2190<a>comp_apply</a> (g := <a>exp</a>), \u2190 <a>tendsto_map'_iff</a>, <a>map_exp_atTop</a>]", [{"full_name": "Function.comp_apply", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Basic.lean | Real.mk_pos | [
341,
1
] | [
343,
47
] | [{"tactic": "rw [\u2190 mk_zero, mk_lt]", "annotated_tactic": ["rw [\u2190 <a>mk_zero</a>, <a>mk_lt</a>]", [{"full_name": "Real.mk_zero", "def_path": "Mathlib/Data/Real/Basic.lean", "def_pos": [325, 9], "def_end_pos": [325, 16]}, {"full_name": "Real.mk_lt", "def_path": "Mathlib/Data/Real/Basic.lean", "def_pos": [321, 9... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_left_cancel | [
202,
1
] | [
203,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasEqualizer_of_hasKernel | [
367,
1
] | [
370,
76
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Basic.lean | Int.natAbs_surjective | [
209,
1
] | [
209,
78
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Torsion.lean | Submodule.torsion_torsion_eq_top | [
653,
1
] | [
654,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ioo_right | [
116,
1
] | [
117,
70
] | [{"tactic": "simp only [\u2190 Ioi_inter_Iio, \u2190 inter_iUnion, iUnion_Iio, inter_univ]", "annotated_tactic": ["simp only [\u2190 <a>Ioi_inter_Iio</a>, \u2190 <a>inter_iUnion</a>, <a>iUnion_Iio</a>, <a>inter_univ</a>]", [{"full_name": "Set.Ioi_inter_Iio", "def_path": "Mathlib/Data/Set/Intervals/Basic.lean", "def_pos... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_one | [
1063,
1
] | [
1064,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WellFoundedSet.lean | Set.IsWf.union | [
237,
18
] | [
237,
94
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.smul_ofFunction | [
814,
1
] | [
820,
50
] | [{"tactic": "simp [m_empty]", "annotated_tactic": ["simp [m_empty]", []], "state_before": "\u03b1 : Type u_1\nm : Set \u03b1 \u2192 \u211d\u22650\u221e\nm_empty : m \u2205 = 0\nc : \u211d\u22650\u221e\nhc : c \u2260 \u22a4\n\u22a2 (c \u2022 m) \u2205 = 0", "state_after": "no goals"}, {"tactic": "ext1 s", "annotated_tac... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_sub | [
2345,
1
] | [
2350,
97
] | [{"tactic": "cases' le_total m n with h h", "annotated_tactic": ["cases' <a>le_total</a> m n with h h", [{"full_name": "le_total", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [295, 9], "def_end_pos": [295, 17]}]], "state_before": "m n : \u2115\n\u22a2 \u2191(m - n) = \u2191m - \u2191n", "state_after": "case ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/PGame.lean | SetTheory.PGame.mk_add_moveLeft_inr | [
1563,
1
] | [
1566,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | topologicalGroup_sInf | [
1870,
1
] | [
1877,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.ssubset_insert | [
1194,
1
] | [
1195,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Basic.lean | AddSubmonoid.bsupr_eq_mrange_dfinsupp_sumAddHom | [
1987,
1
] | [
2000,
16
] | [{"tactic": "apply le_antisymm", "annotated_tactic": ["apply <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": "\u03b9 : Type u\n\u03b3 : Type w\n\u03b2 : \u03b9 \u2192 Type v\n\u03b2\u2081 : \u03b9 \u2192 Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Relation.lean | Acc.TransGen | [
439,
1
] | [
443,
38
] | [{"tactic": "induction' h with x _ H", "annotated_tactic": ["induction' h with x _ H", []], "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 b c d : \u03b1\nh : Acc r a\n\u22a2 Acc (Relation.TransGen r) a", "state_after": "case intro\n\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.comp_eqToHom_iff | [
62,
1
] | [
65,
57
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX Y Y' : C\np : Y = Y'\nf : X \u27f6 Y\ng : X \u27f6 Y'\nh : f \u226b eqToHom p = g\n\u22a2 f = (f \u226b eqToHom p) \u226b eqToHom (_ : Y' = Y)", "state_after": "no goals"}, {"tactic": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.zero_add' | [
185,
9
] | [
190,
6
] | [{"tactic": "rw [\u2190 zero_mk s, mk_add_mk, smul_zero, zero_add, mk_eq]", "annotated_tactic": ["rw [\u2190 <a>zero_mk</a> s, <a>mk_add_mk</a>, <a>smul_zero</a>, <a>zero_add</a>, <a>mk_eq</a>]", [{"full_name": "LocalizedModule.zero_mk", "def_path": "Mathlib/Algebra/Module/LocalizedModule.lean", "def_pos": [146, 9], "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Bitwise.lean | Nat.testBit_eq_inth | [
222,
1
] | [
227,
24
] | [{"tactic": "induction' i with i ih generalizing n", "annotated_tactic": ["induction' i with i ih generalizing n", []], "state_before": "n i : \u2115\n\u22a2 testBit n i = List.getI (bits n) i", "state_after": "case zero\nn\u271d n : \u2115\n\u22a2 testBit n zero = List.getI (bits n) zero\n\ncase succ\nn\u271d i : \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/Hensel.lean | a_soln_is_unique | [
460,
9
] | [
482,
37
] | [{"tactic": "rw [add_comm]", "annotated_tactic": ["rw [<a>add_comm</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}]], "state_before": "p : \u2115\ninst\u271d : Fact (Nat.Prime p)\nF : Polynomial \u2124_[p]\na : \u2124_[p]\nha : Polynomial.e... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Fin.lean | Fin.sum_const | [
169,
1
] | [
169,
89
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : AddCommMonoid \u03b1\nn : \u2115\nx : \u03b1\n\u22a2 \u2211 _i : Fin n, x = n \u2022 x", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Cardinality.lean | continuum_le_cardinal_of_nontriviallyNormedField | [
28,
1
] | [
44,
20
] | [{"tactic": "suffices \u2203 f : (\u2115 \u2192 Bool) \u2192 \ud835\udd5c, range f \u2286 univ \u2227 Continuous f \u2227 Injective f by\n rcases this with \u27e8f, -, -, f_inj\u27e9\n simpa using lift_mk_le_lift_mk_of_injective f_inj", "annotated_tactic": ["suffices \u2203 f : (\u2115 \u2192 <a>Bool</a>) \u2192 \ud8... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Rayleigh.lean | LinearMap.IsSymmetric.subsingleton_of_no_eigenvalue_finiteDimensional | [
282,
1
] | [
285,
62
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | compact_open_separated_mul_left | [
1645,
1
] | [
1652,
45
] | [{"tactic": "rcases compact_open_separated_mul_right (hK.image continuous_op) (opHomeomorph.isOpenMap U hU)\n (image_subset op hKU) with\n \u27e8V, hV : V \u2208 \ud835\udcdd (op (1 : G)), hV' : op '' K * V \u2286 op '' U\u27e9", "annotated_tactic": ["rcases <a>compact_open_separated_mul_right</a> (hK.image <a>cont... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | Continuous.congr | [
1612,
1
] | [
1615,
10
] | [{"tactic": "convert h", "annotated_tactic": ["convert h", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\ninst\u271d\u00b2 : TopologicalSpace \u03b1\ninst\u271d\u00b9 : TopologicalSpace \u03b2\ninst\u271d : TopologicalSpace \u03b3\nf g : \u03b1 \u2192 \u03b2\nh : Conti... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Partition/Finpartition.lean | Finpartition.card_mono | [
340,
1
] | [
349,
97
] | [{"tactic": "classical\n have : \u2200 b \u2208 Q.parts, \u2203 c \u2208 P.parts, c \u2264 b := fun b \u21a6 exists_le_of_le h\n choose f hP hf using this\n rw [\u2190 card_attach]\n refine' card_le_card_of_inj_on (fun b \u21a6 f _ b.2) (fun b _ \u21a6 hP _ b.2) fun b _ c _ h \u21a6 _\n exact\n Subtype.coe_inje... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_nonempty_iff | [
137,
8
] | [
138,
68
] | [{"tactic": "rw [support, support_nonempty_iff, Ne.def, coeff_fun_eq_zero_iff]", "annotated_tactic": ["rw [<a>support</a>, <a>support_nonempty_iff</a>, <a>Ne.def</a>, <a>coeff_fun_eq_zero_iff</a>]", [{"full_name": "HahnSeries.support", "def_path": "Mathlib/RingTheory/HahnSeries.lean", "def_pos": [88, 12], "def_end_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/Basic.lean | Equiv.sumArrowEquivProdArrow_apply_snd | [
956,
1
] | [
958,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Func.lean | List.Func.eq_of_equiv | [
239,
1
] | [
249,
23
] | [{"tactic": "cases h1", "annotated_tactic": ["cases h1", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\na : \u03b1\nas as1 as2 as3 : List \u03b1\ninst\u271d\u00b9 : Inhabited \u03b1\ninst\u271d : Inhabited \u03b2\nhead\u271d : \u03b1\ntail\u271d : List \u03b1\nh1 : length (head\u271d :: tail\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Module.lean | Complex.rank_real_complex | [
155,
1
] | [
155,
101
] | [{"tactic": "simp [\u2190 finrank_eq_rank, finrank_real_complex]", "annotated_tactic": ["simp [\u2190 <a>finrank_eq_rank</a>, <a>finrank_real_complex</a>]", [{"full_name": "FiniteDimensional.finrank_eq_rank", "def_path": "Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean", "def_pos": [74, 9], "def_end_pos": [74, 24]}, ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_finsupp_sum | [
1105,
1
] | [
1107,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.coe_comp | [
314,
1
] | [
315,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Lex.lean | DFinsupp.lt_of_forall_lt_of_lt | [
141,
1
] | [
143,
26
] | [] |
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