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/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_interval | [
140,
1
] | [
141,
53
] | [{"tactic": "rw [\u2190 Icc_min_max, volume_Icc, max_sub_min_eq_abs]", "annotated_tactic": ["rw [\u2190 <a>Icc_min_max</a>, <a>volume_Icc</a>, <a>max_sub_min_eq_abs</a>]", [{"full_name": "Set.Icc_min_max", "def_path": "Mathlib/Data/Set/Intervals/UnorderedInterval.lean", "def_pos": [220, 9], "def_end_pos": [220, 20]}, {... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Hull.lean | convexHull_singleton | [
122,
1
] | [
123,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Analytic.lean | HasFPowerSeriesAt.hasDerivAt | [
179,
11
] | [
181,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Iterate.lean | Function.antitone_iterate_of_le_id | [
151,
1
] | [
152,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Inseparable.lean | Inseparable.trans | [
357,
8
] | [
357,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderivWithin_neg | [
452,
1
] | [
458,
10
] | [{"tactic": "rw [fderivWithin_zero_of_not_differentiableWithinAt h,\n fderivWithin_zero_of_not_differentiableWithinAt, neg_zero]", "annotated_tactic": ["rw [<a>fderivWithin_zero_of_not_differentiableWithinAt</a> h,\n <a>fderivWithin_zero_of_not_differentiableWithinAt</a>, <a>neg_zero</a>]", [{"full_name": "fderiv... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.mem_span_pow_iff_le_valuation | [
527,
1
] | [
542,
39
] | [{"tactic": "rw [Ideal.mem_span_singleton]", "annotated_tactic": ["rw [<a>Ideal.mem_span_singleton</a>]", [{"full_name": "Ideal.mem_span_singleton", "def_path": "Mathlib/RingTheory/Ideal/Basic.lean", "def_pos": [497, 9], "def_end_pos": [497, 27]}]], "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nx : \u2124_[p]\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convolution.lean | HasCompactSupport.convolutionExists_right | [
349,
1
] | [
355,
31
] | [{"tactic": "intro x\u2080", "annotated_tactic": ["intro x\u2080", []], "state_before": "\ud835\udd5c : Type u\ud835\udd5c\nG : Type uG\nE : Type uE\nE' : Type uE'\nE'' : Type uE''\nF : Type uF\nF' : Type uF'\nF'' : Type uF''\nP : Type uP\ninst\u271d\u00b9\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b9\u00b2 : NormedAd... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/PSub.lean | Nat.sub_eq_psub | [
60,
1
] | [
62,
100
] | [{"tactic": "rw [sub_eq_psub m n, psub]", "annotated_tactic": ["rw [sub_eq_psub m n, <a>psub</a>]", [{"full_name": "Nat.psub", "def_path": "Mathlib/Data/Nat/PSub.lean", "def_pos": [46, 5], "def_end_pos": [46, 9]}]], "state_before": "m n : \u2115\n\u22a2 Option.getD (ppred (m - n)) 0 = Option.getD (psub m (n + 1)) 0", "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.mem_sUnion_of_mem | [
1143,
1
] | [
1145,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_X_pow | [
554,
1
] | [
557,
70
] | [{"tactic": "classical\n rw [X_pow_eq_monomial, support_monomial, if_neg (one_ne_zero' R)]", "annotated_tactic": ["classical\n rw [<a>X_pow_eq_monomial</a>, <a>support_monomial</a>, <a>if_neg</a> (<a>one_ne_zero'</a> R)]", [{"full_name": "MvPolynomial.X_pow_eq_monomial", "def_path": "Mathlib/Data/MvPolynomial/Basic... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints | [
272,
1
] | [
286,
9
] | [{"tactic": "apply SetLike.ext'", "annotated_tactic": ["apply <a>SetLike.ext'</a>", [{"full_name": "SetLike.ext'", "def_path": "Mathlib/Data/SetLike/Basic.lean", "def_pos": [145, 9], "def_end_pos": [145, 13]}]], "state_before": "X : Type u_1\ninst\u271d\u00b9 : TopologicalSpace X\ninst\u271d : CompactSpace X\nA : Subal... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/NonUnitalSubalgebra.lean | NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebra | [
734,
1
] | [
736,
35
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "F : Type v'\nR' : Type u'\nR : Type u\nA : Type v\nB : Type w\nC : Type w'\ninst\u271d\u00b9\u00b3 : CommSemiring R\ninst\u271d\u00b9\u00b2 : StarRing R\ninst\u271d\u00b9\u00b9 : NonUnitalSemiring A\ninst\u271d\u00b9\u2070 : StarRing A\ninst\u271d\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_lt_aleph0 | [
1422,
1
] | [
1422,
65
] | [{"tactic": "simpa using nat_lt_aleph0 1", "annotated_tactic": ["simpa using <a>nat_lt_aleph0</a> 1", [{"full_name": "Cardinal.nat_lt_aleph0", "def_path": "Mathlib/SetTheory/Cardinal/Basic.lean", "def_pos": [1414, 9], "def_end_pos": [1414, 22]}]], "state_before": "\u03b1 \u03b2 : Type u\n\u22a2 1 < \u2135\u2080", "stat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.apply_eq_self_iff | [
133,
1
] | [
135,
30
] | [{"tactic": "rw [\u2190 hi, \u2190 mul_apply, \u2190 zpow_one_add, add_comm, zpow_add_one, mul_apply,\n (f ^ i).injective.eq_iff]", "annotated_tactic": ["rw [\u2190 hi, \u2190 <a>mul_apply</a>, \u2190 <a>zpow_one_add</a>, <a>add_comm</a>, <a>zpow_add_one</a>, <a>mul_apply</a>,\n (f ^ i).injective.eq_iff]", [{"full_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | IsGreatest.isLUB | [
281,
1
] | [
282,
28
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.subNatNat_of_sub_eq_succ | [
30,
1
] | [
31,
20
] | [{"tactic": "rw [subNatNat, h]", "annotated_tactic": ["rw [<a>subNatNat</a>, h]", [{"full_name": "Int.subNatNat", "def_path": "lake-packages/lean4/src/lean/Init/Data/Int/Basic.lean", "def_pos": [86, 5], "def_end_pos": [86, 14]}]], "state_before": "m n k : Nat\nh : n - m = succ k\n\u22a2 subNatNat m n = -[k+1]", "state_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_lt_toNNReal | [
2094,
1
] | [
2095,
96
] | [{"tactic": "rwa [\u2190 coe_toNNReal ha, \u2190 coe_toNNReal hb, coe_lt_coe]", "annotated_tactic": ["rwa [\u2190 <a>coe_toNNReal</a> ha, \u2190 <a>coe_toNNReal</a> hb, <a>coe_lt_coe</a>]", [{"full_name": "ENNReal.coe_toNNReal", "def_path": "Mathlib/Data/Real/ENNReal.lean", "def_pos": [180, 9], "def_end_pos": [180, 21]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family | [
116,
1
] | [
135,
46
] | [{"tactic": "rw [cg_def]", "annotated_tactic": ["rw [<a>cg_def</a>]", [{"full_name": "FirstOrder.Language.Substructure.cg_def", "def_path": "Mathlib/ModelTheory/FinitelyGenerated.lean", "def_pos": [107, 9], "def_end_pos": [107, 15]}]], "state_before": "L : Language\nM : Type u_1\ninst\u271d : Structure L M\nN : Substru... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/NormNum/Result.lean | Mathlib.Meta.NormNum.IsInt.nonneg_to_eq | [
179,
1
] | [
180,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_one | [
206,
1
] | [
206,
88
] | [{"tactic": "exact_mod_cast inducedMap_rat \u03b1 \u03b2 1", "annotated_tactic": ["exact_mod_cast <a>inducedMap_rat</a> \u03b1 \u03b2 1", [{"full_name": "LinearOrderedField.inducedMap_rat", "def_path": "Mathlib/Algebra/Order/CompleteField.lean", "def_pos": [190, 9], "def_end_pos": [190, 23]}]], "state_before": "F : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Basic.lean | Fin.image_succAbove_univ | [
831,
1
] | [
833,
7
] | [{"tactic": "ext m", "annotated_tactic": ["ext m", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nn : \u2115\ni : Fin (n + 1)\n\u22a2 image (succAbove i) univ = {i}\u1d9c", "state_after": "case a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nn : \u2115\ni m : Fin (n + 1)\n\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.filter_erase | [
2901,
1
] | [
2903,
61
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\np q : \u03b1 \u2192 Prop\ninst\u271d\u00b2 : DecidablePred p\ninst\u271d\u00b9 : DecidablePred q\ns\u271d : Finset \u03b1\ninst\u271d : DecidableEq \u03b1\na : \u03b1\ns : Finset \u03b1\n\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Coprime/Lemmas.lean | exists_sum_eq_one_iff_pairwise_coprime' | [
178,
1
] | [
181,
97
] | [{"tactic": "convert exists_sum_eq_one_iff_pairwise_coprime Finset.univ_nonempty (s := s) using 1", "annotated_tactic": ["convert <a>exists_sum_eq_one_iff_pairwise_coprime</a> <a>Finset.univ_nonempty</a> (s := s) using 1", [{"full_name": "exists_sum_eq_one_iff_pairwise_coprime", "def_path": "Mathlib/RingTheory/Coprime/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.target_eq | [
254,
1
] | [
256,
38
] | [{"tactic": "rw [\u2190 image_univ, \u2190 I.source_eq]", "annotated_tactic": ["rw [\u2190 <a>image_univ</a>, \u2190 I.source_eq]", [{"full_name": "Set.image_univ", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [718, 9], "def_end_pos": [718, 19]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b3 : N... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Nth.lean | Nat.nth_eq_getD_sort | [
65,
1
] | [
67,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Control/Lawful.lean | ReaderT.run_mk | [
167,
1
] | [
168,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Basic.lean | LieEquiv.trans_apply | [
669,
1
] | [
670,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | MeasureTheory.norm_condexpInd_le | [
311,
1
] | [
312,
88
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_le_of_lipschitz | [
290,
1
] | [
292,
100
] | [{"tactic": "simpa only [dist_zero_right, map_zero] using hf.dist_le_mul x 0", "annotated_tactic": ["simpa only [<a>dist_zero_right</a>, <a>map_zero</a>] using hf.dist_le_mul x 0", [{"full_name": "dist_zero_right", "def_path": "Mathlib/Analysis/Normed/Group/Basic.lean", "def_pos": [395, 3], "def_end_pos": [395, 14]}, {... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.mem_one | [
82,
1
] | [
83,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Periodic.lean | AddCircle.lintegral_preimage | [
147,
11
] | [
162,
8
] | [{"tactic": "have m : MeasurableSet (Ioc t (t + T)) := measurableSet_Ioc", "annotated_tactic": ["have m : <a>MeasurableSet</a> (<a>Ioc</a> t (t + T)) := <a>measurableSet_Ioc</a>", [{"full_name": "MeasurableSet", "def_path": "Mathlib/MeasureTheory/MeasurableSpace/Defs.lean", "def_pos": [64, 5], "def_end_pos": [64, 18]},... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/Basic.lean | Vector.traverse_eq_map_id | [
719,
11
] | [
721,
74
] | [{"tactic": "rintro \u27e8x, rfl\u27e9", "annotated_tactic": ["rintro \u27e8x, rfl\u27e9", []], "state_before": "n : \u2115\nF G : Type u \u2192 Type u\ninst\u271d\u00b3 : Applicative F\ninst\u271d\u00b2 : Applicative G\ninst\u271d\u00b9 : LawfulApplicative F\ninst\u271d : LawfulApplicative G\n\u03b1\u271d \u03b2\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Spectral/Hom.lean | SpectralMap.cancel_right | [
214,
1
] | [
217,
50
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Basic.lean | inv_pow_le_inv_pow_of_le | [
637,
1
] | [
638,
66
] | [{"tactic": "convert one_div_pow_le_one_div_pow_of_le a1 mn using 1 <;> simp", "annotated_tactic": ["convert <a>one_div_pow_le_one_div_pow_of_le</a> a1 mn using 1 <;> simp", [{"full_name": "one_div_pow_le_one_div_pow_of_le", "def_path": "Mathlib/Algebra/Order/Field/Basic.lean", "def_pos": [614, 9], "def_end_pos": [614,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.image_preimage_eq_iff | [
806,
1
] | [
811,
32
] | [{"tactic": "intro h", "annotated_tactic": ["intro h", []], "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\nf\u271d : \u03b9 \u2192 \u03b1\ns\u271d t : Set \u03b1\nf : \u03b1 \u2192 \u03b2\ns : Set \u03b2\n\u22a2 f '' (f \u207b\u00b9' s) = s \u2192 s \u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subring/Basic.lean | Subring.map_id | [
606,
1
] | [
607,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.split_imp_of_iso | [
130,
1
] | [
140,
46
] | [{"tactic": "rcases h with \u27e8Y, i, e, \u27e8h\u2081, h\u2082\u27e9\u27e9", "annotated_tactic": ["rcases h with \u27e8Y, i, e, \u27e8h\u2081, h\u2082\u27e9\u27e9", []], "state_before": "C : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX X' : C\n\u03c6 : X \u2245 X'\np : X \u27f6 X\np' : X' \u27f6 X'\nhpp' : p \u226... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_set_le_iff | [
537,
1
] | [
539,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Iterate.lean | RingHom.iterate_map_neg | [
152,
1
] | [
153,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteLattice.lean | iSup_subtype' | [
1266,
1
] | [
1268,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sups.lean | Finset.singleton_sups_singleton | [
154,
1
] | [
155,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_zero_mul_eq_smul | [
754,
1
] | [
757,
30
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u0393 : Type u_1\nR : Type u_2\ninst\u271d\u00b9 : OrderedCancelAddCommMonoid \u0393\ninst\u271d : Semiring R\nr : R\nx : HahnSeries \u0393 R\n\u22a2 \u2191(single 0) r * x = r \u2022 x", "state_after": "case coeff.h\n\u0393 : Type u_1\nR : Type u_2\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_orbit | [
58,
1
] | [
59,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.symm_mulLeft₀ | [
181,
1
] | [
183,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.assoc_symm_tmul | [
752,
1
] | [
754,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_zero | [
674,
1
] | [
675,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Ideals.lean | ContinuousMap.mem_idealOfSet_compl_singleton | [
156,
1
] | [
158,
76
] | [{"tactic": "simp only [mem_idealOfSet, compl_compl, Set.mem_singleton_iff, forall_eq]", "annotated_tactic": ["simp only [<a>mem_idealOfSet</a>, <a>compl_compl</a>, <a>Set.mem_singleton_iff</a>, <a>forall_eq</a>]", [{"full_name": "ContinuousMap.mem_idealOfSet", "def_path": "Mathlib/Topology/ContinuousFunction/Ideals.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/TwoDim.lean | Orientation.areaForm_swap | [
114,
1
] | [
119,
13
] | [{"tactic": "simp only [areaForm_to_volumeForm]", "annotated_tactic": ["simp only [<a>areaForm_to_volumeForm</a>]", [{"full_name": "Orientation.areaForm_to_volumeForm", "def_path": "Mathlib/Analysis/InnerProductSpace/TwoDim.lean", "def_pos": [103, 9], "def_end_pos": [103, 31]}]], "state_before": "E : Type u_1\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.congr_mono | [
954,
1
] | [
956,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signBijAux_inj | [
331,
1
] | [
341,
40
] | [{"tactic": "unfold signBijAux at h", "annotated_tactic": ["unfold <a>signBijAux</a> at h", [{"full_name": "Equiv.Perm.signBijAux", "def_path": "Mathlib/GroupTheory/Perm/Sign.lean", "def_pos": [325, 5], "def_end_pos": [325, 15]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : DecidableEq \u03b1\nn : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | Filter.Tendsto.piecewise_nhdsWithin | [
347,
1
] | [
350,
56
] | [{"tactic": "apply Tendsto.piecewise <;> rwa [\u2190 nhdsWithin_inter']", "annotated_tactic": ["apply <a>Tendsto.piecewise</a> <;> rwa [\u2190 <a>nhdsWithin_inter'</a>]", [{"full_name": "Filter.Tendsto.piecewise", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [3220, 19], "def_end_pos": [3220, 36]}, {"full_n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_iff' | [
2572,
1
] | [
2575,
49
] | [{"tactic": "simp only [ae_iff, \u2190 compl_setOf, restrict_apply_eq_zero' hs]", "annotated_tactic": ["simp only [<a>ae_iff</a>, \u2190 <a>compl_setOf</a>, <a>restrict_apply_eq_zero'</a> hs]", [{"full_name": "MeasureTheory.ae_iff", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean", "def_pos": [388, 9], ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Arithmetic.lean | List.measurable_prod' | [
858,
1
] | [
863,
28
] | [{"tactic": "induction' l with f l ihl", "annotated_tactic": ["induction' l with f l ihl", []], "state_before": "M : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : MeasurableSpace M\ninst\u271d : MeasurableMul\u2082 M\nm : MeasurableSpace \u03b1\n\u03bc : Measure \u03b1\nl : List (\u03b1 \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/EpsilonNFA.lean | εNFA.εClosure_univ | [
65,
1
] | [
66,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_mul | [
1410,
1
] | [
1411,
62
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Card.lean | Finset.one_lt_card_iff | [
580,
1
] | [
582,
43
] | [{"tactic": "rw [one_lt_card]", "annotated_tactic": ["rw [<a>one_lt_card</a>]", [{"full_name": "Finset.one_lt_card", "def_path": "Mathlib/Data/Finset/Card.lean", "def_pos": [574, 9], "def_end_pos": [574, 20]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ns t : Finset \u03b1\nf : \u03b1 \u2192 \u03b2\nn : \u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.exists_lowerCentralSeries_eq_bot_of_isNilpotent | [
226,
1
] | [
228,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.two_dvd_card_support | [
194,
1
] | [
200,
41
] | [{"tactic": "rw [le_antisymm\n (Nat.le_of_dvd zero_lt_two <|\n (dvd_of_mem_cycleType hn).trans <| orderOf_dvd_of_pow_eq_one h\u03c3)\n (two_le_of_mem_cycleType hn)]", "annotated_tactic": ["rw [<a>le_antisymm</a>\n (<a>Nat.le_of_dvd</a> <a>zero_lt_two</a> <|\n (<a>dvd_of_mem_cycleType</a> ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.inv_unit_app_app | [
677,
1
] | [
679,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_mul | [
230,
1
] | [
264,
35
] | [{"tactic": "let D k := (@hasseDeriv R _ k).toAddMonoidHom", "annotated_tactic": ["let D k := (@<a>hasseDeriv</a> R _ k).<a>toAddMonoidHom</a>", [{"full_name": "Polynomial.hasseDeriv", "def_path": "Mathlib/Data/Polynomial/HasseDeriv.lean", "def_pos": [58, 5], "def_end_pos": [58, 15]}, {"full_name": "LinearMap.toAddMono... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_sup_iff | [
778,
1
] | [
779,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Commute.lean | Commute.neg_right | [
91,
1
] | [
92,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_eq_iSup_orderOf | [
282,
1
] | [
323,
12
] | [{"tactic": "rw [iSup]", "annotated_tactic": ["rw [<a>iSup</a>]", [{"full_name": "iSup", "def_path": "Mathlib/Order/CompleteLattice.lean", "def_pos": [78, 5], "def_end_pos": [78, 9]}]], "state_before": "G : Type u\ninst\u271d : CommMonoid G\nh : \u2200 (g : G), 0 < orderOf g\n\u22a2 exponent G = \u2a06 g, orderOf g", "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/CharP/Two.lean | CharTwo.multiset_sum_mul_self | [
108,
1
] | [
109,
101
] | [{"tactic": "simp_rw [\u2190 pow_two, multiset_sum_sq]", "annotated_tactic": ["simp_rw [\u2190 <a>pow_two</a>, <a>multiset_sum_sq</a>]", [{"full_name": "pow_two", "def_path": "Mathlib/Algebra/GroupPower/Basic.lean", "def_pos": [102, 9], "def_end_pos": [102, 16]}, {"full_name": "CharTwo.multiset_sum_sq", "def_path": "Ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Deprecated/Subgroup.lean | Additive.isAddSubgroup | [
62,
1
] | [
63,
91
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/NNReal.lean | Real.toNNReal_zero | [
620,
1
] | [
620,
82
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_one | [
397,
1
] | [
398,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/GroupWithZero.lean | Filter.tendsto_mul_iff_of_ne_zero | [
166,
1
] | [
172,
69
] | [{"tactic": "refine' \u27e8fun hfg => _, fun hf => hf.mul hg\u27e9", "annotated_tactic": ["refine' \u27e8fun hfg => _, fun hf => hf.mul hg\u27e9", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nG\u2080 : Type u_3\ninst\u271d\u2074 : GroupWithZero G\u2080\ninst\u271d\u00b3 : TopologicalSpace G\u2080\ninst\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | measurable_unit | [
448,
1
] | [
449,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Lattice.lean | InfTopHom.ext | [
895,
1
] | [
896,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_finsupp_prod | [
269,
1
] | [
271,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.image_surjective | [
1565,
1
] | [
1569,
16
] | [{"tactic": "refine' \u27e8fun h y => _, Surjective.image_surjective\u27e9", "annotated_tactic": ["refine' \u27e8fun h y => _, <a>Surjective.image_surjective</a>\u27e9", [{"full_name": "Function.Surjective.image_surjective", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [1319, 9], "def_end_pos": [1319, 36]}]], ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.sub_const | [
328,
8
] | [
330,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Ring.lean | zero_pow | [
32,
1
] | [
33,
43
] | [{"tactic": "rw [pow_succ, zero_mul]", "annotated_tactic": ["rw [<a>pow_succ</a>, <a>zero_mul</a>]", [{"full_name": "pow_succ", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [645, 9], "def_end_pos": [645, 17]}, {"full_name": "MulZeroClass.zero_mul", "def_path": "Mathlib/Algebra/GroupWithZero/Defs.lean", "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Torsion.lean | Module.IsTorsionBySet.mk_smul | [
526,
1
] | [
529,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Subfield.lean | Subfield.comap_top | [
815,
1
] | [
816,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.sub | [
493,
1
] | [
495,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factorial/SuperFactorial.lean | Nat.superFactorial_succ | [
40,
1
] | [
41,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/OrderOfElement.lean | card_zpowers_le | [
931,
1
] | [
934,
49
] | [{"tactic": "rw [\u2190 orderOf_eq_card_zpowers]", "annotated_tactic": ["rw [\u2190 <a>orderOf_eq_card_zpowers</a>]", [{"full_name": "orderOf_eq_card_zpowers", "def_path": "Mathlib/GroupTheory/OrderOfElement.lean", "def_pos": [925, 9], "def_end_pos": [925, 32]}]], "state_before": "G : Type u_1\nH : Type u_2\nA : Type u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.trans_refl | [
817,
1
] | [
818,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_symm_eq_iff_map_eq | [
1510,
1
] | [
1516,
43
] | [{"tactic": "constructor <;> rintro rfl", "annotated_tactic": ["constructor <;> rintro rfl", []], "state_before": "G : Type u_1\nG' : Type u_2\nG'' : Type u_3\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : Group G'\ninst\u271d\u00b3 : Group G''\nA : Type u_4\ninst\u271d\u00b2 : AddGroup A\nH\u271d K : Subgroup G\nk : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Archimedean.lean | exists_pos_rat_lt | [
321,
1
] | [
322,
53
] | [{"tactic": "simpa only [Rat.cast_pos] using exists_rat_btwn x0", "annotated_tactic": ["simpa only [<a>Rat.cast_pos</a>] using <a>exists_rat_btwn</a> x0", [{"full_name": "Rat.cast_pos", "def_path": "Mathlib/Data/Rat/Cast/Order.lean", "def_pos": [74, 9], "def_end_pos": [74, 17]}, {"full_name": "exists_rat_btwn", "def_pa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/GameAdd.lean | Sym2.GameAdd.fix_eq | [
236,
1
] | [
241,
33
] | [{"tactic": "dsimp [GameAdd.fix]", "annotated_tactic": ["dsimp [<a>GameAdd.fix</a>]", [{"full_name": "Sym2.GameAdd.fix", "def_path": "Mathlib/Order/GameAdd.lean", "def_pos": [226, 5], "def_end_pos": [226, 16]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr\u03b1 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr\u03b2 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Ico_real | [
276,
1
] | [
277,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toLp_sub | [
565,
1
] | [
567,
53
] | [{"tactic": "simp only [sub_eq_add_neg, \u2190 toLp_neg, \u2190 toLp_add]", "annotated_tactic": ["simp only [<a>sub_eq_add_neg</a>, \u2190 <a>toLp_neg</a>, \u2190 <a>toLp_add</a>]", [{"full_name": "sub_eq_add_neg", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [975, 3], "def_end_pos": [975, 14]}, {"full_nam... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ico_subset | [
80,
1
] | [
81,
76
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.dist_eq_zero_of_not_reachable | [
95,
1
] | [
96,
11
] | [{"tactic": "simp [h]", "annotated_tactic": ["simp [h]", []], "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\nh : \u00acReachable G u v\n\u22a2 dist G u v = 0", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Irrational.lean | Irrational.of_mul_self | [
467,
1
] | [
468,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/IsometricSMul.lean | nndist_div_left | [
417,
1
] | [
419,
24
] | [{"tactic": "simp [div_eq_mul_inv]", "annotated_tactic": ["simp [<a>div_eq_mul_inv</a>]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}]], "state_before": "M : Type u\nG : Type v\nX : Type w\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Segment.lean | segment_eq_image | [
191,
1
] | [
196,
92
] | [{"tactic": "simp only [add_sub_cancel]", "annotated_tactic": ["simp only [<a>add_sub_cancel</a>]", [{"full_name": "add_sub_cancel", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [739, 30], "def_end_pos": [739, 44]}]], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\n\u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/CondCdf.lean | Real.iInter_Iic_rat | [
84,
1
] | [
87,
24
] | [{"tactic": "ext1 x", "annotated_tactic": ["ext1 x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\n\u22a2 \u22c2 r, Iic \u2191r = \u2205", "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nx : \u211d\n\u22a2 x \u2208 \u22c2 r, Iic \u2191r \u2194 x \u2208 \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/EpsilonNFA.lean | εNFA.evalFrom_singleton | [
100,
1
] | [
101,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Cycle.lean | Cycle.nil_toMultiset | [
696,
1
] | [
697,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofRealLi_apply | [
1084,
1
] | [
1085,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/AffineScheme.lean | AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff | [
769,
1
] | [
776,
25
] | [{"tactic": "rw [\u2190 hU.basicOpen_union_eq_self_iff, @comm _ Eq]", "annotated_tactic": ["rw [\u2190 hU.basicOpen_union_eq_self_iff, @<a>comm</a> _ <a>Eq</a>]", [{"full_name": "comm", "def_path": "Mathlib/Order/RelClasses.lean", "def_pos": [33, 9], "def_end_pos": [33, 13]}, {"full_name": "Eq", "def_path": "lake-packa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homeomorph.lean | Homeomorph.isOpenMap | [
354,
11
] | [
354,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Module.lean | IsSelfAdjoint.coe_selfAdjointPart_apply | [
138,
1
] | [
140,
90
] | [{"tactic": "rw [selfAdjointPart_apply_coe, hx.star_eq, smul_add, invOf_two_smul_add_invOf_two_smul]", "annotated_tactic": ["rw [<a>selfAdjointPart_apply_coe</a>, hx.star_eq, <a>smul_add</a>, <a>invOf_two_smul_add_invOf_two_smul</a>]", [{"full_name": "selfAdjointPart_apply_coe", "def_path": "Mathlib/Algebra/Star/Module... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Support.lean | Function.support_mul | [
357,
1
] | [
359,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongMono.iff_of_arrow_iso | [
179,
1
] | [
182,
69
] | [{"tactic": "constructor <;> intro", "annotated_tactic": ["constructor <;> intro", []], "state_before": "C : Type u\ninst\u271d : Category.{v, u} C\nP Q R : C\nf\u271d : P \u27f6 Q\ng\u271d : Q \u27f6 R\nA B A' B' : C\nf : A \u27f6 B\ng : A' \u27f6 B'\ne : Arrow.mk f \u2245 Arrow.mk g\n\u22a2 StrongMono f \u2194 Strong... |
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