url stringclasses 3
values | commit stringclasses 3
values | file_path stringlengths 20 79 | full_name stringlengths 3 115 | start list | end list | traced_tactics stringlengths 2 997k |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.list_prod_subset_list_prod | [
108,
1
] | [
114,
56
] | [{"tactic": "induction' t with h tl ih", "annotated_tactic": ["induction' t with h tl ih", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nF : Type u_4\ninst\u271d\u00b2 : CommMonoid \u03b1\ninst\u271d\u00b9 : CommMonoid \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nt : List \u03b9... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivWithinAt.ccos | [
185,
1
] | [
187,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_pow | [
165,
1
] | [
166,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Opposites.lean | MulOpposite.unop_smul | [
323,
1
] | [
324,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Embedding/Basic.lean | subtypeOrLeftEmbedding_apply_left | [
481,
1
] | [
484,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty | [
920,
1
] | [
923,
53
] | [{"tactic": "rw [sum_centroidWeightsIndicator]", "annotated_tactic": ["rw [<a>sum_centroidWeightsIndicator</a>]", [{"full_name": "Finset.sum_centroidWeightsIndicator", "def_path": "Mathlib/LinearAlgebra/AffineSpace/Combination.lean", "def_pos": [904, 9], "def_end_pos": [904, 37]}]], "state_before": "k : Type u_1\nV : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Prod.lean | Set.offDiag_eq_sep_prod | [
596,
1
] | [
597,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.range_coe' | [
160,
1
] | [
160,
61
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Sum/Lemmas.lean | Sum.liftRel_subrelation_lex | [
200,
1
] | [
200,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Heyting/Basic.lean | PUnit.sup_eq | [
1356,
1
] | [
1357,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/Jacobian.lean | exists_partition_approximatesLinearOn_of_hasFDerivWithinAt | [
254,
1
] | [
269,
94
] | [{"tactic": "rcases exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAt f s f' hf' r rpos with\n \u27e8t, A, t_closed, st, t_approx, ht\u27e9", "annotated_tactic": ["rcases <a>exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAt</a> f s f' hf' r rpos with\n \u27e8t, A, t_closed, st, t_approx, ht\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.BoundedFormula.listEncode_sigma_injective | [
306,
1
] | [
308,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Order.lean | Left.one_le_pow_of_le | [
113,
1
] | [
117,
57
] | [{"tactic": "rw [pow_succ]", "annotated_tactic": ["rw [<a>pow_succ</a>]", [{"full_name": "pow_succ", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [645, 9], "def_end_pos": [645, 17]}]], "state_before": "\u03b2 : Type u_1\nA : Type u_2\nG : Type u_3\nM : Type u_4\nR : Type u_5\ninst\u271d\u00b2 : Monoid M\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Sequences.lean | SeqCompact.lebesgue_number_lemma_of_metric | [
407,
8
] | [
410,
55
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Basic.lean | Fin.succAbove_pred | [
1424,
1
] | [
1427,
54
] | [{"tactic": "rw [succAbove_above, succ_pred]", "annotated_tactic": ["rw [<a>succAbove_above</a>, <a>succ_pred</a>]", [{"full_name": "Fin.succAbove_above", "def_path": "Mathlib/Data/Fin/Basic.lean", "def_pos": [1356, 9], "def_end_pos": [1356, 24]}, {"full_name": "Fin.succ_pred", "def_path": "lake-packages/std/Std/Data/F... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Order.lean | DFinsupp.bot_eq_zero | [
155,
11
] | [
156,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Between.lean | Wbtw.right_mem_affineSpan_of_left_ne | [
696,
1
] | [
699,
42
] | [{"tactic": "rcases h.right_mem_image_Ici_of_left_ne hne with \u27e8r, \u27e8-, rfl\u27e9\u27e9", "annotated_tactic": ["rcases h.right_mem_image_Ici_of_left_ne hne with \u27e8r, \u27e8-, rfl\u27e9\u27e9", []], "state_before": "R : Type u_1\nV : Type u_2\nV' : Type u_3\nP : Type u_4\nP' : Type u_5\ninst\u271d\u00b3 : Li... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean | Matrix.nondegenerate_of_det_ne_zero | [
50,
1
] | [
63,
18
] | [{"tactic": "intro v hv", "annotated_tactic": ["intro v hv", []], "state_before": "m : Type u_1\nR : Type u_2\nA : Type u_3\ninst\u271d\u2074 : Fintype m\ninst\u271d\u00b3 : CommRing R\ninst\u271d\u00b2 : CommRing A\ninst\u271d\u00b9 : IsDomain A\ninst\u271d : DecidableEq m\nM : Matrix m m A\nhM : det M \u2260 0\n\u22a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_neg | [
1132,
1
] | [
1135,
88
] | [{"tactic": "rw [\u2190 MultilinearMap.map_add, add_left_neg, f.map_coord_zero i (update_same i 0 m)]", "annotated_tactic": ["rw [\u2190 <a>MultilinearMap.map_add</a>, <a>add_left_neg</a>, f.map_coord_zero i (<a>update_same</a> i 0 m)]", [{"full_name": "MultilinearMap.map_add", "def_path": "Mathlib/LinearAlgebra/Multil... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.maximal_of_isField | [
234,
1
] | [
243,
77
] | [{"tactic": "apply Ideal.isMaximal_iff.2", "annotated_tactic": ["apply <a>Ideal.isMaximal_iff</a>.2", [{"full_name": "Ideal.isMaximal_iff", "def_path": "Mathlib/RingTheory/Ideal/Basic.lean", "def_pos": [302, 9], "def_end_pos": [302, 22]}]], "state_before": "R : Type u\ninst\u271d : CommRing R\nI\u271d : Ideal R\na b : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.algebraMap_eq_zero_iff | [
498,
1
] | [
499,
68
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.count_cons_of_ne | [
2364,
1
] | [
2365,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Process/Stopping.lean | MeasureTheory.IsStoppingTime.measurable | [
579,
11
] | [
582,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Ideal.lean | IsCoatom.isMaximal | [
241,
1
] | [
242,
81
] | [{"tactic": "simp [hI.2 _ hJ]", "annotated_tactic": ["simp [hI.2 _ hJ]", []], "state_before": "P : Type u_1\ninst\u271d\u00b2 : LE P\ninst\u271d\u00b9 : IsDirected P fun x x_1 => x \u2264 x_1\ninst\u271d : Nonempty P\nI : Ideal P\nhI : IsCoatom I\nsrc\u271d : IsProper I := IsCoatom.isProper hI\nx\u271d : Ideal P\nhJ : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/DenseEmbedding.lean | DenseInducing.continuous | [
54,
11
] | [
55,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_generate | [
241,
1
] | [
243,
84
] | [{"tactic": "simp only [mem_generate_iff, exists_prop, and_assoc, and_left_comm]", "annotated_tactic": ["simp only [<a>mem_generate_iff</a>, <a>exists_prop</a>, <a>and_assoc</a>, <a>and_left_comm</a>]", [{"full_name": "Filter.mem_generate_iff", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [363, 9], "def_en... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Monoidal/Center.lean | CategoryTheory.Center.rightUnitor_hom_f | [
284,
1
] | [
285,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Squarefree.lean | squarefree_one | [
46,
1
] | [
47,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Basic.lean | List.map_injective_iff | [
1774,
1
] | [
1784,
33
] | [{"tactic": "constructor <;> intro h x y hxy", "annotated_tactic": ["constructor <;> intro h x y hxy", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nl\u2081 l\u2082 : List \u03b1\nf : \u03b1 \u2192 \u03b2\n\u22a2 Injective (map f) \u2194 Injective f", "state_after": "case m... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Star/Spectrum.lean | unitary.spectrum_subset_circle | [
31,
1
] | [
41,
61
] | [{"tactic": "nontriviality E", "annotated_tactic": ["nontriviality E", []], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2075 : NormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2074 : NormedRing E\ninst\u271d\u00b3 : StarRing E\ninst\u271d\u00b2 : CstarRing E\ninst\u271d\u00b9 : NormedAlgebra \ud835\udd5c E... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Maps.lean | quotientMap_iff_closed | [
282,
1
] | [
285,
49
] | [{"tactic": "simp only [isOpen_compl_iff, preimage_compl]", "annotated_tactic": ["simp only [<a>isOpen_compl_iff</a>, <a>preimage_compl</a>]", [{"full_name": "isOpen_compl_iff", "def_path": "Mathlib/Topology/Basic.lean", "def_pos": [205, 17], "def_end_pos": [205, 33]}, {"full_name": "Set.preimage_compl", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition | [
268,
1
] | [
270,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.cast_int_mul_right | [
1038,
1
] | [
1039,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sigma/Basic.lean | Function.Injective.of_sigma_map | [
134,
1
] | [
137,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOn_iff_tendstoUniformlyOnFilter | [
107,
1
] | [
112,
7
] | [{"tactic": "simp only [TendstoUniformlyOn, TendstoUniformlyOnFilter]", "annotated_tactic": ["simp only [<a>TendstoUniformlyOn</a>, <a>TendstoUniformlyOnFilter</a>]", [{"full_name": "TendstoUniformlyOn", "def_path": "Mathlib/Topology/UniformSpace/UniformConvergence.lean", "def_pos": [103, 5], "def_end_pos": [103, 23]},... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Perm.lean | List.singleton_perm | [
211,
1
] | [
212,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure | [
360,
1
] | [
368,
46
] | [{"tactic": "apply Set.Subset.antisymm", "annotated_tactic": ["apply <a>Set.Subset.antisymm</a>", [{"full_name": "Set.Subset.antisymm", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [370, 9], "def_end_pos": [370, 24]}]], "state_before": "R : Type u_1\nA : Type u_2\ninst\u271d\u00b3 : CommSemiring R\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Norm.lean | Ideal.irreducible_of_irreducible_absNorm | [
408,
1
] | [
416,
58
] | [{"tactic": "simpa only [Ideal.isUnit_iff, Nat.isUnit_iff, absNorm_eq_one_iff] using h", "annotated_tactic": ["simpa only [<a>Ideal.isUnit_iff</a>, <a>Nat.isUnit_iff</a>, <a>absNorm_eq_one_iff</a>] using h", [{"full_name": "Ideal.isUnit_iff", "def_path": "Mathlib/RingTheory/Ideal/Operations.lean", "def_pos": [1336, 9],... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree | [
382,
1
] | [
396,
52
] | [{"tactic": "rw [coeff_mul]", "annotated_tactic": ["rw [<a>coeff_mul</a>]", [{"full_name": "Polynomial.coeff_mul", "def_path": "Mathlib/Data/Polynomial/Coeff.lean", "def_pos": [116, 9], "def_end_pos": [116, 18]}]], "state_before": "R : Type u\nS : Type v\na b : R\nn m : \u2115\ninst\u271d : Semiring R\np q r : R[X]\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | RightDerivMeasurableAux.le_of_mem_A | [
522,
1
] | [
527,
78
] | [{"tactic": "rcases hx with \u27e8r', r'mem, hr'\u27e9", "annotated_tactic": ["rcases hx with \u27e8r', r'mem, hr'\u27e9", []], "state_before": "F : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \u211d F\nf : \u211d \u2192 F\nK : Set F\nr \u03b5 : \u211d\nL : F\nx : \u211d\nhx : x \u2208 A... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.stalkAlgebra_map | [
938,
1
] | [
940,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Valuation/ValuationSubring.lean | Valuation.mem_valuationSubring_iff | [
437,
1
] | [
437,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | tangentMapWithin_comp_at | [
1028,
1
] | [
1035,
6
] | [{"tactic": "simp only [tangentMapWithin, mfld_simps]", "annotated_tactic": ["simp only [<a>tangentMapWithin</a>, mfld_simps]", [{"full_name": "tangentMapWithin", "def_path": "Mathlib/Geometry/Manifold/MFDeriv.lean", "def_pos": [304, 5], "def_end_pos": [304, 21]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Prod.lean | Set.mem_pi | [
670,
1
] | [
671,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sigma.lean | Set.sigma_univ_range_eq | [
197,
1
] | [
199,
25
] | [{"tactic": "simp [range]", "annotated_tactic": ["simp [<a>range</a>]", [{"full_name": "Set.range", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [668, 5], "def_end_pos": [668, 10]}]], "state_before": "\u03b9 : Type u_1\n\u03b9' : Type u_2\n\u03b1 : \u03b9 \u2192 Type u_3\n\u03b2 : \u03b9 \u2192 Type u_4\ns s\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | span_gramSchmidtNormed_range | [
329,
1
] | [
331,
67
] | [{"tactic": "simpa only [image_univ.symm] using span_gramSchmidtNormed f univ", "annotated_tactic": ["simpa only [image_univ.symm] using <a>span_gramSchmidtNormed</a> f <a>univ</a>", [{"full_name": "span_gramSchmidtNormed", "def_path": "Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean", "def_pos": [316, 9], "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/ModEq.lean | Dvd.dvd.zero_modEq_int | [
90,
1
] | [
91,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.eq_bot_of_card_eq | [
162,
1
] | [
163,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.one_ne_coe | [
151,
1
] | [
152,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.trans_assoc | [
181,
1
] | [
183,
45
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "C : Type u\ninst\u271d : Category.{v, u} C\nX Y Z Z' : C\n\u03b1 : X \u2245 Y\n\u03b2 : Y \u2245 Z\n\u03b3 : Z \u2245 Z'\n\u22a2 (\u03b1 \u226a\u226b \u03b2) \u226a\u226b \u03b3 = \u03b1 \u226a\u226b \u03b2 \u226a\u226b \u03b3", "state_after": "case w... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Matrix/Kronecker.lean | Matrix.det_kroneckerTMul | [
562,
1
] | [
570,
36
] | [{"tactic": "refine' (det_kroneckerMapBilinear (TensorProduct.mk R \u03b1 \u03b2) tmul_mul_tmul _ _).trans _", "annotated_tactic": ["refine' (<a>det_kroneckerMapBilinear</a> (<a>TensorProduct.mk</a> R \u03b1 \u03b2) <a>tmul_mul_tmul</a> _ _).<a>trans</a> _", [{"full_name": "Matrix.det_kroneckerMapBilinear", "def_path":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/SemiNormedGroupCat/Kernels.lean | SemiNormedGroupCat.explicitCokernelIso_hom_desc | [
394,
1
] | [
399,
40
] | [{"tactic": "ext1", "annotated_tactic": ["ext1", []], "state_before": "X Y Z : SemiNormedGroupCat\nf : X \u27f6 Y\ng : Y \u27f6 Z\nw : f \u226b g = 0\n\u22a2 (explicitCokernelIso f).hom \u226b cokernel.desc f g w = explicitCokernelDesc w", "state_after": "case h\nX Y Z : SemiNormedGroupCat\nf : X \u27f6 Y\ng : Y \u27f6... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_add_of_natDegree_lt_right | [
170,
1
] | [
178,
57
] | [{"tactic": "ext n", "annotated_tactic": ["ext n", []], "state_before": "R : Type u_1\ninst\u271d : Semiring R\nf p q : R[X]\npq : natDegree p < natDegree q\n\u22a2 eraseLead (p + q) = p + eraseLead q", "state_after": "case a\nR : Type u_1\ninst\u271d : Semiring R\nf p q : R[X]\npq : natDegree p < natDegree q\nn : \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.uniformEmbedding_pureCauchy | [
170,
1
] | [
172,
72
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/UniqueFactorizationDomain.lean | irreducible_iff_prime_of_exists_unique_irreducible_factors | [
375,
1
] | [
412,
23
] | [{"tactic": "simp [ha0]", "annotated_tactic": ["simp [ha0]", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : CancelCommMonoidWithZero \u03b1\neif : \u2200 (a : \u03b1), a \u2260 0 \u2192 \u2203 f, (\u2200 (b : \u03b1), b \u2208 f \u2192 Irreducible b) \u2227 Multiset.prod f ~\u1d64 a\nuif :\n \u2200 (f g : Multi... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_inter_Ico_consecutive | [
620,
1
] | [
621,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/NhdsSet.lean | Iio_mem_nhdsSet_Ico | [
115,
1
] | [
116,
47
] | [{"tactic": "simpa", "annotated_tactic": ["simpa", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : LinearOrder \u03b1\ninst\u271d\u00b9 : TopologicalSpace \u03b1\ninst\u271d : OrderClosedTopology \u03b1\na b c d : \u03b1\nh : b \u2264 c\n\u22a2 Iio c \u2208 \ud835\udcdd\u02e2 (Iio b)", "state_after": "no go... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_ae_map_iff | [
2460,
1
] | [
2462,
80
] | [{"tactic": "simp only [mem_ae_iff, map_apply_of_aemeasurable hf hs.compl, preimage_compl]", "annotated_tactic": ["simp only [<a>mem_ae_iff</a>, <a>map_apply_of_aemeasurable</a> hf hs.compl, <a>preimage_compl</a>]", [{"full_name": "MeasureTheory.mem_ae_iff", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpaceDef.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/StrictConvexBetween.lean | Wbtw.dist_le_max_dist | [
41,
1
] | [
46,
35
] | [{"tactic": "by_cases hp\u2081 : p\u2082 = p\u2081", "annotated_tactic": ["by_cases hp\u2081 : p\u2082 = p\u2081", []], "state_before": "V : Type u_1\nP : Type u_2\ninst\u271d\u2074 : NormedAddCommGroup V\ninst\u271d\u00b3 : NormedSpace \u211d V\ninst\u271d\u00b2 : PseudoMetricSpace P\ninst\u271d\u00b9 : NormedAddTorso... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_nnnorm_prod | [
630,
1
] | [
631,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/LinearIndependent.lean | eq_of_linearIndependent_of_span_subtype | [
1013,
1
] | [
1025,
29
] | [{"tactic": "let f : t \u21aa s :=\n \u27e8fun x => \u27e8x.1, h x.2\u27e9, fun a b hab => Subtype.coe_injective (Subtype.mk.inj hab)\u27e9", "annotated_tactic": ["let f : t \u21aa s :=\n \u27e8fun x => \u27e8x.1, h x.2\u27e9, fun a b hab => <a>Subtype.coe_injective</a> (Subtype.mk.inj hab)\u27e9", [{"full_name": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousWithinAt.inv₀ | [
121,
8
] | [
123,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sigma.lean | Finset.pairwiseDisjoint_map_sigmaMk | [
75,
1
] | [
81,
43
] | [{"tactic": "intro i _ j _ hij", "annotated_tactic": ["intro i _ j _ hij", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\n\u03b2 : Type u_3\ns s\u2081 s\u2082 : Finset \u03b9\nt t\u2081 t\u2082 : (i : \u03b9) \u2192 Finset (\u03b1 i)\n\u22a2 Set.PairwiseDisjoint \u2191s fun i => map (Embeddin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Invertible/Basic.lean | Ring.inverse_invertible | [
170,
1
] | [
171,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasDerivAt_sinh | [
112,
1
] | [
113,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Basic.lean | Ring.isField_iff_isSimpleOrder_ideal | [
782,
1
] | [
790,
37
] | [{"tactic": "cases subsingleton_or_nontrivial R", "annotated_tactic": ["cases <a>subsingleton_or_nontrivial</a> R", [{"full_name": "subsingleton_or_nontrivial", "def_path": "Mathlib/Logic/Nontrivial/Defs.lean", "def_pos": [94, 9], "def_end_pos": [94, 35]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nR : Type u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_funUnique | [
2525,
1
] | [
2526,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_monomial | [
167,
1
] | [
168,
80
] | [{"tactic": "rw [\u2190 one_mul (X ^ n), \u2190 one_mul (X ^ revAt N n), \u2190 C_1, reflect_C_mul_X_pow]", "annotated_tactic": ["rw [\u2190 <a>one_mul</a> (<a>X</a> ^ n), \u2190 <a>one_mul</a> (<a>X</a> ^ <a>revAt</a> N n), \u2190 <a>C_1</a>, <a>reflect_C_mul_X_pow</a>]", [{"full_name": "one_mul", "def_path": "Mathlib... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Basic.lean | mul_div_cancel'' | [
740,
1
] | [
741,
51
] | [{"tactic": "rw [div_eq_mul_inv, mul_inv_cancel_right a b]", "annotated_tactic": ["rw [<a>div_eq_mul_inv</a>, <a>mul_inv_cancel_right</a> a b]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}, {"full_name": "mul_inv_cancel_right", "def_path... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Compare.lean | Ordering.Compares.eq_lt | [
82,
1
] | [
85,
77
] | [{"tactic": "injection h", "annotated_tactic": ["injection h", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : Compares eq a b\nh : eq = lt\n\u22a2 a < b", "state_after": "no goals"}, {"tactic": "injection h", "annotated_tactic": ["injection h", []], "st... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.singleton_inter_of_mem | [
1706,
1
] | [
1707,
78
] | [{"tactic": "rw [insert_inter_of_mem H, empty_inter]", "annotated_tactic": ["rw [<a>insert_inter_of_mem</a> H, <a>empty_inter</a>]", [{"full_name": "Finset.insert_inter_of_mem", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1680, 9], "def_end_pos": [1680, 28]}, {"full_name": "Finset.empty_inter", "def_path"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Partrec.lean | Computable.of_eq | [
280,
1
] | [
281,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Function/Basic.lean | Function.partialInv_left | [
419,
1
] | [
420,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | exists_stronglyMeasurable_limit_of_tendsto_ae | [
1685,
1
] | [
1697,
18
] | [{"tactic": "borelize \u03b2", "annotated_tactic": ["borelize \u03b2", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\ninst\u271d\u00b3 : Countable \u03b9\nm : MeasurableSpace \u03b1\n\u03bc : Measure \u03b1\ninst\u271d\u00b2 : TopologicalSpace \u03b2\ninst\u271d\u00b9 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_mul_right | [
214,
1
] | [
215,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/JordanHolder.lean | CompositionSeries.append_succ_natAdd | [
535,
1
] | [
537,
48
] | [{"tactic": "rw [coe_append, append_succ_natAdd_aux _ _ i]", "annotated_tactic": ["rw [<a>coe_append</a>, <a>append_succ_natAdd_aux</a> _ _ i]", [{"full_name": "CompositionSeries.coe_append", "def_path": "Mathlib/Order/JordanHolder.lean", "def_pos": [511, 9], "def_end_pos": [511, 19]}, {"full_name": "CompositionSeries.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | IsGreatest.dual | [
157,
1
] | [
158,
4
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.coe_injective' | [
417,
1
] | [
418,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Pointwise.lean | Filter.mul_eq_bot_iff | [
320,
1
] | [
321,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | IsSelfAdjoint.conj_adjoint | [
290,
1
] | [
294,
45
] | [{"tactic": "rw [isSelfAdjoint_iff'] at hT \u22a2", "annotated_tactic": ["rw [<a>isSelfAdjoint_iff'</a>] at hT \u22a2", [{"full_name": "ContinuousLinearMap.isSelfAdjoint_iff'", "def_path": "Mathlib/Analysis/InnerProductSpace/Adjoint.lean", "def_pos": [223, 9], "def_end_pos": [223, 27]}]], "state_before": "\ud835\udd5c ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sum/Order.lean | Sum.not_inl_le_inr | [
149,
1
] | [
150,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_distrib | [
2244,
1
] | [
2245,
12
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_quotient_center | [
619,
1
] | [
636,
73
] | [{"tactic": "generalize hn : Group.nilpotencyClass G = n", "annotated_tactic": ["generalize hn : <a>Group.nilpotencyClass</a> G = n", [{"full_name": "Group.nilpotencyClass", "def_path": "Mathlib/GroupTheory/Nilpotent.lean", "def_pos": [362, 19], "def_end_pos": [362, 40]}]], "state_before": "G : Type u_1\ninst\u271d\u00... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.multispan_obj_left | [
266,
1
] | [
267,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/ContMDiff.lean | SmoothOn.comp' | [
985,
8
] | [
987,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le' | [
795,
1
] | [
796,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mem_colon_singleton | [
399,
1
] | [
401,
84
] | [{"tactic": "simp only [\u2190 Ideal.submodule_span_eq, Submodule.mem_colon_singleton, smul_eq_mul]", "annotated_tactic": ["simp only [\u2190 <a>Ideal.submodule_span_eq</a>, <a>Submodule.mem_colon_singleton</a>, <a>smul_eq_mul</a>]", [{"full_name": "Ideal.submodule_span_eq", "def_path": "Mathlib/RingTheory/Ideal/Basic.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm/TensorProduct.lean | BilinForm.tensorDistribEquiv_tmul | [
128,
1
] | [
132,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_sSup | [
2452,
1
] | [
2454,
83
] | [{"tactic": "simp only [ENNReal.toReal, toNNReal_sSup s hf, NNReal.coe_sSup, Set.image_image]", "annotated_tactic": ["simp only [<a>ENNReal.toReal</a>, <a>toNNReal_sSup</a> s hf, <a>NNReal.coe_sSup</a>, <a>Set.image_image</a>]", [{"full_name": "ENNReal.toReal", "def_path": "Mathlib/Data/Real/ENNReal.lean", "def_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Basic.lean | Int.neg_nat_succ | [
183,
1
] | [
183,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Monotone/Basic.lean | monotone_fst | [
1185,
1
] | [
1185,
70
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_injective | [
99,
1
] | [
100,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioo_self | [
109,
1
] | [
109,
81
] | [{"tactic": "rw [Ioo, Finset.Ioo_self, Finset.empty_val]", "annotated_tactic": ["rw [<a>Ioo</a>, <a>Finset.Ioo_self</a>, <a>Finset.empty_val</a>]", [{"full_name": "Multiset.Ioo", "def_path": "Mathlib/Order/LocallyFinite.lean", "def_pos": [546, 5], "def_end_pos": [546, 8]}, {"full_name": "Finset.Ioo_self", "def_path": "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Vector/Basic.lean | Vector.get_set_of_ne | [
628,
1
] | [
633,
18
] | [{"tactic": "cases v", "annotated_tactic": ["cases v", []], "state_before": "n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nv : Vector \u03b1 n\ni j : Fin n\nh : i \u2260 j\na : \u03b1\n\u22a2 get (set v i a) j = get v j", "state_after": "case mk\nn : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Alternating.lean | ContinuousAlternatingMap.toAlternatingMap_injective | [
98,
1
] | [
100,
50
] | [{"tactic": "convert FunLike.ext'_iff.1 h", "annotated_tactic": ["convert <a>FunLike.ext'_iff</a>.1 h", [{"full_name": "FunLike.ext'_iff", "def_path": "Mathlib/Data/FunLike/Basic.lean", "def_pos": [173, 9], "def_end_pos": [173, 17]}]], "state_before": "R : Type u_1\nM : Type u_2\nM' : Type u_3\nN : Type u_4\nN' : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_sub_le' | [
938,
1
] | [
945,
46
] | [{"tactic": "rw [tsub_le_iff_right]", "annotated_tactic": ["rw [<a>tsub_le_iff_right</a>]", [{"full_name": "tsub_le_iff_right", "def_path": "Mathlib/Algebra/Order/Sub/Defs.lean", "def_pos": [65, 9], "def_end_pos": [65, 26]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_inf | [
111,
1
] | [
111,
89
] | [{"tactic": "rw [inf_comm, inf_inf_sdiff]", "annotated_tactic": ["rw [<a>inf_comm</a>, <a>inf_inf_sdiff</a>]", [{"full_name": "inf_comm", "def_path": "Mathlib/Order/Lattice.lean", "def_pos": [500, 9], "def_end_pos": [500, 17]}, {"full_name": "inf_inf_sdiff", "def_path": "Mathlib/Order/BooleanAlgebra.lean", "def_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ext | [
328,
11
] | [
330,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Lemmas.lean | List.mapAccumr_eq_foldr | [
93,
1
] | [
100,
58
] | [{"tactic": "simp only [mapAccumr, foldr, mapAccumr_eq_foldr f as]", "annotated_tactic": ["simp only [<a>mapAccumr</a>, <a>foldr</a>, mapAccumr_eq_foldr f as]", [{"full_name": "List.mapAccumr", "def_path": "Mathlib/Init/Data/List/Lemmas.lean", "def_pos": [139, 5], "def_end_pos": [139, 14]}, {"full_name": "List.foldr", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | Convex.smul_mem_of_zero_mem | [
505,
1
] | [
507,
62
] | [{"tactic": "simpa using hs.add_smul_mem zero_mem (by simpa using hx) ht", "annotated_tactic": ["simpa using hs.add_smul_mem zero_mem (by simpa using hx) ht", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\n\u03b2 : Type u_4\ninst\u271d\u2074 : OrderedRing \ud835\udd5c\ninst\u271d\u00b3 : Add... |
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