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/Algebra/Lie/Submodule.lean | LieSubmodule.map_sup | [
817,
1
] | [
818,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/DFinsupp.lean | CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective | [
521,
1
] | [
523,
93
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Matrix.lean | Matrix.frobenius_nnnorm_diagonal | [
510,
1
] | [
521,
77
] | [{"tactic": "simp_rw [frobenius_nnnorm_def, \u2190 Finset.sum_product', Finset.univ_product_univ,\n PiLp.nnnorm_eq_of_L2]", "annotated_tactic": ["simp_rw [<a>frobenius_nnnorm_def</a>, \u2190 <a>Finset.sum_product'</a>, <a>Finset.univ_product_univ</a>,\n <a>PiLp.nnnorm_eq_of_L2</a>]", [{"full_name": "Matrix.frobeniu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.ppow | [
845,
1
] | [
850,
21
] | [{"tactic": "induction' k with k hi", "annotated_tactic": ["induction' k with k hi", []], "state_before": "R : Type u_1\ninst\u271d : CommSemiring R\nf : ArithmeticFunction R\nhf : IsMultiplicative f\nk : \u2115\n\u22a2 IsMultiplicative (ArithmeticFunction.ppow f k)", "state_after": "case zero\nR : Type u_1\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Basic.lean | Nat.div_le_div_right | [
650,
11
] | [
652,
70
] | [{"tactic": "simp [k0]", "annotated_tactic": ["simp [k0]", []], "state_before": "m\u271d n\u271d k\u271d n m : \u2115\nh : n \u2264 m\nk : \u2115\nk0 : k = 0\n\u22a2 n / k \u2264 m / k", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Antisymmetrization.lean | toAntisymmetrization_lt_toAntisymmetrization_iff | [
186,
1
] | [
188,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsComplProd_apply | [
285,
1
] | [
287,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | zero_le_bit0 | [
919,
1
] | [
920,
69
] | [{"tactic": "rw [bit0, \u2190 two_mul, zero_le_mul_left (zero_lt_two : 0 < (2 : \u03b1))]", "annotated_tactic": ["rw [<a>bit0</a>, \u2190 <a>two_mul</a>, <a>zero_le_mul_left</a> (<a>zero_lt_two</a> : 0 < (2 : \u03b1))]", [{"full_name": "bit0", "def_path": "Mathlib/Init/ZeroOne.lean", "def_pos": [36, 34], "def_end_pos":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | continuousOn_iff' | [
659,
1
] | [
668,
78
] | [{"tactic": "rw [continuousOn_iff_continuous_restrict, continuous_def]", "annotated_tactic": ["rw [<a>continuousOn_iff_continuous_restrict</a>, <a>continuous_def</a>]", [{"full_name": "continuousOn_iff_continuous_restrict", "def_path": "Mathlib/Topology/ContinuousOn.lean", "def_pos": [643, 9], "def_end_pos": [643, 45]}... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/NhdsSet.lean | mem_nhdsSet_empty | [
120,
1
] | [
120,
58
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : TopologicalSpace \u03b1\ninst\u271d : TopologicalSpace \u03b2\nf : Filter \u03b1\ns t s\u2081 s\u2082 t\u2081 t\u2082 : Set \u03b1\nx : \u03b1\n\u22a2 s \u2208 \ud835\udcdd\u02e2 \u2205", "sta... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_sub_cons | [
516,
1
] | [
517,
67
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u\nm n o : \u2115\nm' : Type u_1\nn' : Type u_2\no' : Type u_3\ninst\u271d : Sub \u03b1\nx : \u03b1\nv : Fin n \u2192 \u03b1\ny : \u03b1\nw : Fin n \u2192 \u03b1\n\u22a2 vecCons x v - vecCons y w = vecCons (x - y) (v - w)", "state_afte... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_of_coprime_right | [
768,
1
] | [
771,
67
] | [{"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\nhab : Coprime a b\nhpb : p \u2208 factors b\n\u22a2 \u2191(factorization (a * b)) p = \u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/InformationTheory/Hamming.lean | hammingDist_triangle | [
62,
1
] | [
68,
77
] | [{"tactic": "classical\n unfold hammingDist\n refine le_trans (card_mono ?_) (card_union_le _ _)\n rw [\u2190 filter_or]\n exact monotone_filter_right _ fun i h \u21a6 (h.ne_or_ne _).imp_right Ne.symm", "annotated_tactic": ["classical\n unfold <a>hammingDist</a>\n refine <a>le_trans</a> (<a>card_mono</a> ?_) ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Basic.lean | star_eq_iff_star_eq | [
112,
1
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113,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_diff_lt_of_lt_add | [
265,
1
] | [
268,
54
] | [{"tactic": "rw [measure_diff hst hs hs']", "annotated_tactic": ["rw [<a>measure_diff</a> hst hs hs']", [{"full_name": "MeasureTheory.measure_diff", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpace.lean", "def_pos": [252, 9], "def_end_pos": [252, 21]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.coe_restrictScalars | [
692,
1
] | [
693,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Holor.lean | HolorIndex.drop_drop | [
81,
1
] | [
82,
92
] | [{"tactic": "simp [add_comm, assocRight, drop, cast_type, List.drop_drop]", "annotated_tactic": ["simp [<a>add_comm</a>, <a>assocRight</a>, <a>drop</a>, <a>cast_type</a>, <a>List.drop_drop</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/SuccPred/Basic.lean | Order.pred_covby_of_not_isMin | [
634,
1
] | [
635,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_isEmpty_of_subsingleton | [
511,
1
] | [
512,
58
] | [{"tactic": "rw [sphere_eq_empty_of_subsingleton h\u03b5]", "annotated_tactic": ["rw [<a>sphere_eq_empty_of_subsingleton</a> h\u03b5]", [{"full_name": "Metric.sphere_eq_empty_of_subsingleton", "def_path": "Mathlib/Topology/MetricSpace/Basic.lean", "def_pos": [507, 9], "def_end_pos": [507, 40]}]], "state_before": "\u03b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_strictMono | [
227,
1
] | [
228,
56
] | [{"tactic": "classical exact (@orderIsoMultiset \u03b9 _).strictMono", "annotated_tactic": ["classical exact (@<a>orderIsoMultiset</a> \u03b9 _).<a>strictMono</a>", [{"full_name": "Finsupp.orderIsoMultiset", "def_path": "Mathlib/Data/Finsupp/Multiset.lean", "def_pos": [211, 5], "def_end_pos": [211, 21]}, {"full_name": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.deriv | [
47,
19
] | [
47,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.pb_inv | [
344,
1
] | [
347,
27
] | [{"tactic": "rw [PB, Matrix.fromBlocks_multiply, mul_invOf_self]", "annotated_tactic": ["rw [<a>PB</a>, <a>Matrix.fromBlocks_multiply</a>, <a>mul_invOf_self</a>]", [{"full_name": "LieAlgebra.Orthogonal.PB", "def_path": "Mathlib/Algebra/Lie/Classical.lean", "def_pos": [338, 5], "def_end_pos": [338, 7]}, {"full_name": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.exist_integer_multiples | [
94,
1
] | [
106,
6
] | [{"tactic": "haveI := Classical.propDecidable", "annotated_tactic": ["haveI := <a>Classical.propDecidable</a>", [{"full_name": "Classical.propDecidable", "def_path": "lake-packages/lean4/src/lean/Init/Classical.lean", "def_pos": [69, 49], "def_end_pos": [69, 62]}]], "state_before": "R : Type u_1\ninst\u271d\u2074 : Com... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.ofPiFork_π_app_left | [
462,
1
] | [
464,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.smul | [
1331,
11
] | [
1334,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Tower.lean | Submodule.span_algebraMap_image | [
350,
1
] | [
352,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | MeasureTheory.condexpIndL1_of_not_measurableSet | [
197,
1
] | [
199,
70
] | [{"tactic": "simp only [condexpIndL1, hs, dif_neg, not_false_iff, false_and_iff]", "annotated_tactic": ["simp only [<a>condexpIndL1</a>, hs, <a>dif_neg</a>, <a>not_false_iff</a>, <a>false_and_iff</a>]", [{"full_name": "MeasureTheory.condexpIndL1", "def_path": "Mathlib/MeasureTheory/Function/ConditionalExpectation/Conde... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.surj'' | [
90,
1
] | [
94,
7
] | [{"tactic": "rcases IsLocalization.surj M z with \u27e8\u27e8r, m\u27e9, e : z * _ = algebraMap R S r\u27e9", "annotated_tactic": ["rcases <a>IsLocalization.surj</a> M z with \u27e8\u27e8r, m\u27e9, e : z * _ = <a>algebraMap</a> R S r\u27e9", [{"full_name": "IsLocalization.surj", "def_path": "Mathlib/RingTheory/Localiz... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/LocallyFinite.lean | Finset.not_mem_uIcc_of_lt | [
1050,
1
] | [
1052,
31
] | [{"tactic": "rw [mem_uIcc]", "annotated_tactic": ["rw [<a>mem_uIcc</a>]", [{"full_name": "Finset.mem_uIcc", "def_path": "Mathlib/Order/LocallyFinite.lean", "def_pos": [502, 9], "def_end_pos": [502, 17]}]], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Locally... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_zero | [
119,
1
] | [
119,
55
] | [{"tactic": "simp [arg, le_refl]", "annotated_tactic": ["simp [<a>arg</a>, <a>le_refl</a>]", [{"full_name": "Complex.arg", "def_path": "Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean", "def_pos": [31, 19], "def_end_pos": [31, 22]}, {"full_name": "le_refl", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [50,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | MDifferentiable.prod_mk | [
781,
1
] | [
783,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/Group.lean | eq_inv_smul_iff | [
115,
1
] | [
116,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | IsSelfAdjoint.adjoint_conj | [
298,
1
] | [
302,
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/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_eq_union_of_projection | [
437,
1
] | [
450,
42
] | [{"tactic": "erw [mem_coe_basicOpen, TopologicalSpace.Opens.mem_sSup]", "annotated_tactic": ["erw [<a>mem_coe_basicOpen</a>, <a>TopologicalSpace.Opens.mem_sSup</a>]", [{"full_name": "ProjectiveSpectrum.mem_coe_basicOpen", "def_path": "Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean", "def_pos": [393, 9], "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_zero | [
79,
1
] | [
81,
80
] | [{"tactic": "rw [gramSchmidt_def, Iio_eq_Ico, Finset.Ico_self, Finset.sum_empty, sub_zero]", "annotated_tactic": ["rw [<a>gramSchmidt_def</a>, <a>Iio_eq_Ico</a>, <a>Finset.Ico_self</a>, <a>Finset.sum_empty</a>, <a>sub_zero</a>]", [{"full_name": "gramSchmidt_def", "def_path": "Mathlib/Analysis/InnerProductSpace/GramSchm... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | commutative_of_cyclic_center_quotient | [
471,
1
] | [
488,
26
] | [{"tactic": "simpa [Subtype.ext_iff] using hm", "annotated_tactic": ["simpa [<a>Subtype.ext_iff</a>] using hm", [{"full_name": "Subtype.ext_iff", "def_path": "Mathlib/Data/Subtype.lean", "def_pos": [69, 9], "def_end_pos": [69, 16]}]], "state_before": "\u03b1 : Type u\na\u271d : \u03b1\nG : Type u_1\nH : Type u_2\ninst\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_fix | [
1871,
1
] | [
1874,
28
] | [{"tactic": "simp [codeSupp, codeSupp', contSupp, Finset.union_assoc, Finset.union_left_comm,\n Finset.union_left_idem]", "annotated_tactic": ["simp [<a>codeSupp</a>, <a>codeSupp'</a>, <a>contSupp</a>, <a>Finset.union_assoc</a>, <a>Finset.union_left_comm</a>,\n <a>Finset.union_left_idem</a>]", [{"full_name": "Turin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.le_mulRothNumber | [
350,
1
] | [
352,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/AddCharacter.lean | AddChar.zmodChar_apply' | [
330,
1
] | [
332,
64
] | [{"tactic": "rw [pow_eq_pow_mod a h\u03b6, zmodChar_apply, ZMod.val_nat_cast a]", "annotated_tactic": ["rw [<a>pow_eq_pow_mod</a> a h\u03b6, <a>zmodChar_apply</a>, <a>ZMod.val_nat_cast</a> a]", [{"full_name": "pow_eq_pow_mod", "def_path": "Mathlib/Algebra/GroupPower/Basic.lean", "def_pos": [178, 9], "def_end_pos": [178... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesMonomorphisms_of_adjunction | [
190,
1
] | [
197,
41
] | [{"tactic": "intro Z g h H", "annotated_tactic": ["intro Z g h H", []], "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\nD : Type u\u2082\ninst\u271d\u00b9 : Category.{v\u2082, u\u2082} D\nE : Type u\u2083\ninst\u271d : Category.{v\u2083, u\u2083} E\nF : C \u2964 D\nG : D \u2964 C\na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/SumTwoSquares.lean | Nat.sq_add_sq_mul | [
55,
1
] | [
60,
38
] | [{"tactic": "zify at ha hb \u22a2", "annotated_tactic": ["zify at ha hb \u22a2", []], "state_before": "a b x y u v : \u2115\nha : a = x ^ 2 + y ^ 2\nhb : b = u ^ 2 + v ^ 2\n\u22a2 \u2203 r s, a * b = r ^ 2 + s ^ 2", "state_after": "a b x y u v : \u2115\nha : \u2191a = \u2191x ^ 2 + \u2191y ^ 2\nhb : \u2191b = \u2191u ^... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Span.lean | Submodule.span_neg | [
805,
1
] | [
809,
28
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R : Type u_1\nR\u2082 : Type u_2\nK : Type u_3\nM : Type u_4\nM\u2082 : Type u_5\nV : Type u_6\nS : Type u_7\ninst\u271d\u00b2 : Ring R\ninst\u271d\u00b9 : AddCommGroup M\ninst\u271d : Module R M\ns : Set M\n\u22a2 span R (-s) = span R (\u2191(-Line... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/GoldenRatio.lean | gold_irrational | [
139,
1
] | [
145,
13
] | [{"tactic": "have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)", "annotated_tactic": ["have := <a>Nat.Prime.irrational_sqrt</a> (show <a>Nat.Prime</a> 5 by norm_num)", [{"full_name": "Nat.Prime.irrational_sqrt", "def_path": "Mathlib/Data/Real/Irrational.lean", "def_pos": [100, 9], "def_end_pos": [100, 34... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | PMF.normalize_apply | [
250,
1
] | [
250,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Fintype.card_eq | [
205,
1
] | [
209,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Control/ULift.lean | PLift.bind_up | [
55,
1
] | [
56,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean | NonUnitalSubalgebra.ext | [
86,
1
] | [
87,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Torsion.lean | Submodule.mem_torsion'_iff | [
609,
1
] | [
610,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/PEquiv.lean | Equiv.toPEquiv_refl | [
478,
1
] | [
479,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Pointwise.lean | Filter.inv_le_iff_le_inv | [
259,
1
] | [
259,
90
] | [{"tactic": "rw [\u2190 Filter.inv_le_inv_iff, inv_inv]", "annotated_tactic": ["rw [\u2190 <a>Filter.inv_le_inv_iff</a>, <a>inv_inv</a>]", [{"full_name": "Filter.inv_le_inv_iff", "def_path": "Mathlib/Order/Filter/Pointwise.lean", "def_pos": [253, 19], "def_end_pos": [253, 33]}, {"full_name": "inv_inv", "def_path": "Mat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/CondCdf.lean | ProbabilityTheory.set_lintegral_preCdf_fst | [
307,
1
] | [
315,
35
] | [{"tactic": "have : \u2200 r, \u222b\u207b x in s, preCdf \u03c1 r x \u2202\u03c1.fst = \u222b\u207b x in s, (preCdf \u03c1 r * 1) x \u2202\u03c1.fst := by\n simp only [mul_one, eq_self_iff_true, forall_const]", "annotated_tactic": ["have : \u2200 r, \u222b\u207b x in s, <a>preCdf</a> \u03c1 r x \u2202\u03c1.fst = \u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_of_card_mul_and_disjoint | [
678,
1
] | [
682,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_eq_iff_exists_eq | [
132,
1
] | [
134,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.CompactSpace.isFiniteMeasure | [
3890,
1
] | [
3892,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Torsion.lean | Ideal.torsionOf_eq_top_iff | [
94,
1
] | [
97,
26
] | [{"tactic": "refine' \u27e8fun h => _, fun h => by simp [h]\u27e9", "annotated_tactic": ["refine' \u27e8fun h => _, fun h => by simp [h]\u27e9", []], "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u00b2 : Semiring R\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module R M\nm : M\n\u22a2 torsionOf R M m = \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.lift_cone | [
280,
1
] | [
281,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Analytic/Composition.lean | Composition.sigma_composition_eq_iff | [
953,
1
] | [
960,
37
] | [{"tactic": "refine' \u27e8by rintro rfl; exact \u27e8rfl, rfl\u27e9, _\u27e9", "annotated_tactic": ["refine' \u27e8by rintro rfl; exact \u27e8<a>rfl</a>, <a>rfl</a>\u27e9, _\u27e9", [{"full_name": "rfl", "def_path": "lake-packages/lean4/src/lean/Init/Prelude.lean", "def_pos": [281, 22], "def_end_pos": [281, 25]}, {"fu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/GroupAction/Embedding.lean | Function.Embedding.smul_apply | [
39,
1
] | [
40,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_finset_sup | [
916,
1
] | [
919,
49
] | [{"tactic": "rw [Finset.inf_eq_iInf]", "annotated_tactic": ["rw [<a>Finset.inf_eq_iInf</a>]", [{"full_name": "Finset.inf_eq_iInf", "def_path": "Mathlib/Data/Finset/Lattice.lean", "def_pos": [731, 9], "def_end_pos": [731, 20]}]], "state_before": "R : Type u_1\nR' : Type u_2\n\ud835\udd5c : Type u_3\n\ud835\udd5c\u2082 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.toLinearPMap_range | [
1068,
1
] | [
1071,
67
] | [{"tactic": "rwa [\u2190 LinearPMap.graph_map_snd_eq_range, toLinearPMap_graph_eq]", "annotated_tactic": ["rwa [\u2190 <a>LinearPMap.graph_map_snd_eq_range</a>, <a>toLinearPMap_graph_eq</a>]", [{"full_name": "LinearPMap.graph_map_snd_eq_range", "def_path": "Mathlib/LinearAlgebra/LinearPMap.lean", "def_pos": [797, 9], "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_eq_pow | [
376,
1
] | [
377,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioo.coe_mul | [
357,
1
] | [
358,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.uniqueDiffOn_image_iff | [
524,
1
] | [
526,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_sub | [
1134,
1
] | [
1135,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Nth.lean | Nat.range_nth_of_infinite | [
167,
1
] | [
171,
51
] | [{"tactic": "rw [nth_eq_orderIsoOfNat hf]", "annotated_tactic": ["rw [<a>nth_eq_orderIsoOfNat</a> hf]", [{"full_name": "Nat.nth_eq_orderIsoOfNat", "def_path": "Mathlib/Data/Nat/Nth.lean", "def_pos": [141, 9], "def_end_pos": [141, 29]}]], "state_before": "p : \u2115 \u2192 Prop\nhf : Set.Infinite (setOf p)\n\u22a2 Set.r... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_of_tendsto_zero | [
710,
1
] | [
712,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/Basic.lean | SetTheory.PGame.rightMoves_mul_cases | [
378,
1
] | [
384,
13
] | [{"tactic": "rw [\u2190 toRightMovesMul.apply_symm_apply k]", "annotated_tactic": ["rw [\u2190 toRightMovesMul.apply_symm_apply k]", []], "state_before": "x y : PGame\nk : RightMoves (x * y)\nP : RightMoves (x * y) \u2192 Prop\nhl : \u2200 (ix : LeftMoves x) (jy : RightMoves y), P (\u2191toRightMovesMul (Sum.inl (ix, j... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/EReal.lean | EReal.coe_nsmul | [
361,
1
] | [
362,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Lemmas.lean | Int.natAbs_inj_of_nonneg_of_nonpos | [
71,
1
] | [
73,
96
] | [{"tactic": "simpa only [Int.natAbs_neg] using natAbs_inj_of_nonneg_of_nonneg ha (neg_nonneg_of_nonpos hb)", "annotated_tactic": ["simpa only [<a>Int.natAbs_neg</a>] using <a>natAbs_inj_of_nonneg_of_nonneg</a> ha (<a>neg_nonneg_of_nonpos</a> hb)", [{"full_name": "Int.natAbs_neg", "def_path": "lake-packages/std/Std/Data... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Iic | [
95,
1
] | [
96,
39
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Fin/Lemmas.lean | Fin.succRecOn_succ | [
578,
9
] | [
580,
15
] | [{"tactic": "cases i", "annotated_tactic": ["cases i", []], "state_before": "motive : (n : Nat) \u2192 Fin n \u2192 Sort u_1\nzero : (n : Nat) \u2192 motive (n + 1) 0\nsucc : (n : Nat) \u2192 (i : Fin n) \u2192 motive n i \u2192 motive (Nat.succ n) (Fin.succ i)\nn : Nat\ni : Fin n\n\u22a2 succRecOn (Fin.succ i) zero su... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_inter_Iic | [
1745,
1
] | [
1747,
13
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : SemilatticeInf \u03b1\na b : \u03b1\n\u22a2 Iic a \u2229 Iic b = Iic (a \u2293 b)", "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : SemilatticeInf \u03b1\na b x : \u03b1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_left_addition | [
122,
1
] | [
124,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableOn.sum | [
367,
1
] | [
369,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Derivative.lean | Polynomial.coeff_derivative | [
56,
1
] | [
72,
13
] | [{"tactic": "rw [derivative_apply]", "annotated_tactic": ["rw [<a>derivative_apply</a>]", [{"full_name": "Polynomial.derivative_apply", "def_path": "Mathlib/Data/Polynomial/Derivative.lean", "def_pos": [52, 9], "def_end_pos": [52, 25]}]], "state_before": "R : Type u\nS : Type v\nT : Type w\n\u03b9 : Type y\nA : Type z\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuous_const | [
188,
1
] | [
189,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Disjoint.lean | disjoint_iff_inf_le | [
122,
1
] | [
123,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | all_mem_nhds_filter | [
1033,
1
] | [
1035,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/LocalCohomology.lean | localCohomology.Ideal.exists_pow_le_of_le_radical_of_fG | [
232,
1
] | [
238,
16
] | [{"tactic": "obtain \u27e8k, hk\u27e9 := J.exists_radical_pow_le_of_fg hJ", "annotated_tactic": ["obtain \u27e8k, hk\u27e9 := J.exists_radical_pow_le_of_fg hJ", []], "state_before": "R : Type u\ninst\u271d : CommRing R\nI J K : Ideal R\nhIJ : I \u2264 Ideal.radical J\nhJ : Ideal.FG (Ideal.radical J)\n\u22a2 \u2203 k, I... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.isPrimePow_of_has_chain | [
214,
1
] | [
218,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RepresentationTheory/Rep.lean | Rep.of_ρ | [
85,
1
] | [
86,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.inter_eq_iInter | [
1482,
1
] | [
1483,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.ofReal_set_integral_one_of_measure_ne_top | [
188,
1
] | [
196,
35
] | [{"tactic": "simp only [norm_one]", "annotated_tactic": ["simp only [<a>norm_one</a>]", [{"full_name": "NormOneClass.norm_one", "def_path": "Mathlib/Analysis/Normed/Field/Basic.lean", "def_pos": [134, 3], "def_end_pos": [134, 11]}]], "state_before": "\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\nE : Type u_3\nF : Type u_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.fromSubtype_eq_lift | [
767,
1
] | [
770,
34
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "J : Type w\nK : Type u_1\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasZeroMorphisms C\nf : J \u2192 C\ninst\u271d\u00b2 : HasBiproduct f\np : J \u2192 Prop\ninst\u271d\u00b9 : HasBiproduct (Subtype.restrict p f)\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mk_coe | [
191,
1
] | [
193,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_piEquivPiSubtypeProd | [
734,
1
] | [
744,
67
] | [{"tactic": "set e := (MeasurableEquiv.piEquivPiSubtypeProd \u03b1 p).symm", "annotated_tactic": ["set e := (<a>MeasurableEquiv.piEquivPiSubtypeProd</a> \u03b1 p).<a>symm</a>", [{"full_name": "MeasurableEquiv.piEquivPiSubtypeProd", "def_path": "Mathlib/MeasureTheory/MeasurableSpace/Basic.lean", "def_pos": [1670, 5], "d... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Fin/Lemmas.lean | USize.le_def | [
740,
9
] | [
740,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/ZMod/Basic.lean | ZMod.ringChar_zmod_n | [
126,
1
] | [
128,
21
] | [{"tactic": "rw [ringChar.eq_iff]", "annotated_tactic": ["rw [<a>ringChar.eq_iff</a>]", [{"full_name": "ringChar.eq_iff", "def_path": "Mathlib/Algebra/CharP/Basic.lean", "def_pos": [226, 9], "def_end_pos": [226, 15]}]], "state_before": "n : \u2115\n\u22a2 ringChar (ZMod n) = n", "state_after": "n : \u2115\n\u22a2 CharP... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.erase | [
174,
1
] | [
175,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order.lean | continuous_induced_dom | [
730,
1
] | [
731,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_left_ne_zero | [
436,
1
] | [
443,
7
] | [{"tactic": "by_cases h : p = 1", "annotated_tactic": ["by_cases h : p = 1", []], "state_before": "R : Type u\nS : Type v\na b : R\nm n : \u2115\n\u03b9 : Type y\ninst\u271d : Semiring R\np : R[X]\nhp : Monic p\nq : R[X]\nhq : q \u2260 0\n\u22a2 q * p \u2260 0", "state_after": "case pos\nR : Type u\nS : Type v\na b : R... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Quaternion.lean | Quaternion.algebraMap_def | [
1103,
1
] | [
1104,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_subgroup | [
80,
1
] | [
81,
50
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiffDef.lean | support_iteratedFDeriv_subset | [
1578,
1
] | [
1579,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Filter.mem_sets | [
116,
11
] | [
117,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.eq_zero_iff_dvd | [
133,
1
] | [
134,
64
] | [{"tactic": "rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_span_singleton]", "annotated_tactic": ["rw [<a>Ideal.Quotient.eq_zero_iff_mem</a>, <a>Ideal.mem_span_singleton</a>]", [{"full_name": "Ideal.Quotient.eq_zero_iff_mem", "def_path": "Mathlib/RingTheory/Ideal/Quotient.lean", "def_pos": [129, 9], "def_end_pos": [129... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/Computation.lean | Computation.destruct_map | [
701,
1
] | [
702,
35
] | [{"tactic": "apply s.recOn <;> intro <;> simp", "annotated_tactic": ["apply s.recOn <;> intro <;> simp", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nf : \u03b1 \u2192 \u03b2\ns : Computation \u03b1\n\u22a2 destruct (map f s) = lmap f (rmap (map f) (destruct s))", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.zero_cpow | [
56,
1
] | [
56,
81
] | [{"tactic": "simp [cpow_def, *]", "annotated_tactic": ["simp [<a>cpow_def</a>, *]", [{"full_name": "Complex.cpow_def", "def_path": "Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean", "def_pos": [37, 9], "def_end_pos": [37, 17]}]], "state_before": "x : \u2102\nh : x \u2260 0\n\u22a2 0 ^ x = 0", "state_after": "no goal... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.le_of_op_nnnorm_le | [
467,
1
] | [
468,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Functor.mapIso_refl | [
610,
1
] | [
611,
24
] | [] |
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