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/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjectionFn_vsub_mem_direction_orthogonal | [
266,
1
] | [
270,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupPower/Order.lean | sq_le_one_iff_abs_le_one | [
725,
1
] | [
726,
56
] | [{"tactic": "simpa only [one_pow, abs_one] using @sq_le_sq _ _ x 1", "annotated_tactic": ["simpa only [<a>one_pow</a>, <a>abs_one</a>] using @<a>sq_le_sq</a> _ _ x 1", [{"full_name": "one_pow", "def_path": "Mathlib/Algebra/GroupPower/Basic.lean", "def_pos": [90, 9], "def_end_pos": [90, 16]}, {"full_name": "abs_one", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.apply_mem_support | [
356,
1
] | [
357,
65
] | [{"tactic": "rw [mem_support, mem_support, Ne.def, Ne.def, apply_eq_iff_eq]", "annotated_tactic": ["rw [<a>mem_support</a>, <a>mem_support</a>, <a>Ne.def</a>, <a>Ne.def</a>, <a>apply_eq_iff_eq</a>]", [{"full_name": "Equiv.Perm.mem_support", "def_path": "Mathlib/GroupTheory/Perm/Support.lean", "def_pos": [290, 9], "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Prod.lean | Finset.product_empty | [
188,
1
] | [
189,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_const' | [
887,
1
] | [
887,
94
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 \u03b2 \u03b9 : Type u\na : Cardinal.{u}\n\u22a2 (sum fun x => a) = #\u03b9 * a", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_head_tail | [
168,
1
] | [
169,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Notation.lean | ONote.add_nfBelow | [
461,
1
] | [
474,
70
] | [{"tactic": "have h' := add_nfBelow (h\u2081.snd.mono <| le_of_lt h\u2081.lt) h\u2082", "annotated_tactic": ["have h' := add_nfBelow (h\u2081.snd.mono <| <a>le_of_lt</a> h\u2081.lt) h\u2082", [{"full_name": "le_of_lt", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [110, 9], "def_end_pos": [110, 17]}]], "state_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | MeasurableSpace.comap_map_le | [
180,
1
] | [
181,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.secondCountableTopology | [
672,
11
] | [
674,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Opposite.lean | Set.singleton_unop | [
84,
1
] | [
88,
25
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b1 : Type u_1\nx : \u03b1\u1d52\u1d56\n\u22a2 Set.unop {x} = {x.unop}", "state_after": "case h\n\u03b1 : Type u_1\nx : \u03b1\u1d52\u1d56\nx\u271d : \u03b1\n\u22a2 x\u271d \u2208 Set.unop {x} \u2194 x\u271d \u2208 {x.unop}"}, {"tactic": "construct... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/ContMDiff.lean | ContMDiffWithinAt.prod_map | [
1688,
1
] | [
1691,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Seminorm.lean | Seminorm.ball_finset_sup' | [
759,
1
] | [
765,
33
] | [{"tactic": "induction' H using Finset.Nonempty.cons_induction with a a s ha hs ih", "annotated_tactic": ["induction' H using <a>Finset.Nonempty.cons_induction</a> with a a s ha hs ih", [{"full_name": "Finset.Nonempty.cons_induction", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1275, 9], "def_end_pos": [1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Prod.lean | Filter.coprod_mono | [
501,
1
] | [
503,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/Slope.lean | HasDerivWithinAt.limsup_slope_norm_le | [
222,
1
] | [
227,
37
] | [{"tactic": "apply (hf.limsup_norm_slope_le hr).mono", "annotated_tactic": ["apply (hf.limsup_norm_slope_le hr).<a>mono</a>", [{"full_name": "Filter.Eventually.mono", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [1140, 9], "def_end_pos": [1140, 24]}]], "state_before": "E : Type u\ninst\u271d\u00b9 : Normed... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean | NonUnitalSubalgebra.iSupLift_mk | [
929,
1
] | [
933,
26
] | [{"tactic": "subst hT", "annotated_tactic": ["subst hT", []], "state_before": "R : Type u\nA : Type v\nB : Type w\ninst\u271d\u2079 : CommSemiring R\ninst\u271d\u2078 : NonUnitalNonAssocSemiring A\ninst\u271d\u2077 : Module R A\ninst\u271d\u2076 : IsScalarTower R A A\ninst\u271d\u2075 : SMulCommClass R A A\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Baire.lean | mem_residual | [
229,
1
] | [
236,
56
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\ninst\u271d\u00b9 : TopologicalSpace \u03b1\ninst\u271d : BaireSpace \u03b1\ns : Set \u03b1\n\u22a2 s \u2208 residual \u03b1 \u2194 \u2203 t x, IsG\u03b4 t \u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.isLimit_ext | [
50,
1
] | [
52,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullback_symmetry | [
1504,
1
] | [
1506,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Distribution/SchwartzSpace.lean | SchwartzMap.one_add_le_sup_seminorm_apply | [
530,
1
] | [
552,
72
] | [{"tactic": "rw [add_comm, add_pow]", "annotated_tactic": ["rw [<a>add_comm</a>, <a>add_pow</a>]", [{"full_name": "add_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [301, 3], "def_end_pos": [301, 14]}, {"full_name": "add_pow", "def_path": "Mathlib/Data/Nat/Choose/Sum.lean", "def_pos": [83, 9], "def_e... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IsAdjoinRoot.lean | IsAdjoinRootMonic.isIntegral_root | [
600,
1
] | [
601,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Basic.lean | Finset.mem_univ_val | [
77,
1
] | [
78,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.isUniformOfEmpty | [
252,
1
] | [
253,
36
] | [{"tactic": "simp [IsUniform, hP, nonUniforms]", "annotated_tactic": ["simp [<a>IsUniform</a>, hP, <a>nonUniforms</a>]", [{"full_name": "Finpartition.IsUniform", "def_path": "Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean", "def_pos": [229, 5], "def_end_pos": [229, 14]}, {"full_name": "Finpartition.nonUnifor... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Multiset.lean | Multiset.toDFinsupp_singleton | [
75,
1
] | [
76,
45
] | [{"tactic": "rw [\u2190 replicate_one, toDFinsupp_replicate]", "annotated_tactic": ["rw [\u2190 <a>replicate_one</a>, <a>toDFinsupp_replicate</a>]", [{"full_name": "Multiset.replicate_one", "def_path": "Mathlib/Data/Multiset/Basic.lean", "def_pos": [910, 9], "def_end_pos": [910, 22]}, {"full_name": "Multiset.toDFinsupp... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/Basic.lean | Set.not_one_mem_div_iff | [
1168,
1
] | [
1169,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Bool/Basic.lean | Bool.lt_iff | [
345,
1
] | [
345,
75
] | [{"tactic": "decide", "annotated_tactic": ["decide", []], "state_before": "\u22a2 \u2200 {x y : Bool}, x < y \u2194 x = false \u2227 y = true", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_sup | [
118,
1
] | [
121,
90
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\ninst\u271d : DecidableEq \u03b1\nf g : \u03b1 \u2192\u2080 \u2115\n\u22a2 \u2191toMultiset (f \u2294 g) = \u2191toMultiset f \u222a \u2191toMultiset g", "state_after": "case a\n\u03b1 : Type u_1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Fib.lean | Nat.fib_le_fib_succ | [
97,
1
] | [
97,
91
] | [{"tactic": "cases n <;> simp [fib_add_two]", "annotated_tactic": ["cases n <;> simp [<a>fib_add_two</a>]", [{"full_name": "Nat.fib_add_two", "def_path": "Mathlib/Data/Nat/Fib.lean", "def_pos": [90, 9], "def_end_pos": [90, 20]}]], "state_before": "n : \u2115\n\u22a2 fib n \u2264 fib (n + 1)", "state_after": "no goals"}... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.coe_lt_inducedMap_iff | [
215,
1
] | [
221,
22
] | [{"tactic": "refine \u27e8fun h => ?_, fun hq => ?_\u27e9", "annotated_tactic": ["refine \u27e8fun h => ?_, fun hq => ?_\u27e9", []], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\ninst\u271d\u00b3 : LinearOrderedField \u03b1\ninst\u271d\u00b2 : ConditionallyCompleteLinearOrdere... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Basic.lean | mul_rotate' | [
120,
1
] | [
121,
41
] | [{"tactic": "simp only [mul_left_comm, mul_comm]", "annotated_tactic": ["simp only [<a>mul_left_comm</a>, <a>mul_comm</a>]", [{"full_name": "mul_left_comm", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [96, 9], "def_end_pos": [96, 22]}, {"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.nfpBFamily_lt_ord_lift | [
394,
1
] | [
397,
69
] | [{"tactic": "rwa [mk_ordinal_out]", "annotated_tactic": ["rwa [<a>mk_ordinal_out</a>]", [{"full_name": "Cardinal.mk_ordinal_out", "def_path": "Mathlib/SetTheory/Ordinal/Basic.lean", "def_pos": [1303, 9], "def_end_pos": [1303, 23]}]], "state_before": "\u03b1 : Type u_1\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\no : Ordinal.... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Congruence.lean | RingCon.eq | [
164,
11
] | [
165,
16
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Associated.lean | Associates.quotient_mk_eq_mk | [
773,
1
] | [
774,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.closedUnder_univ | [
68,
1
] | [
68,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.volume_subtype_coe_le_volume | [
1467,
1
] | [
1469,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_le_of_lt | [
959,
1
] | [
965,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.IsLimit.isSuccLimit | [
849,
11
] | [
850,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finiteAt_principal | [
4080,
1
] | [
4081,
93
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.dvd_term_of_dvd_eval_of_dvd_terms | [
451,
1
] | [
462,
14
] | [{"tactic": "by_cases hi : i \u2208 f.support", "annotated_tactic": ["by_cases hi : i \u2208 f.support", []], "state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type u_1\nB' : Type u_2\na b : R\nn : \u2115\ninst\u271d\u2077 : CommSemiring A'\ninst\u271d\u2076 : Semiring B'\ninst\u271d\u2075 : CommSem... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.eq_empty_of_ssubset_singleton | [
1527,
1
] | [
1528,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_iUnion₂ | [
731,
1
] | [
733,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/PathConnected.lean | Path.coe_toContinuousMap | [
137,
1
] | [
138,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_toNat | [
108,
1
] | [
109,
47
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | t2_iff_isClosed_diagonal | [
983,
1
] | [
985,
76
] | [{"tactic": "simp only [t2Space_iff_disjoint_nhds, \u2190 isOpen_compl_iff, isOpen_iff_mem_nhds, Prod.forall,\n nhds_prod_eq, compl_diagonal_mem_prod, mem_compl_iff, mem_diagonal_iff]", "annotated_tactic": ["simp only [<a>t2Space_iff_disjoint_nhds</a>, \u2190 <a>isOpen_compl_iff</a>, <a>isOpen_iff_mem_nhds</a>, <a>Pro... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.addLsb_eq_twice_add_one | [
82,
1
] | [
83,
25
] | [{"tactic": "simp [addLsb, two_mul]", "annotated_tactic": ["simp [<a>addLsb</a>, <a>two_mul</a>]", [{"full_name": "Bitvec.addLsb", "def_path": "Mathlib/Data/Bitvec/Defs.lean", "def_pos": [278, 5], "def_end_pos": [278, 11]}, {"full_name": "two_mul", "def_path": "Mathlib/Algebra/Ring/Defs.lean", "def_pos": [177, 9], "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_mul_self_real | [
1052,
1
] | [
1055,
16
] | [{"tactic": "have h := @norm_add_mul_self \u211d _ _ _ _ x y", "annotated_tactic": ["have h := @<a>norm_add_mul_self</a> \u211d _ _ _ _ x y", [{"full_name": "norm_add_mul_self", "def_path": "Mathlib/Analysis/InnerProductSpace/Basic.lean", "def_pos": [1045, 9], "def_end_pos": [1045, 26]}]], "state_before": "\ud835\udd5c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Constructions.lean | isOpen_sigma_fst_preimage | [
1560,
1
] | [
1563,
55
] | [{"tactic": "rw [\u2190 biUnion_of_singleton s, preimage_iUnion\u2082]", "annotated_tactic": ["rw [\u2190 <a>biUnion_of_singleton</a> s, <a>preimage_iUnion\u2082</a>]", [{"full_name": "Set.biUnion_of_singleton", "def_path": "Mathlib/Data/Set/Lattice.lean", "def_pos": [1090, 9], "def_end_pos": [1090, 29]}, {"full_name":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Data/Nat/Bitwise.lean | Nat.mod_two_of_bodd | [
90,
1
] | [
100,
62
] | [{"tactic": "have := congr_arg bodd (mod_add_div n 2)", "annotated_tactic": ["have := <a>congr_arg</a> <a>bodd</a> (<a>mod_add_div</a> n 2)", [{"full_name": "congr_arg", "def_path": "Mathlib/Init/Logic.lean", "def_pos": [43, 7], "def_end_pos": [43, 16]}, {"full_name": "Nat.bodd", "def_path": "Mathlib/Init/Data/Nat/Bitw... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_const | [
717,
1
] | [
718,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_eq_sum | [
49,
1
] | [
50,
17
] | [{"tactic": "rw [eval\u2082_def]", "annotated_tactic": ["rw [<a>eval\u2082_def</a>]", [{"full_name": "Polynomial.eval\u2082_def", "def_path": "Mathlib/Data/Polynomial/Eval.lean", "def_pos": [1, 1], "def_end_pos": [1, 1]}]], "state_before": "R : Type u\nS : Type v\nT : Type w\n\u03b9 : Type y\na b : R\nm n : \u2115\nins... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.CokernelCofork.condition | [
540,
1
] | [
541,
35
] | [{"tactic": "rw [Cofork.condition, zero_comp]", "annotated_tactic": ["rw [<a>Cofork.condition</a>, <a>zero_comp</a>]", [{"full_name": "CategoryTheory.Limits.Cofork.condition", "def_path": "Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean", "def_pos": [396, 9], "def_end_pos": [396, 25]}, {"full_name": "CategoryTheor... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basic.lean | Submodule.comapSubtypeEquivOfLe_apply_coe | [
2364,
1
] | [
2367,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_map | [
336,
1
] | [
339,
6
] | [{"tactic": "rcases a with \u27e8\u27e9", "annotated_tactic": ["rcases a with \u27e8\u27e9", []], "state_before": "\u03b1 : Type u_1\nX : Type u_2\nY : Type u_3\nZ : Type u_4\ninst\u271d\u00b2 : TopologicalSpace X\ninst\u271d\u00b9 : TopologicalSpace Y\ninst\u271d : TopologicalSpace Z\nS : DiscreteQuotient X\nf : C(X, ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.eq_top_iff | [
719,
1
] | [
721,
61
] | [{"tactic": "rw [h]", "annotated_tactic": ["rw [h]", []], "state_before": "F : Type u_1\nR : Type u_2\nA : Type u_3\nB : Type u_4\ninst\u271d\u2079 : CommSemiring R\ninst\u271d\u2078 : StarRing R\ninst\u271d\u2077 : Semiring A\ninst\u271d\u2076 : Algebra R A\ninst\u271d\u2075 : StarRing A\ninst\u271d\u2074 : StarModule... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.lt_tsub_iff_right | [
431,
11
] | [
432,
77
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Basic.lean | norm_div_eq_zero_iff | [
2043,
1
] | [
2043,
89
] | [{"tactic": "rw [norm_eq_zero'', div_eq_one]", "annotated_tactic": ["rw [<a>norm_eq_zero''</a>, <a>div_eq_one</a>]", [{"full_name": "norm_eq_zero''", "def_path": "Mathlib/Analysis/Normed/Group/Basic.lean", "def_pos": [2019, 9], "def_end_pos": [2019, 23]}, {"full_name": "div_eq_one", "def_path": "Mathlib/Algebra/Group/B... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Periodic.lean | Function.Periodic.image_Ioc | [
306,
1
] | [
310,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.corepresentable_of_nat_iso | [
283,
1
] | [
285,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.exists_homeomorph_extension | [
488,
1
] | [
508,
35
] | [{"tactic": "obtain \u27e8u, hu, uf\u27e9 :\n \u2203 u : E \u2192 F, LipschitzWith (lipschitzExtensionConstant F * c) u \u2227 EqOn (f - \u21d1f') u s :=\n hf.lipschitzOnWith.extend_finite_dimension", "annotated_tactic": ["obtain \u27e8u, hu, uf\u27e9 :\n \u2203 u : E \u2192 F, <a>LipschitzWith</a> (<a>lipschitzEx... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Deprecated/Group.lean | Additive.isAddGroupHom | [
462,
1
] | [
464,
39
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.star_smul | [
702,
1
] | [
704,
92
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sum.lean | Finset.disj_sum_strictMono_right | [
108,
1
] | [
110,
58
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Dedup.lean | List.sum_map_count_dedup_eq_length | [
171,
1
] | [
173,
69
] | [{"tactic": "simpa using sum_map_count_dedup_filter_eq_countP (fun _ => True) l", "annotated_tactic": ["simpa using <a>sum_map_count_dedup_filter_eq_countP</a> (fun _ => <a>True</a>) l", [{"full_name": "List.sum_map_count_dedup_filter_eq_countP", "def_path": "Mathlib/Data/List/Dedup.lean", "def_pos": [147, 9], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Div.lean | Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zero | [
649,
1
] | [
662,
56
] | [{"tactic": "classical\nhaveI : Nontrivial R := Nontrivial.of_polynomial_ne hp\nrw [Ne.def, \u2190 IsRoot.def, \u2190 dvd_iff_isRoot]\nrintro \u27e8q, hq\u27e9\nhave := divByMonic_mul_pow_rootMultiplicity_eq p a\nrw [mul_comm, hq, \u2190 mul_assoc, \u2190 pow_succ', rootMultiplicity_eq_multiplicity, dif_neg hp] at this... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Lie/Abelian.lean | LieAlgebra.self_module_ker_eq_center | [
268,
1
] | [
270,
93
] | [{"tactic": "ext y", "annotated_tactic": ["ext y", []], "state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w\u2081\ninst\u271d\u00b9\u2070 : CommRing R\ninst\u271d\u2079 : LieRing L\ninst\u271d\u2078 : LieAlgebra R L\ninst\u271d\u2077 : AddCommGroup M\ninst\u271d\u2076 : Module R M\ninst\u271d\u2075 : LieRin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_neg | [
404,
1
] | [
405,
95
] | [{"tactic": "rw [\u2190 add_halves \u03c0, arccos, arcsin_neg, arccos, add_sub_assoc, sub_sub_self, sub_neg_eq_add]", "annotated_tactic": ["rw [\u2190 <a>add_halves</a> \u03c0, <a>arccos</a>, <a>arcsin_neg</a>, <a>arccos</a>, <a>add_sub_assoc</a>, <a>sub_sub_self</a>, <a>sub_neg_eq_add</a>]", [{"full_name": "add_halves... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Maps.lean | Embedding.map_nhds_of_mem | [
235,
1
] | [
237,
27
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.div_neg | [
66,
19
] | [
69,
56
] | [{"tactic": "rw [Nat.div_zero]", "annotated_tactic": ["rw [<a>Nat.div_zero</a>]", [{"full_name": "Nat.div_zero", "def_path": "lake-packages/std/Std/Data/Nat/Lemmas.lean", "def_pos": [559, 27], "def_end_pos": [559, 35]}]], "state_before": "m : Nat\n\u22a2 ofNat (m / 0) = -\u2191(m / 0)", "state_after": "m : Nat\n\u22a2 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Interval.lean | Finsupp.mem_rangeIcc_apply_iff | [
83,
1
] | [
83,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_subset_smul_left | [
173,
1
] | [
174,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.left_not_mem | [
179,
1
] | [
180,
8
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.one_eq_top | [
441,
1
] | [
441,
94
] | [{"tactic": "erw [Submodule.one_eq_range, LinearMap.range_id]", "annotated_tactic": ["erw [<a>Submodule.one_eq_range</a>, <a>LinearMap.range_id</a>]", [{"full_name": "Submodule.one_eq_range", "def_path": "Mathlib/Algebra/Algebra/Operations.lean", "def_pos": [86, 9], "def_end_pos": [86, 21]}, {"full_name": "LinearMap.ra... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_of_norm_sub_le | [
785,
1
] | [
794,
52
] | [{"tactic": "apply h.mono", "annotated_tactic": ["apply h.mono", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\nm : MeasurableSpace \u03b1\n\u03bc \u03bd : Measure \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b4\ninst\u271d\u00b9 : NormedAddCommGroup \u03b2\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_eq_iInter_thickening' | [
1393,
1
] | [
1396,
58
] | [{"tactic": "rw [\u2190 cthickening_zero]", "annotated_tactic": ["rw [\u2190 <a>cthickening_zero</a>]", [{"full_name": "Metric.cthickening_zero", "def_path": "Mathlib/Topology/MetricSpace/HausdorffDistance.lean", "def_pos": [1080, 9], "def_end_pos": [1080, 25]}]], "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.approximates_deriv_on_open_nhds | [
562,
1
] | [
569,
85
] | [{"tactic": "simp only [\u2190 and_assoc]", "annotated_tactic": ["simp only [\u2190 <a>and_assoc</a>]", [{"full_name": "and_assoc", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [177, 9], "def_end_pos": [177, 18]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2079 : NontriviallyNormedField \ud83... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_neg | [
89,
1
] | [
90,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_le_of_tendsto | [
1163,
1
] | [
1173,
46
] | [{"tactic": "obtain \u27e8i, hi\u27e9 := hCF.exists", "annotated_tactic": ["obtain \u27e8i, hi\u27e9 := hCF.exists", []], "state_before": "\u03b1 : Type u_1\nE : \u03b1 \u2192 Type u_2\np q : \u211d\u22650\u221e\ninst\u271d\u00b9 : (i : \u03b1) \u2192 NormedAddCommGroup (E i)\n\u03b9 : Type u_3\nl : Filter \u03b9\ninst... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_add | [
510,
1
] | [
513,
98
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/CubicDiscriminant.lean | Cubic.map_toPoly | [
458,
1
] | [
459,
100
] | [{"tactic": "simp only [map, toPoly, map_C, map_X, Polynomial.map_add, Polynomial.map_mul, Polynomial.map_pow]", "annotated_tactic": ["simp only [<a>map</a>, <a>toPoly</a>, <a>map_C</a>, <a>map_X</a>, <a>Polynomial.map_add</a>, <a>Polynomial.map_mul</a>, <a>Polynomial.map_pow</a>]", [{"full_name": "Cubic.map", "def_pat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Composition.lean | Composition.disjoint_range | [
395,
1
] | [
409,
51
] | [{"tactic": "classical\n wlog h' : i\u2081 < i\u2082\n exact (this c h.symm (h.lt_or_lt.resolve_left h')).symm\n by_contra d\n obtain \u27e8x, hx\u2081, hx\u2082\u27e9 :\n \u2203 x : Fin n, x \u2208 Set.range (c.embedding i\u2081) \u2227 x \u2208 Set.range (c.embedding i\u2082) :=\n Set.not_disjoint_iff.1 d\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | MeasurableEquiv.symm_apply_apply | [
1382,
1
] | [
1383,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Data/Bool/Lemmas.lean | Bool.not_eq_true_eq_eq_false | [
96,
1
] | [
96,
97
] | [{"tactic": "cases a <;> simp", "annotated_tactic": ["cases a <;> simp", []], "state_before": "a : Bool\n\u22a2 ((!a) = true) = (a = false)", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.congr_F | [
431,
1
] | [
431,
93
] | [{"tactic": "rw [h]", "annotated_tactic": ["rw [h]", []], "state_before": "C : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\ninst\u271d : HasFiniteCoproducts C\nS\u2081 S\u2082 : Split C\n\u03a6\u2081 \u03a6\u2082 : S\u2081 \u27f6 S\u2082\nh : \u03a6\u2081 = \u03a6\u2082\n\u22a2 \u03a6\u2081.f = \u03a6\u2082.f", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteBooleanAlgebra.lean | iInf_sup_eq | [
309,
1
] | [
310,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_insert' | [
873,
1
] | [
877,
47
] | [{"tactic": "rw [insert_eq, finprod_mem_union' _ _ hs, finprod_mem_singleton]", "annotated_tactic": ["rw [<a>insert_eq</a>, <a>finprod_mem_union'</a> _ _ hs, <a>finprod_mem_singleton</a>]", [{"full_name": "Set.insert_eq", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1310, 9], "def_end_pos": [1310, 18]}, {"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Filtered/Basic.lean | CategoryTheory.IsFiltered.of_right_adjoint | [
343,
1
] | [
345,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.nullHomotopicMap'_f_eq_zero | [
428,
1
] | [
432,
44
] | [{"tactic": "simp only [nullHomotopicMap']", "annotated_tactic": ["simp only [<a>nullHomotopicMap'</a>]", [{"full_name": "Homotopy.nullHomotopicMap'", "def_path": "Mathlib/Algebra/Homology/Homotopy.lean", "def_pos": [262, 5], "def_end_pos": [262, 22]}]], "state_before": "\u03b9 : Type u_1\nV : Type u\ninst\u271d\u00b9 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | MDifferentiable.const_smul | [
1625,
1
] | [
1626,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/Basic.lean | Equiv.sumCompl_apply_inr | [
580,
1
] | [
582,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.left_of_add_measure | [
704,
1
] | [
705,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenspace_div | [
132,
1
] | [
141,
96
] | [{"tactic": "rw [div_eq_mul_inv, mul_comm]", "annotated_tactic": ["rw [<a>div_eq_mul_inv</a>, <a>mul_comm</a>]", [{"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_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean | Orientation.oangle_sign_sub_left_swap | [
1026,
1
] | [
1027,
74
] | [{"tactic": "rw [oangle_sign_sub_left_eq_neg, o.oangle_rev y x, Real.Angle.sign_neg]", "annotated_tactic": ["rw [<a>oangle_sign_sub_left_eq_neg</a>, o.oangle_rev y x, <a>Real.Angle.sign_neg</a>]", [{"full_name": "Orientation.oangle_sign_sub_left_eq_neg", "def_path": "Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.empty | [
114,
1
] | [
116,
40
] | [{"tactic": "have := \u03bc.sup_disjoint' \u22a5 \u22a5", "annotated_tactic": ["have := \u03bc.sup_disjoint' \u22a5 \u22a5", []], "state_before": "G : Type w\ninst\u271d : TopologicalSpace G\n\u03bc : Content G\n\u22a2 (fun s => \u2191(toFun \u03bc s)) \u22a5 = 0", "state_after": "G : Type w\ninst\u271d : TopologicalSp... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Category/NonemptyFinLinOrd.lean | NonemptyFinLinOrd.mono_iff_injective | [
147,
1
] | [
160,
10
] | [{"tactic": "refine' \u27e8_, ConcreteCategory.mono_of_injective f\u27e9", "annotated_tactic": ["refine' \u27e8_, <a>ConcreteCategory.mono_of_injective</a> f\u27e9", [{"full_name": "CategoryTheory.ConcreteCategory.mono_of_injective", "def_path": "Mathlib/CategoryTheory/ConcreteCategory/Basic.lean", "def_pos": [153, 9],... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Disjoint.lean | codisjoint_top_left | [
243,
1
] | [
243,
68
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/PFilter.lean | Order.PFilter.mem_principal | [
121,
9
] | [
121,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/InitialSeg.lean | PrincipalSeg.subrelIso_apply | [
415,
1
] | [
417,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.ofEquiv_F | [
204,
1
] | [
205,
22
] | [{"tactic": "delta ofEquiv", "annotated_tactic": ["delta <a>ofEquiv</a>", [{"full_name": "Ctop.Realizer.ofEquiv", "def_path": "Mathlib/Data/Analysis/Topology.lean", "def_pos": [192, 5], "def_end_pos": [192, 12]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03c3 : Type u_3\n\u03c4 : Type u_4\ninst\u271d :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Opposites.lean | AddOpposite.unop_div | [
427,
1
] | [
428,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Finprod.lean | finsum_mul | [
1219,
1
] | [
1221,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.preimage_Iio | [
38,
1
] | [
40,
23
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_2\n\u03b2 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b1\ninst\u271d : Preorder \u03b2\ne : \u03b1 \u2243o \u03b2\nb : \u03b2\n\u22a2 \u2191e \u207b\u00b9' Iio b = Iio (\u2191(symm e) b)", "state_after": "case h\n\u03b1 : Type u_2\... |
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