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/NumberTheory/RamificationInertia.lean | Ideal.rank_prime_pow_ramificationIdx | [
649,
1
] | [
659,
45
] | [{"tactic": "letI : NeZero e := \u27e8he\u27e9", "annotated_tactic": ["letI : <a>NeZero</a> e := \u27e8he\u27e9", [{"full_name": "NeZero", "def_path": "Mathlib/Algebra/NeZero.lean", "def_pos": [25, 7], "def_end_pos": [25, 13]}]], "state_before": "R : Type u\ninst\u271d\u2075 : CommRing R\nS : Type v\ninst\u271d\u2074 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Quot.lean | Quotient.liftOn₂'_mk'' | [
647,
11
] | [
649,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Maps.lean | openEmbedding_iff_continuous_injective_open | [
632,
1
] | [
635,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.isoWhiskerLeft_hom | [
159,
1
] | [
161,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Minimal.lean | maximals_Ioc | [
401,
1
] | [
403,
88
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.of_map_of_injective | [
513,
1
] | [
521,
39
] | [{"tactic": "apply_fun f", "annotated_tactic": ["apply_fun f", []], "state_before": "M : Type u_1\nN : Type u_2\nG : Type u_3\nR : Type u_4\nS : Type u_5\nF : Type u_6\ninst\u271d\u00b3 : CommMonoid M\ninst\u271d\u00b2 : CommMonoid N\ninst\u271d\u00b9 : DivisionCommMonoid G\nk l : \u2115\n\u03b6 : M\nf : F\nh\u271d : I... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.algebraMap_lift | [
939,
1
] | [
940,
68
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | imp_false | [
124,
1
] | [
124,
48
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.fdiv_nonpos | [
107,
1
] | [
108,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Basic.lean | Multiset.map_map | [
1283,
1
] | [
1284,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | OrderIso.tendsto_atTop_iff | [
476,
1
] | [
478,
47
] | [{"tactic": "rw [\u2190 e.comap_atTop, tendsto_comap_iff]", "annotated_tactic": ["rw [\u2190 e.comap_atTop, <a>tendsto_comap_iff</a>]", [{"full_name": "Filter.tendsto_comap_iff", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [3069, 9], "def_end_pos": [3069, 26]}]], "state_before": "\u03b9 : Type u_1\n\u03b9... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/QPF/Multivariate/Constructions/Cofix.lean | MvQPF.corec_roll | [
520,
1
] | [
526,
33
] | [{"tactic": "mv_bisim x\u2080 with R a b x Ha Hb", "annotated_tactic": ["mv_bisim x\u2080 with R a b x Ha Hb", []], "state_before": "n : \u2115\nF : TypeVec.{u} (n + 1) \u2192 Type u\nmvf : MvFunctor F\nq : MvQPF F\n\u03b1 : TypeVec.{u} n\nX Y : Type u\nx\u2080 : X\nf : X \u2192 Y\ng : Y \u2192 F (\u03b1 ::: X)\n\u22a2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/Minimal.lean | IsOpen.exists_smul_mem | [
70,
1
] | [
72,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.image_preimage_subset | [
501,
1
] | [
502,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_sub | [
1266,
1
] | [
1269,
61
] | [{"tactic": "simp only [hf', sub_apply, mapRange_apply]", "annotated_tactic": ["simp only [hf', <a>sub_apply</a>, <a>mapRange_apply</a>]", [{"full_name": "Finsupp.sub_apply", "def_path": "Mathlib/Data/Finsupp/Defs.lean", "def_pos": [1262, 9], "def_end_pos": [1262, 18]}, {"full_name": "Finsupp.mapRange_apply", "def_path... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Noetherian.lean | isNoetherianRing_of_surjective | [
608,
1
] | [
611,
82
] | [{"tactic": "rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H \u22a2", "annotated_tactic": ["rw [<a>isNoetherianRing_iff</a>, <a>isNoetherian_iff_wellFounded</a>] at H \u22a2", [{"full_name": "isNoetherianRing_iff", "def_path": "Mathlib/RingTheory/Noetherian.lean", "def_pos": [512, 9], "def_end_pos": [512, ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Finite/Basic.lean | ZMod.pow_card_pow | [
508,
1
] | [
511,
43
] | [{"tactic": "induction' n with n ih", "annotated_tactic": ["induction' n with n ih", []], "state_before": "K : Type u_1\nR : Type u_2\nn p : \u2115\ninst\u271d : Fact (Nat.Prime p)\nx : ZMod p\n\u22a2 x ^ p ^ n = x", "state_after": "case zero\nK : Type u_1\nR : Type u_2\np : \u2115\ninst\u271d : Fact (Nat.Prime p)\nx :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Gauge.lean | gauge_smul_left_of_nonneg | [
285,
1
] | [
303,
40
] | [{"tactic": "obtain rfl | ha' := ha.eq_or_lt", "annotated_tactic": ["obtain rfl | ha' := ha.eq_or_lt", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\ninst\u271d\u2078 : AddCommGroup E\ninst\u271d\u2077 : Module \u211d E\ns\u271d t : Set E\na\u271d : \u211d\n\u03b1 : Type u_4\ninst\u271d\u207... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/ModEq.lean | Int.ModEq.refl | [
46,
11
] | [
47,
11
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.iota_eq_reverse_range' | [
2106,
1
] | [
2108,
99
] | [{"tactic": "simp [iota, range'_concat, iota_eq_reverse_range' n, reverse_append, Nat.add_comm]", "annotated_tactic": ["simp [<a>iota</a>, <a>range'_concat</a>, iota_eq_reverse_range' n, <a>reverse_append</a>, <a>Nat.add_comm</a>]", [{"full_name": "List.iota", "def_path": "lake-packages/lean4/src/lean/Init/Data/List/Ba... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.natDegree_basisDivisor_of_ne | [
186,
1
] | [
187,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.induction | [
193,
1
] | [
215,
35
] | [{"tactic": "let s : Subalgebra R (TensorAlgebra R M) :=\n { carrier := C\n mul_mem' := @h_mul\n add_mem' := @h_add\n algebraMap_mem' := h_grade0 }", "annotated_tactic": ["let s : <a>Subalgebra</a> R (<a>TensorAlgebra</a> R M) :=\n { carrier := C\n mul_mem' := @h_mul\n add_mem' := @h_add\n a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_X_add_C_of_degree_eq_one | [
452,
1
] | [
455,
73
] | [{"tactic": "simp only [leadingCoeff, natDegree_eq_of_degree_eq_some h]", "annotated_tactic": ["simp only [<a>leadingCoeff</a>, <a>natDegree_eq_of_degree_eq_some</a> h]", [{"full_name": "Polynomial.leadingCoeff", "def_path": "Mathlib/Data/Polynomial/Degree/Definitions.lean", "def_pos": [70, 5], "def_end_pos": [70, 17]}... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_mono | [
2456,
1
] | [
2457,
31
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | or_iff_right_iff_imp | [
298,
9
] | [
299,
36
] | [{"tactic": "rw [or_comm, or_iff_left_iff_imp]", "annotated_tactic": ["rw [<a>or_comm</a>, <a>or_iff_left_iff_imp</a>]", [{"full_name": "or_comm", "def_path": "lake-packages/std/Std/Logic.lean", "def_pos": [263, 9], "def_end_pos": [263, 16]}, {"full_name": "or_iff_left_iff_imp", "def_path": "lake-packages/std/Std/Logic... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sups.lean | Finset.biUnion_image_inf_right | [
388,
1
] | [
389,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.const_mul_atBot | [
1264,
1
] | [
1266,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesEpimorphisms.iso_iff | [
142,
1
] | [
144,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct/Tower.lean | TensorProduct.AlgebraTensorModule.rid_eq_rid | [
308,
1
] | [
309,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Interval.lean | NonemptyInterval.fst_dual | [
108,
1
] | [
109,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/TopologicalSimplex.lean | SimplexCategory.coe_toTopMap | [
73,
1
] | [
75,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ContinuedFractions/Computation/Approximations.lean | GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv | [
114,
1
] | [
126,
28
] | [{"tactic": "suffices (\u230aifp_n.fr\u207b\u00b9\u230b : K) \u2264 ifp_n.fr\u207b\u00b9 by\n cases' ifp_n with _ ifp_n_fr\n have : ifp_n_fr \u2260 0 := by\n intro h\n simp [h, IntFractPair.stream, nth_stream_eq] at succ_nth_stream_eq\n have : IntFractPair.of ifp_n_fr\u207b\u00b9 = ifp_succ_n := by\n simpa ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_bit1 | [
149,
1
] | [
149,
97
] | [{"tactic": "simp [bit1]", "annotated_tactic": ["simp [<a>bit1</a>]", [{"full_name": "bit1", "def_path": "Mathlib/Init/ZeroOne.lean", "def_pos": [39, 34], "def_end_pos": [39, 38]}]], "state_before": "R : Type u\nS : Type v\nT : Type w\n\u03b9 : Type y\nA : Type z\na\u271d b : R\nn : \u2115\ninst\u271d : Semiring R\na :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Card.lean | Finset.two_lt_card_iff | [
588,
1
] | [
600,
28
] | [{"tactic": "refine' \u27e8fun h => _, _\u27e9", "annotated_tactic": ["refine' \u27e8fun h => _, _\u27e9", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ns t : Finset \u03b1\nf : \u03b1 \u2192 \u03b2\nn : \u2115\n\u22a2 2 < card s \u2194 \u2203 a b c, a \u2208 s \u2227 b \u2208 s \u2227 c \u2208 s \u2227 a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/ModularLattice.lean | Disjoint.disjoint_sup_right_of_disjoint_sup_left | [
395,
1
] | [
401,
77
] | [{"tactic": "rw [disjoint_iff_inf_le, \u2190 h.eq_bot, sup_comm]", "annotated_tactic": ["rw [<a>disjoint_iff_inf_le</a>, \u2190 h.eq_bot, <a>sup_comm</a>]", [{"full_name": "disjoint_iff_inf_le", "def_path": "Mathlib/Order/Disjoint.lean", "def_pos": [122, 9], "def_end_pos": [122, 28]}, {"full_name": "sup_comm", "def_pat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finmap.lean | Finmap.union_toFinmap | [
574,
1
] | [
575,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_div | [
1396,
1
] | [
1397,
59
] | [{"tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, coe_mul, coe_inv hr]", "annotated_tactic": ["rw [<a>div_eq_mul_inv</a>, <a>div_eq_mul_inv</a>, <a>coe_mul</a>, <a>coe_inv</a> hr]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}, {"full_name... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | Filter.le_lift'_closure | [
594,
1
] | [
595,
57
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/Basic.lean | Complex.ringHom_eq_ofReal_of_continuous | [
390,
1
] | [
392,
23
] | [{"tactic": "convert congr_arg AlgHom.toRingHom <| Subsingleton.elim (AlgHom.mk' f <| map_real_smul f h)\n (Algebra.ofId \u211d \u2102)", "annotated_tactic": ["convert <a>congr_arg</a> <a>AlgHom.toRingHom</a> <| <a>Subsingleton.elim</a> (<a>AlgHom.mk'</a> f <| <a>map_real_smul</a> f h)\n (<a>Algebra.ofId</a> \u211d... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/Lemmas.lean | Int.neg_add_lt_of_lt_add | [
1070,
11
] | [
1072,
37
] | [{"tactic": "have h := Int.add_lt_add_left h (-b)", "annotated_tactic": ["have h := <a>Int.add_lt_add_left</a> h (-b)", [{"full_name": "Int.add_lt_add_left", "def_path": "lake-packages/std/Std/Data/Int/Lemmas.lean", "def_pos": [754, 19], "def_end_pos": [754, 34]}]], "state_before": "a b c : Int\nh : a < b + c\n\u22a2 -... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.eq_re_iff_mem_range_coe | [
710,
1
] | [
712,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Multiset/Fold.lean | Multiset.fold_dedup_idem | [
115,
1
] | [
120,
67
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nop : \u03b1 \u2192 \u03b1 \u2192 \u03b1\nhc : IsCommutative \u03b1 op\nha : IsAssociative \u03b1 op\ninst\u271d : DecidableEq \u03b1\nhi : IsIdempotent \u03b1 op\ns : Multiset \u03b1\nb : \u03b1\n\u22a2 fold op ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.pullbackIsoPullback_inv_fst | [
696,
1
] | [
698,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Operations.lean | Ideal.isPrimary_inf | [
1938,
1
] | [
1947,
24
] | [{"tactic": "rw [radical_inf, hij, inf_idem]", "annotated_tactic": ["rw [<a>radical_inf</a>, hij, <a>inf_idem</a>]", [{"full_name": "Ideal.radical_inf", "def_path": "Mathlib/RingTheory/Ideal/Operations.lean", "def_pos": [995, 9], "def_end_pos": [995, 20]}, {"full_name": "inf_idem", "def_path": "Mathlib/Order/Lattice.le... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.le_max_of_eq | [
1309,
1
] | [
1310,
51
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.IsFraction.eq_mk' | [
108,
1
] | [
118,
21
] | [{"tactic": "rcases hf with \u27e8r, s, h\u27e9", "annotated_tactic": ["rcases hf with \u27e8r, s, h\u27e9", []], "state_before": "R : Type u\ninst\u271d : CommRing R\nU : Opens \u2191(PrimeSpectrum.Top R)\nf : (x : { x // x \u2208 U }) \u2192 Localizations R \u2191x\nhf : IsFraction f\n\u22a2 \u2203 r s,\n \u2200 (... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right | [
544,
1
] | [
549,
94
] | [{"tactic": "simpa only [integral_const, smul_eq_mul, mul_one] using\n measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right hab hmeas hf hu hv", "annotated_tactic": ["simpa only [<a>integral_const</a>, <a>smul_eq_mul</a>, <a>mul_one</a>] using\n <a>measure_integral_sub_integral_sub_linear_isLittle... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/Defs.lean | Equiv.sigmaCongrRight_refl | [
745,
1
] | [
746,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean | jacobiSym.pow_left | [
201,
1
] | [
203,
56
] | [{"tactic": "rw [_root_.pow_zero, _root_.pow_zero, one_left]", "annotated_tactic": ["rw [<a>_root_.pow_zero</a>, <a>_root_.pow_zero</a>, <a>one_left</a>]", [{"full_name": "pow_zero", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [639, 9], "def_end_pos": [639, 17]}, {"full_name": "pow_zero", "def_path": "Mat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Setoid/Partition.lean | Setoid.sUnion_classes | [
196,
1
] | [
197,
95
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Hausdorff.lean | MeasureTheory.OuterMeasure.trim_mkMetric | [
414,
1
] | [
419,
7
] | [{"tactic": "simp only [mkMetric, mkMetric'.eq_iSup_nat, trim_iSup]", "annotated_tactic": ["simp only [<a>mkMetric</a>, <a>mkMetric'.eq_iSup_nat</a>, <a>trim_iSup</a>]", [{"full_name": "MeasureTheory.OuterMeasure.mkMetric", "def_path": "Mathlib/MeasureTheory/Measure/Hausdorff.lean", "def_pos": [264, 5], "def_end_pos": ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Congruence.lean | Con.map_apply | [
1058,
1
] | [
1060,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Semiquot.lean | Semiquot.mem_pure_self | [
164,
1
] | [
165,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IsAdjoinRoot.lean | IsAdjoinRoot.map_X | [
141,
1
] | [
141,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.inter_mul_subset | [
448,
1
] | [
449,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.aroots_X_sub_C | [
942,
1
] | [
944,
67
] | [{"tactic": "rw [aroots_def, Polynomial.map_sub, map_X, map_C, roots_X_sub_C]", "annotated_tactic": ["rw [<a>aroots_def</a>, <a>Polynomial.map_sub</a>, <a>map_X</a>, <a>map_C</a>, <a>roots_X_sub_C</a>]", [{"full_name": "Polynomial.aroots_def", "def_path": "Mathlib/Data/Polynomial/RingDivision.lean", "def_pos": [920, 9]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_lt_two | [
707,
1
] | [
714,
68
] | [{"tactic": "norm_num", "annotated_tactic": ["norm_num", []], "state_before": "x : \u211d\n\u22a2 sqrtTwoAddSeries 0 0 < 2", "state_after": "no goals"}, {"tactic": "refine' lt_of_lt_of_le _ (sqrt_sq zero_lt_two.le).le", "annotated_tactic": ["refine' <a>lt_of_lt_of_le</a> _ (<a>sqrt_sq</a> zero_lt_two.le).<a>le</a>", [{... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.ext | [
121,
1
] | [
122,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.det_of_card_zero | [
93,
1
] | [
97,
17
] | [{"tactic": "rw [Fintype.card_eq_zero_iff] at h", "annotated_tactic": ["rw [<a>Fintype.card_eq_zero_iff</a>] at h", [{"full_name": "Fintype.card_eq_zero_iff", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [533, 9], "def_end_pos": [533, 25]}]], "state_before": "R : Type u\ninst\u271d\u00b3 : CommRing R\nn G :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/CondDistrib.lean | MeasureTheory.Integrable.integral_condDistrib_map | [
176,
1
] | [
180,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Subfield.lean | Subfield.coe_iSup_of_directed | [
841,
1
] | [
843,
53
] | [{"tactic": "simp [mem_iSup_of_directed hS]", "annotated_tactic": ["simp [<a>mem_iSup_of_directed</a> hS]", [{"full_name": "Subfield.mem_iSup_of_directed", "def_path": "Mathlib/FieldTheory/Subfield.lean", "def_pos": [822, 9], "def_end_pos": [822, 29]}]], "state_before": "K : Type u\nL : Type v\nM : Type w\ninst\u271d\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul | [
1188,
1
] | [
1201,
62
] | [{"tactic": "rw [IntegrableOn, \u2190 restrict_map_withDensity_abs_det_fderiv_eq_addHaar \u03bc hs hf' hf,\n (measurableEmbedding_of_fderivWithin hs hf' hf).integrable_map_iff]", "annotated_tactic": ["rw [<a>IntegrableOn</a>, \u2190 <a>restrict_map_withDensity_abs_det_fderiv_eq_addHaar</a> \u03bc hs hf' hf,\n (<a>m... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Bounds/Basic.lean | isLUB_empty | [
895,
1
] | [
896,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_sup_sup_boundary_inf | [
126,
1
] | [
129,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Hom/Bounded.lean | TopHom.dual_id | [
729,
1
] | [
730,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.eq_smul_exp_of_ne_zero | [
183,
1
] | [
186,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Lex.lean | List.Lex.nil_left_or_eq_nil | [
64,
1
] | [
67,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Process/Stopping.lean | MeasureTheory.IsStoppingTime.measurableSet_inter_le_iff | [
655,
1
] | [
666,
14
] | [{"tactic": "constructor <;> intro h", "annotated_tactic": ["constructor <;> intro h", []], "state_before": "\u03a9 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nm : MeasurableSpace \u03a9\ninst\u271d\u2075 : LinearOrder \u03b9\nf : Filtration \u03b9 m\n\u03c4 \u03c0 : \u03a9 \u2192 \u03b9\ninst\u271d\u2074 : Topol... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_torsionBySet_eq_top | [
370,
1
] | [
371,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/MongePoint.lean | Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter | [
199,
1
] | [
206,
64
] | [{"tactic": "simp_rw [mongePoint_eq_affineCombination_of_pointsWithCircumcenter,\n centroid_eq_affineCombination_of_pointsWithCircumcenter, affineCombination_vsub,\n mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub h]", "annotated_tactic": ["simp_rw [<a>mongePoint_eq_affineCombination_of_pointsWithCircumcente... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Permutation.lean | List.permutationsAux_nil | [
214,
1
] | [
215,
44
] | [{"tactic": "rw [permutationsAux, permutationsAux.rec]", "annotated_tactic": ["rw [<a>permutationsAux</a>, <a>permutationsAux.rec</a>]", [{"full_name": "List.permutationsAux", "def_path": "Mathlib/Data/List/Defs.lean", "def_pos": [268, 5], "def_end_pos": [268, 20]}, {"full_name": "List.permutationsAux.rec", "def_path":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/DedekindDomain/PID.lean | IsDedekindDomain.isPrincipalIdealRing_localization_over_prime | [
256,
1
] | [
270,
101
] | [{"tactic": "letI := Classical.decEq (Ideal S\u209a)", "annotated_tactic": ["letI := <a>Classical.decEq</a> (<a>Ideal</a> S\u209a)", [{"full_name": "Classical.decEq", "def_path": "Mathlib/Logic/Basic.lean", "def_pos": [983, 19], "def_end_pos": [983, 24]}, {"full_name": "Ideal", "def_path": "Mathlib/RingTheory/Ideal/Bas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.image_injective | [
1573,
1
] | [
1576,
44
] | [{"tactic": "refine' \u27e8fun h x x' hx => _, Injective.image_injective\u27e9", "annotated_tactic": ["refine' \u27e8fun h x x' hx => _, <a>Injective.image_injective</a>\u27e9", [{"full_name": "Function.Injective.image_injective", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [1330, 9], "def_end_pos": [1330, 34... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_toLp | [
277,
1
] | [
278,
55
] | [{"tactic": "erw [norm_def, snorm_congr_ae (Mem\u2112p.coeFn_toLp hf)]", "annotated_tactic": ["erw [<a>norm_def</a>, <a>snorm_congr_ae</a> (<a>Mem\u2112p.coeFn_toLp</a> hf)]", [{"full_name": "MeasureTheory.Lp.norm_def", "def_path": "Mathlib/MeasureTheory/Function/LpSpace.lean", "def_pos": [259, 9], "def_end_pos": [259,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsClosed.Icc_subset_of_forall_mem_nhdsWithin | [
380,
1
] | [
387,
70
] | [{"tactic": "apply hs.Icc_subset_of_forall_exists_gt ha", "annotated_tactic": ["apply hs.Icc_subset_of_forall_exists_gt ha", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2077 : ConditionallyCompleteLinearOrder \u03b1\ninst\u271d\u2076 : TopologicalSpace \u03b1\ninst\u271d\u2075 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Order.lean | Complex.zero_le_real | [
74,
1
] | [
75,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.zero_div_subset | [
1189,
1
] | [
1189,
84
] | [{"tactic": "simp [subset_iff, mem_div]", "annotated_tactic": ["simp [<a>subset_iff</a>, <a>mem_div</a>]", [{"full_name": "Finset.subset_iff", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [371, 9], "def_end_pos": [371, 19]}, {"full_name": "Finset.mem_div", "def_path": "Mathlib/Data/Finset/Pointwise.lean", "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.toOrderIso_eq_coe | [
414,
1
] | [
415,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RepresentationTheory/Rep.lean | Rep.MonoidalClosed.linearHomEquiv_hom | [
490,
1
] | [
492,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Pairing.lean | Nat.pair_lt_max_add_one_sq | [
152,
1
] | [
158,
24
] | [{"tactic": "rw [pair, add_sq, mul_one, two_mul, sq, add_assoc, add_assoc]", "annotated_tactic": ["rw [<a>pair</a>, <a>add_sq</a>, <a>mul_one</a>, <a>two_mul</a>, <a>sq</a>, <a>add_assoc</a>, <a>add_assoc</a>]", [{"full_name": "Nat.pair", "def_path": "Mathlib/Data/Nat/Pairing.lean", "def_pos": [37, 5], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.preimage_smul_inv | [
905,
1
] | [
906,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_carrier | [
171,
1
] | [
172,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Pointwise.lean | Filter.neBot_inv_iff | [
221,
1
] | [
222,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Dilation.lean | Dilation.ratio_pos | [
161,
1
] | [
162,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.qRight_one_left | [
190,
1
] | [
196,
21
] | [{"tactic": "dsimp only", "annotated_tactic": ["dsimp only", []], "state_before": "\u03b8 : \u2191I\n\u22a2 1 * (1 + \u2191(1, \u03b8).2) \u2264 2 * \u2191(1, \u03b8).1", "state_after": "\u03b8 : \u2191I\n\u22a2 1 * (1 + \u2191\u03b8) \u2264 2 * \u21911"}, {"tactic": "rw [coe_one, one_mul, mul_one, add_comm, \u2190 one... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.comap_jacobson | [
204,
1
] | [
206,
50
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.mul_eq_one_iff | [
529,
11
] | [
537,
36
] | [{"tactic": "refine' \u27e8fun h => _, _\u27e9", "annotated_tactic": ["refine' \u27e8fun h => _, _\u27e9", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\ninst\u271d : OrderedCommGroup \u03b1\ns t : NonemptyInterval \u03b1\n\u22a2 s * t = 1 \u2194 \u2203 a b, s = pure a \u2227 t = pure b \u2227 a * b = 1", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.measure_le_bound | [
142,
1
] | [
144,
78
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WellFoundedSet.lean | Finset.isPwo_bUnion | [
634,
1
] | [
636,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.norm_sq_diff_sum | [
2084,
1
] | [
2106,
19
] | [{"tactic": "rw [\u2190 Finset.sum_sdiff_sub_sum_sdiff, sub_eq_add_neg, \u2190 Finset.sum_neg_distrib]", "annotated_tactic": ["rw [\u2190 <a>Finset.sum_sdiff_sub_sum_sdiff</a>, <a>sub_eq_add_neg</a>, \u2190 <a>Finset.sum_neg_distrib</a>]", [{"full_name": "Finset.sum_sdiff_sub_sum_sdiff", "def_path": "Mathlib/Algebra/Bi... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean | Orientation.oangle_rotation_self_right | [
257,
1
] | [
258,
52
] | [{"tactic": "simp [hx]", "annotated_tactic": ["simp [hx]", []], "state_before": "V : Type u_1\nV' : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup V\ninst\u271d\u2074 : NormedAddCommGroup V'\ninst\u271d\u00b3 : InnerProductSpace \u211d V\ninst\u271d\u00b2 : InnerProductSpace \u211d V'\ninst\u271d\u00b9 : Fact (finrank... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.min_of_nonempty | [
1358,
1
] | [
1360,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/TwoDim.lean | Complex.kahler | [
625,
11
] | [
627,
16
] | [{"tactic": "rw [Orientation.kahler_apply_apply]", "annotated_tactic": ["rw [<a>Orientation.kahler_apply_apply</a>]", [{"full_name": "Orientation.kahler_apply_apply", "def_path": "Mathlib/Analysis/InnerProductSpace/TwoDim.lean", "def_pos": [481, 9], "def_end_pos": [481, 27]}]], "state_before": "E : Type u_1\ninst\u271d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.subset_extend | [
1375,
1
] | [
1378,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Zip.lean | List.lt_length_left_of_zipWith | [
67,
1
] | [
70,
15
] | [{"tactic": "rw [length_zipWith, lt_min_iff] at h", "annotated_tactic": ["rw [<a>length_zipWith</a>, <a>lt_min_iff</a>] at h", [{"full_name": "List.length_zipWith", "def_path": "lake-packages/std/Std/Data/List/Lemmas.lean", "def_pos": [176, 17], "def_end_pos": [176, 31]}, {"full_name": "lt_min_iff", "def_path": "Mathli... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.commonNeighbors_subset_neighborSet_left | [
1050,
1
] | [
1052,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_add_adjacent_intervals | [
900,
1
] | [
903,
90
] | [{"tactic": "rw [\u2190 add_neg_eq_zero, \u2190 integral_symm, integral_add_adjacent_intervals_cancel hab hbc]", "annotated_tactic": ["rw [\u2190 <a>add_neg_eq_zero</a>, \u2190 <a>integral_symm</a>, <a>integral_add_adjacent_intervals_cancel</a> hab hbc]", [{"full_name": "add_neg_eq_zero", "def_path": "Mathlib/Algebra/G... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Iio | [
140,
1
] | [
141,
50
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Log.lean | Int.log_mono_right | [
143,
1
] | [
154,
48
] | [{"tactic": "cases' le_or_lt b 1 with hb hb", "annotated_tactic": ["cases' <a>le_or_lt</a> b 1 with hb hb", [{"full_name": "le_or_lt", "def_path": "Mathlib/Init/Order/Defs.lean", "def_pos": [340, 9], "def_end_pos": [340, 17]}]], "state_before": "R : Type u_1\ninst\u271d\u00b9 : LinearOrderedSemifield R\ninst\u271d : Fl... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order.lean | isOpen_induced_iff | [
394,
1
] | [
396,
10
] | [] |
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