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/TrivSqZeroExt.lean | TrivSqZeroExt.snd_nat_cast | [
524,
1
] | [
525,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_sub_linearMap | [
449,
1
] | [
450,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Free.lean | Magma.AssocQuotient.hom_ext | [
392,
1
] | [
393,
81
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.map_smulₛₗ₂ | [
301,
1
] | [
302,
68
] | [{"tactic": "rw [f.map_smul\u209b\u2097, smul_apply]", "annotated_tactic": ["rw [f.map_smul\u209b\u2097, <a>smul_apply</a>]", [{"full_name": "ContinuousLinearMap.smul_apply", "def_path": "Mathlib/Topology/Algebra/Module/Basic.lean", "def_pos": [602, 9], "def_end_pos": [602, 19]}]], "state_before": "\ud835\udd5c : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/PeriodicPts.lean | Function.Commute.minimalPeriod_of_comp_dvd_mul | [
432,
1
] | [
434,
62
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.mul_one | [
303,
11
] | [
305,
81
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "R : Type u\ninst\u271d\u00b9 : CommMonoid R\nR' : Type v\ninst\u271d : CommMonoidWithZero R'\n\u03c7 : MulChar R R'\n\u22a2 \u03c7 * 1 = \u03c7", "state_after": "case h\nR : Type u\ninst\u271d\u00b9 : CommMonoid R\nR' : Type v\ninst\u271d : CommMonoid... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_iff_infinitesimal_inv_pos | [
732,
1
] | [
743,
74
] | [{"tactic": "convert hip r\u207b\u00b9", "annotated_tactic": ["convert hip r\u207b\u00b9", []], "state_before": "x : \u211d*\nhip : InfinitePos x\nr : \u211d\nhr : 0 < r\n\u22a2 (\u2191r)\u207b\u00b9 < x", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finsupp_lift_of_infinite' | [
1054,
1
] | [
1061,
38
] | [{"tactic": "cases fintypeOrInfinite \u03b1", "annotated_tactic": ["cases <a>fintypeOrInfinite</a> \u03b1", [{"full_name": "fintypeOrInfinite", "def_path": "Mathlib/Data/Fintype/Card.lean", "def_pos": [975, 19], "def_end_pos": [975, 36]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : Nonempty ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/IsAdjoinRoot.lean | IsAdjoinRootMonic.basis_one | [
500,
1
] | [
501,
77
] | [{"tactic": "rw [h.basis_apply, Fin.val_mk, pow_one]", "annotated_tactic": ["rw [h.basis_apply, <a>Fin.val_mk</a>, <a>pow_one</a>]", [{"full_name": "Fin.val_mk", "def_path": "lake-packages/std/Std/Data/Fin/Lemmas.lean", "def_pos": [51, 9], "def_end_pos": [51, 15]}, {"full_name": "pow_one", "def_path": "Mathlib/Algebra/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Pointwise.lean | Filter.one_neBot | [
106,
1
] | [
107,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.arrowCongr_trans | [
477,
1
] | [
481,
6
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "R : Type uR\nA\u2081 : Type uA\u2081\nA\u2082 : Type uA\u2082\nA\u2083 : Type uA\u2083\nA\u2081' : Type uA\u2081'\nA\u2082' : Type uA\u2082'\nA\u2083' : Type uA\u2083'\ninst\u271d\u00b9\u00b2 : CommSemiring R\ninst\u271d\u00b9\u00b9 : Semiring A\u2081... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_apply_apply | [
360,
1
] | [
361,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/Basic.lean | Complex.nndist_of_im_eq | [
120,
1
] | [
121,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.abs_log_mul_self_lt | [
324,
1
] | [
336,
13
] | [{"tactic": "have : 0 < 1 / x := by simpa only [one_div, inv_pos] using h1", "annotated_tactic": ["have : 0 < 1 / x := by simpa only [<a>one_div</a>, <a>inv_pos</a>] using h1", [{"full_name": "one_div", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [318, 9], "def_end_pos": [318, 16]}, {"full_name": "inv_po... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.map_normNoninc | [
993,
1
] | [
995,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.sup_N | [
136,
1
] | [
137,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_comp_of_isSheaf | [
670,
1
] | [
673,
65
] | [{"tactic": "rw [isSheaf_iff_isLimit] at h \u22a2", "annotated_tactic": ["rw [<a>isSheaf_iff_isLimit</a>] at h \u22a2", [{"full_name": "CategoryTheory.Presheaf.isSheaf_iff_isLimit", "def_path": "Mathlib/CategoryTheory/Sites/Sheaf.lean", "def_pos": [186, 9], "def_end_pos": [186, 28]}]], "state_before": "C : Type u\u2081... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.cancel_right | [
330,
1
] | [
332,
75
] | [{"tactic": "rw [h]", "annotated_tactic": ["rw [h]", []], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\n\u03b4 : Type u_5\ninst\u271d\u2077 : NonAssocSemiring \u03b1\ninst\u271d\u2076 : Preorder \u03b1\ninst\u271d\u2075 : NonAssocSemiring \u03b2\ninst\u271d\u2074 : Preorder \u0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_isLimit | [
519,
1
] | [
520,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Basic.lean | Finset.coe_pair | [
1149,
1
] | [
1151,
7
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ninst\u271d : DecidableEq \u03b1\ns t u v : Finset \u03b1\na\u271d b\u271d a b : \u03b1\n\u22a2 \u2191{a, b} = {a, b}", "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_transpose_apply | [
66,
1
] | [
67,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.map_smul | [
100,
1
] | [
101,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_snd | [
818,
1
] | [
819,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Bicategory/Coherence.lean | CategoryTheory.FreeBicategory.normalize_naturality | [
161,
1
] | [
183,
14
] | [{"tactic": "rcases \u03b7 with \u27e8\u03b7'\u27e9", "annotated_tactic": ["rcases \u03b7 with \u27e8\u03b7'\u27e9", []], "state_before": "B : Type u\ninst\u271d : Quiver B\na b c : B\np : Path a b\nf g : Hom b c\n\u03b7 : f \u27f6 g\n\u22a2 (\u2191(preinclusion B)).map { as := p } \u25c1 \u03b7 \u226b (normalizeIso p ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.inter_ae_eq_left_of_ae_eq_univ | [
550,
1
] | [
552,
18
] | [{"tactic": "convert ae_eq_set_inter (ae_eq_refl s) h", "annotated_tactic": ["convert <a>ae_eq_set_inter</a> (<a>ae_eq_refl</a> s) h", [{"full_name": "MeasureTheory.ae_eq_set_inter", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean", "def_pos": [515, 9], "def_end_pos": [515, 24]}, {"full_name": "MeasureT... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.neighborSet_union_compl_neighborSet_eq | [
1003,
1
] | [
1008,
8
] | [{"tactic": "ext w", "annotated_tactic": ["ext w", []], "state_before": "\u03b9 : Sort u_1\n\ud835\udd5c : Type u_2\nV : Type u\nW : Type v\nX : Type w\nG\u271d : SimpleGraph V\nG' : SimpleGraph W\na b c u v\u271d w : V\ne : Sym2 V\nG : SimpleGraph V\nv : V\n\u22a2 neighborSet G v \u222a neighborSet G\u1d9c v = {v}\u1d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_def | [
840,
1
] | [
841,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lcurry_apply | [
609,
1
] | [
610,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ico_iff | [
559,
1
] | [
561,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Regular/Basic.lean | isRegular_iff_ne_zero | [
386,
1
] | [
387,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasFDerivAt.clog | [
94,
1
] | [
96,
61
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | continuous_if_const | [
1239,
1
] | [
1242,
22
] | [{"tactic": "split_ifs with h", "annotated_tactic": ["split_ifs with h", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\ninst\u271d\u2074 : TopologicalSpace \u03b1\ninst\u271d\u00b3 : TopologicalSpace \u03b2\ninst\u271d\u00b2 : TopologicalSpace \u03b3\ninst\u271d\u00b9 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/NormNum/Inv.lean | Mathlib.Meta.NormNum.isRat_inv_neg | [
124,
1
] | [
131,
74
] | [{"tactic": "rintro \u27e8_, rfl\u27e9", "annotated_tactic": ["rintro \u27e8_, rfl\u27e9", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : DivisionRing \u03b1\ninst\u271d : CharZero \u03b1\na : \u03b1\nn d : \u2115\n\u22a2 IsRat a (Int.negOfNat (Nat.succ n)) d \u2192 IsRat a\u207b\u00b9 (Int.negOfNat d) (Na... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Encoding.lean | Computability.unary_decode_encode_nat | [
198,
1
] | [
199,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/Over.lean | Ideal.IntegralClosure.comap_ne_bot | [
345,
1
] | [
347,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.self_comp_symm | [
842,
1
] | [
843,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/UniformGroup.lean | UniformGroup.toUniformSpace_eq | [
700,
1
] | [
703,
71
] | [{"tactic": "ext : 1", "annotated_tactic": ["ext : 1", []], "state_before": "G\u271d : Type u_1\ninst\u271d\u2074 : CommGroup G\u271d\ninst\u271d\u00b3 : TopologicalSpace G\u271d\ninst\u271d\u00b2 : TopologicalGroup G\u271d\nG : Type u_2\nu : UniformSpace G\ninst\u271d\u00b9 : Group G\ninst\u271d : UniformGroup G\n\u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Integral.lean | MeasureTheory.integral_smul_eq_self | [
167,
1
] | [
170,
34
] | [{"tactic": "have h : MeasurableEmbedding fun x : \u03b1 => g \u2022 x := (MeasurableEquiv.smul g).measurableEmbedding", "annotated_tactic": ["have h : <a>MeasurableEmbedding</a> fun x : \u03b1 => g \u2022 x := (<a>MeasurableEquiv.smul</a> g).<a>measurableEmbedding</a>", [{"full_name": "MeasurableEmbedding", "def_path"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.iIndepFun_indicator | [
634,
1
] | [
637,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/CoprodI.lean | Monoid.CoprodI.ext_hom | [
140,
1
] | [
145,
38
] | [{"tactic": "erw [MonoidHom.comp_apply, MonoidHom.comp_apply, \u2190 of_apply, \u2190 MonoidHom.comp_apply, \u2190\n MonoidHom.comp_apply, h]", "annotated_tactic": ["erw [<a>MonoidHom.comp_apply</a>, <a>MonoidHom.comp_apply</a>, \u2190 <a>of_apply</a>, \u2190 <a>MonoidHom.comp_apply</a>, \u2190\n <a>MonoidHom.c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ContinuedFractions/Computation/Approximations.lean | GeneralizedContinuedFraction.of_one_le_get?_part_denom | [
138,
1
] | [
146,
74
] | [{"tactic": "obtain \u27e8gp_n, nth_s_eq, \u27e8-\u27e9\u27e9 : \u2203 gp_n, (of v).s.get? n = some gp_n \u2227 gp_n.b = b", "annotated_tactic": ["obtain \u27e8gp_n, nth_s_eq, \u27e8-\u27e9\u27e9 : \u2203 gp_n, (<a>of</a> v).s.get? n = <a>some</a> gp_n \u2227 gp_n.b = b", [{"full_name": "GeneralizedContinuedFraction.of... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.linearIndependent_X | [
124,
1
] | [
126,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Spectrum.lean | LinearMap.IsSymmetric.hasEigenvalue_eigenvalues | [
241,
1
] | [
242,
87
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_apply | [
1584,
1
] | [
1585,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/ConditionalExpectation/AEMeasurable.lean | MeasureTheory.Lp.induction_stronglyMeasurable_aux | [
568,
1
] | [
610,
72
] | [{"tactic": "intro f hf", "annotated_tactic": ["intro f hf", []], "state_before": "\u03b1 : Type u_1\nE' : Type u_2\nF : Type u_3\nF' : Type u_4\n\ud835\udd5c : Type u_5\np : \u211d\u22650\u221e\ninst\u271d\u00b9\u00b2 : IsROrC \ud835\udd5c\ninst\u271d\u00b9\u00b9 : NormedAddCommGroup E'\ninst\u271d\u00b9\u2070 : Inner... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_sup | [
485,
1
] | [
487,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Basic.lean | Fin.coe_ofNat_eq_mod | [
1779,
1
] | [
1781,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/GroupRingAction/Invariant.lean | IsInvariantSubring.coe_subtypeHom | [
57,
1
] | [
58,
70
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Finset.card_univ | [
247,
1
] | [
248,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/QuadraticForm/IsometryEquiv.lean | QuadraticForm.equivalent_weightedSumSquares | [
166,
1
] | [
169,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.mono | [
369,
11
] | [
376,
38
] | [{"tactic": "let f_approx : \u2115 \u2192 @SimpleFunc \u03b1 m \u03b2 := fun n =>\n @SimpleFunc.mk \u03b1 m \u03b2\n (hf.approx n)\n (fun x => h_mono _ (SimpleFunc.measurableSet_fiber' _ x))\n (SimpleFunc.finite_range (hf.approx n))", "annotated_tactic": ["let f_approx : \u2115 \u2192 @<a>SimpleFunc</a> \u03b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_le_of_le_add_nat | [
828,
1
] | [
829,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Sym/Sym2.lean | Sym2.map_map | [
257,
1
] | [
258,
34
] | [{"tactic": "revert x", "annotated_tactic": ["revert x", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ng : \u03b2 \u2192 \u03b3\nf : \u03b1 \u2192 \u03b2\nx : Sym2 \u03b1\n\u22a2 map g (map f x) = map (g \u2218 f) x", "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TuringMachine.lean | Turing.frespects_eq | [
962,
1
] | [
965,
40
] | [{"tactic": "unfold FRespects", "annotated_tactic": ["unfold <a>FRespects</a>", [{"full_name": "Turing.FRespects", "def_path": "Mathlib/Computability/TuringMachine.lean", "def_pos": [957, 5], "def_end_pos": [957, 14]}]], "state_before": "\u03c3\u2081 : Type u_1\n\u03c3\u2082 : Type u_2\nf\u2082 : \u03c3\u2082 \u2192 Op... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_toSubsemiring | [
516,
1
] | [
517,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_inv_mul_swap | [
137,
1
] | [
139,
67
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_coe_atTop | [
121,
1
] | [
123,
25
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean | Orientation.inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two | [
822,
1
] | [
823,
89
] | [{"tactic": "rw [real_inner_comm, o.inner_eq_zero_of_oangle_eq_neg_pi_div_two h]", "annotated_tactic": ["rw [<a>real_inner_comm</a>, o.inner_eq_zero_of_oangle_eq_neg_pi_div_two h]", [{"full_name": "real_inner_comm", "def_path": "Mathlib/Analysis/InnerProductSpace/Basic.lean", "def_pos": [442, 9], "def_end_pos": [442, 2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Filtered/Small.lean | CategoryTheory.IsCofiltered.small_fullSubcategory_cofilteredClosure | [
226,
1
] | [
244,
55
] | [{"tactic": "refine' small_of_injective_of_exists\n (CofilteredClosureSmall.abstractCofilteredClosureRealization f) FullSubcategory.ext _", "annotated_tactic": ["refine' <a>small_of_injective_of_exists</a>\n (<a>CofilteredClosureSmall.abstractCofilteredClosureRealization</a> f) <a>FullSubcategory.ext</a> _", [{"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_le | [
263,
1
] | [
265,
65
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_add_left | [
1312,
1
] | [
1317,
44
] | [{"tactic": "by_cases hf : Integrable f \u03bc", "annotated_tactic": ["by_cases hf : <a>Integrable</a> f \u03bc", [{"full_name": "MeasureTheory.Integrable", "def_path": "Mathlib/MeasureTheory/Function/L1Space.lean", "def_pos": [442, 5], "def_end_pos": [442, 15]}]], "state_before": "\u03b1 : Type u_1\nE : Type u_2\nF : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/NonUnitalSubring/Basic.lean | NonUnitalSubring.coe_inf | [
536,
1
] | [
538,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Intrinsic.lean | intrinsicFrontier_subset_intrinsicClosure | [
103,
1
] | [
104,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/TwoPointing.lean | TwoPointing.swap_swap | [
65,
1
] | [
65,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/Basic.lean | star_invOf | [
572,
1
] | [
578,
31
] | [{"tactic": "have : star (\u215f r) = star (\u215f r) * ((star r) * \u215f (star r)) := by\n simp only [mul_invOf_self, mul_one]", "annotated_tactic": ["have : <a>star</a> (\u215f r) = <a>star</a> (\u215f r) * ((<a>star</a> r) * \u215f (<a>star</a> r)) := by\n simp only [<a>mul_invOf_self</a>, <a>mul_one</a>]", [{"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/GCD.lean | Nat.gcdA_zero_left | [
83,
1
] | [
85,
28
] | [{"tactic": "unfold gcdA", "annotated_tactic": ["unfold <a>gcdA</a>", [{"full_name": "Nat.gcdA", "def_path": "Mathlib/Data/Int/GCD.lean", "def_pos": [73, 5], "def_end_pos": [73, 9]}]], "state_before": "s : \u2115\n\u22a2 gcdA 0 s = 0", "state_after": "s : \u2115\n\u22a2 (xgcd 0 s).1 = 0"}, {"tactic": "rw [xgcd, xgcd_ze... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_zero | [
143,
1
] | [
144,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_addEquiv_refl | [
251,
1
] | [
252,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.of_smul | [
357,
1
] | [
359,
46
] | [{"tactic": "simpa [inv_smul_smul\u2080 hc] using hf.smul c\u207b\u00b9", "annotated_tactic": ["simpa [<a>inv_smul_smul\u2080</a> hc] using hf.smul c\u207b\u00b9", [{"full_name": "inv_smul_smul\u2080", "def_path": "Mathlib/GroupTheory/GroupAction/Group.lean", "def_pos": [192, 9], "def_end_pos": [192, 23]}]], "state_bef... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_pair_rev | [
1263,
1
] | [
1264,
34
] | [{"tactic": "rw [pair_comm, vectorSpan_pair]", "annotated_tactic": ["rw [<a>pair_comm</a>, <a>vectorSpan_pair</a>]", [{"full_name": "Set.pair_comm", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1402, 9], "def_end_pos": [1402, 18]}, {"full_name": "vectorSpan_pair", "def_path": "Mathlib/LinearAlgebra/AffineSpac... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Pell.lean | Pell.IsFundamental.x_pos | [
495,
1
] | [
496,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.mem_target | [
387,
1
] | [
388,
35
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Dioph.lean | Dioph.pow_dioph | [
763,
1
] | [
788,
74
] | [{"tactic": "have proof :=\n let D_pell := pell_dioph.reindex_dioph (Fin2 9) [&4, &8, &1, &0]\n (D&2 D= D.0 D\u2227 D&0 D= D.1) D\u2228 (D.0 D< D&2 D\u2227\n ((D&1 D= D.0 D\u2227 D&0 D= D.0) D\u2228 (D.0 D< D&1 D\u2227\n ((D\u2203) 3 <| (D\u2203) 4 <| (D\u2203) 5 <| (D\u2203) 6 $ (D\u2203) 7 <| (D\u2203) 8 <| D_pel... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.union_distrib_iInter₂_left | [
1542,
1
] | [
1543,
92
] | [{"tactic": "simp_rw [union_distrib_iInter_left]", "annotated_tactic": ["simp_rw [<a>union_distrib_iInter_left</a>]", [{"full_name": "Set.union_distrib_iInter_left", "def_path": "Mathlib/Data/Set/Lattice.lean", "def_pos": [1536, 9], "def_end_pos": [1536, 34]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Inseparable.lean | not_inseparable_iff_exists_open | [
290,
1
] | [
292,
59
] | [{"tactic": "simp [inseparable_iff_forall_open, \u2190 xor_iff_not_iff]", "annotated_tactic": ["simp [<a>inseparable_iff_forall_open</a>, \u2190 <a>xor_iff_not_iff</a>]", [{"full_name": "inseparable_iff_forall_open", "def_path": "Mathlib/Topology/Inseparable.lean", "def_pos": [285, 9], "def_end_pos": [285, 36]}, {"full... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_eq_univ | [
565,
1
] | [
565,
79
] | [{"tactic": "simp [SetLike.ext'_iff]", "annotated_tactic": ["simp [<a>SetLike.ext'_iff</a>]", [{"full_name": "SetLike.ext'_iff", "def_path": "Mathlib/Data/SetLike/Basic.lean", "def_pos": [149, 9], "def_end_pos": [149, 17]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Sort u_4\n\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.sup_lt_ord_lift_of_isRegular | [
1070,
1
] | [
1072,
39
] | [{"tactic": "rwa [hc.cof_eq]", "annotated_tactic": ["rwa [hc.cof_eq]", []], "state_before": "\u03b1 : Type u_1\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\n\u03b9 : Type u\nf : \u03b9 \u2192 Ordinal.{max u v}\nc : Cardinal.{max u v}\nhc : IsRegular c\nh\u03b9 : lift.{v, u} #\u03b9 < c\n\u22a2 lift.{v, u} #\u03b9 < Ordinal.co... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Gcd.lean | Nat.Coprime.pow | [
390,
1
] | [
391,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.mono | [
69,
1
] | [
71,
73
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.comp' | [
652,
1
] | [
654,
69
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_cons | [
1401,
1
] | [
1402,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_iff | [
669,
1
] | [
670,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/Morphisms/QuasiSeparated.lean | AlgebraicGeometry.exists_eq_pow_mul_of_is_compact_of_quasi_separated_space_aux | [
312,
1
] | [
370,
10
] | [{"tactic": "erw [X.basicOpen_res]", "annotated_tactic": ["erw [X.basicOpen_res]", []], "state_before": "X\u271d Y : Scheme\nf\u271d : X\u271d \u27f6 Y\nX : Scheme\nS : \u2191(Scheme.affineOpens X)\nU\u2081 U\u2082 : Opens \u2191\u2191X.toPresheafedSpace\nn\u2081 n\u2082 : \u2115\ny\u2081 : \u2191(X.presheaf.obj (op U\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/RingedSpace/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.id_c | [
130,
1
] | [
132,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_one_preimage | [
311,
1
] | [
313,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.ball_image_of_ball | [
253,
1
] | [
255,
21
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Basic.lean | eq_div_of_mul_eq' | [
757,
1
] | [
757,
71
] | [{"tactic": "simp [\u2190 h]", "annotated_tactic": ["simp [\u2190 h]", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nG : Type u_3\ninst\u271d : Group G\na b c d : G\nh : a * c = b\n\u22a2 a = b / c", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factors.lean | Nat.dvd_of_mem_factors | [
146,
1
] | [
149,
64
] | [{"tactic": "rcases n.eq_zero_or_pos with (rfl | hn)", "annotated_tactic": ["rcases n.eq_zero_or_pos with (rfl | hn)", []], "state_before": "n p : \u2115\nh : p \u2208 factors n\n\u22a2 p \u2223 n", "state_after": "case inl\np : \u2115\nh : p \u2208 factors 0\n\u22a2 p \u2223 0\n\ncase inr\nn p : \u2115\nh : p \u2208 f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Abelian/LeftDerived.lean | CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv | [
95,
1
] | [
119,
31
] | [{"tactic": "dsimp [leftDerivedZeroToSelfApp, leftDerivedZeroToSelfAppInv]", "annotated_tactic": ["dsimp [<a>leftDerivedZeroToSelfApp</a>, <a>leftDerivedZeroToSelfAppInv</a>]", [{"full_name": "CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp", "def_path": "Mathlib/CategoryTheory/Abelian/LeftDerived.lean", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Lattice.lean | inf_le_left' | [
394,
1
] | [
395,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.toLin'Flip_apply | [
471,
1
] | [
472,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ico | [
594,
1
] | [
595,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.toSubmonoid_le | [
476,
1
] | [
477,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Floor.lean | Nat.floor_le | [
153,
1
] | [
154,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.iInter_setOf | [
551,
1
] | [
553,
19
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Sort u_4\n\u03b9' : Sort u_5\n\u03b9\u2082 : Sort u_6\n\u03ba : \u03b9 \u2192 Sort u_7\n\u03ba\u2081 : \u03b9 \u2192 Sort u_8\n\u03ba\u2082 : \u03b9 \u2192 Sort u_9\n\u03ba' : \u03b9' \... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.of_correctness_of_terminatedAt | [
247,
1
] | [
251,
44
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.sub_const | [
529,
1
] | [
531,
54
] | [{"tactic": "simpa only [sub_eq_add_neg] using hf.add_const (-c)", "annotated_tactic": ["simpa only [<a>sub_eq_add_neg</a>] using hf.add_const (-c)", [{"full_name": "sub_eq_add_neg", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [975, 3], "def_end_pos": [975, 14]}]], "state_before": "\ud835\udd5c : Type u_1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/GaussSum.lean | MulChar.IsQuadratic.gaussSum_frob | [
164,
8
] | [
168,
28
] | [{"tactic": "rw [gaussSum_frob, pow_mulShift, h\u03c7.pow_char p, \u2190 gaussSum_mulShift \u03c7 \u03c8 hp.unit, \u2190 mul_assoc,\n hp.unit_spec, \u2190 pow_two, \u2190 pow_apply' _ (by norm_num : 0 < 2), h\u03c7.sq_eq_one, \u2190 hp.unit_spec,\n one_apply_coe, one_mul]", "annotated_tactic": ["rw [<a>gaussSum_frob<... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Algebra/Classes.lean | StrictWeakOrder.etrans | [
410,
1
] | [
411,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/Rayleigh.lean | IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn | [
122,
1
] | [
140,
63
] | [{"tactic": "have H : IsLocalExtrOn T.reApplyInnerSelf {x : F | \u2016x\u2016 ^ 2 = \u2016x\u2080\u2016 ^ 2} x\u2080 := by\n convert hextr\n ext x\n simp [dist_eq_norm]", "annotated_tactic": ["have H : <a>IsLocalExtrOn</a> T.reApplyInnerSelf {x : F | \u2016x\u2016 ^ 2 = \u2016x\u2080\u2016 ^ 2} x\u2080 := by\n co... |
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