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/SetTheory/Ordinal/Notation.lean | ONote.split_eq_scale_split' | [
709,
1
] | [
730,
25
] | [{"tactic": "injection p", "annotated_tactic": ["injection p", []], "state_before": "o' : ONote\nm : \u2115\nx\u271d : NF 0\np : split' 0 = (o', m)\n\u22a2 split 0 = (scale 1 o', m)", "state_after": "o' : ONote\nm : \u2115\nx\u271d : NF 0\nfst_eq\u271d : 0 = o'\nsnd_eq\u271d : 0 = m\n\u22a2 split 0 = (scale 1 o', m)"},... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_inv_mul_iff | [
411,
1
] | [
413,
26
] | [{"tactic": "rw [\u2190 mul_lt_mul_iff_left d, \u2190 mul_lt_mul_iff_right b, mul_inv_cancel_left, mul_assoc,\n inv_mul_cancel_right]", "annotated_tactic": ["rw [\u2190 <a>mul_lt_mul_iff_left</a> d, \u2190 <a>mul_lt_mul_iff_right</a> b, <a>mul_inv_cancel_left</a>, <a>mul_assoc</a>,\n <a>inv_mul_cancel_right</a>]", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two | [
364,
1
] | [
369,
75
] | [{"tactic": "erw [dist_comm p3 p2, dist_eq_norm_vsub V p1 p3, dist_eq_norm_vsub V p1 p2,\n dist_eq_norm_vsub V p2 p3, \u2190 norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two,\n vsub_sub_vsub_cancel_right p1, \u2190 neg_vsub_eq_vsub_rev p2 p3, norm_neg]", "annotated_tactic": ["erw [<a>dist_comm</a> p3 p2, <a... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Integration.lean | ProbabilityTheory.IndepFun.integral_mul_of_nonneg | [
203,
1
] | [
218,
69
] | [{"tactic": "have h1 : AEMeasurable (fun a => ENNReal.ofReal (X a)) \u03bc :=\n ENNReal.measurable_ofReal.comp_aemeasurable hXm", "annotated_tactic": ["have h1 : <a>AEMeasurable</a> (fun a => <a>ENNReal.ofReal</a> (X a)) \u03bc :=\n ENNReal.measurable_ofReal.comp_aemeasurable hXm", [{"full_name": "AEMeasurable", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/CrossProduct.lean | jacobi_cross | [
158,
1
] | [
159,
19
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.length_removeNth | [
972,
1
] | [
978,
93
] | [{"tactic": "simp [removeNth]", "annotated_tactic": ["simp [<a>removeNth</a>]", [{"full_name": "List.removeNth", "def_path": "lake-packages/std/Std/Data/List/Basic.lean", "def_pos": [366, 13], "def_end_pos": [366, 22]}]], "state_before": "\u03b1 : Type u_1\nhead\u271d : \u03b1\ntail\u271d : List \u03b1\nx\u271d : 0 < l... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Algebra.lean | dist_pair_smul | [
145,
1
] | [
146,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Connected/Basic.lean | IsPreconnected.union | [
135,
1
] | [
138,
49
] | [{"tactic": "rintro r (rfl | rfl | h) <;> assumption", "annotated_tactic": ["rintro r (rfl | rfl | h) <;> assumption", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Type u_1\n\u03c0 : \u03b9 \u2192 Type u_2\ninst\u271d : TopologicalSpace \u03b1\ns\u271d t\u271d u v : Set \u03b1\nx : \u03b1\ns t : Set... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/GCD.lean | Int.lcm_self | [
479,
1
] | [
481,
21
] | [{"tactic": "rw [Int.lcm]", "annotated_tactic": ["rw [<a>Int.lcm</a>]", [{"full_name": "Int.lcm", "def_path": "Mathlib/Data/Int/GCD.lean", "def_pos": [235, 5], "def_end_pos": [235, 8]}]], "state_before": "i : \u2124\n\u22a2 lcm i i = natAbs i", "state_after": "i : \u2124\n\u22a2 Nat.lcm (natAbs i) (natAbs i) = natAbs i... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/CountableInter.lean | EventuallyLE.countable_iUnion | [
74,
1
] | [
76,
99
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_isLeast | [
177,
1
] | [
179,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Seq/Computation.lean | Computation.map_pure' | [
873,
1
] | [
874,
11
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/DFinsupp/Basic.lean | DFinsupp.prod_finset_sum_index | [
2109,
1
] | [
2116,
85
] | [{"tactic": "classical\nexact Finset.induction_on s (by simp [prod_zero_index])\n (by simp (config := { contextual := true }) [prod_add_index, h_zero, h_add])", "annotated_tactic": ["classical\n exact <a>Finset.induction_on</a> s (by simp [<a>prod_zero_index</a>])\n (by simp (config := { contextual := <a>t... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Sqrt.lean | Real.le_sqrt_of_sq_le | [
326,
1
] | [
327,
43
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.const_mul_right' | [
1591,
1
] | [
1593,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_iInf₂ | [
409,
1
] | [
411,
25
] | [{"tactic": "simp_rw [toIdeal_iInf]", "annotated_tactic": ["simp_rw [<a>toIdeal_iInf</a>]", [{"full_name": "HomogeneousIdeal.toIdeal_iInf", "def_path": "Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean", "def_pos": [397, 9], "def_end_pos": [397, 21]}]], "state_before": "\u03b9 : Type u_1\n\u03c3 : Type u_2\nR : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.inv_singleton | [
249,
1
] | [
250,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/IndicatorFunction.lean | mulIndicator_eventuallyEq | [
29,
1
] | [
34,
77
] | [{"tactic": "simp only [*, hst.1 hxs, mulIndicator_of_mem]", "annotated_tactic": ["simp only [*, hst.1 hxs, <a>mulIndicator_of_mem</a>]", [{"full_name": "Set.mulIndicator_of_mem", "def_path": "Mathlib/Algebra/IndicatorFunction.lean", "def_pos": [68, 9], "def_end_pos": [68, 28]}]], "state_before": "\u03b1 : Type u_1\n\u... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.average_eq_integral_normalize | [
394,
1
] | [
399,
72
] | [{"tactic": "rw [\u03bc.toMeasure_normalize_eq_of_nonzero nonzero, average]", "annotated_tactic": ["rw [\u03bc.toMeasure_normalize_eq_of_nonzero nonzero, <a>average</a>]", [{"full_name": "MeasureTheory.average", "def_path": "Mathlib/MeasureTheory/Integral/Average.lean", "def_pos": [247, 19], "def_end_pos": [247, 26]}]]... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_dvd_left | [
30,
1
] | [
31,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Deprecated/Subgroup.lean | Group.closure_subset | [
546,
1
] | [
547,
84
] | [{"tactic": "induction ha <;> simp [h _, *, ht.one_mem, ht.mul_mem, IsSubgroup.inv_mem_iff]", "annotated_tactic": ["induction ha <;> simp [h _, *, ht.one_mem, ht.mul_mem, <a>IsSubgroup.inv_mem_iff</a>]", [{"full_name": "IsSubgroup.inv_mem_iff", "def_path": "Mathlib/Deprecated/Subgroup.lean", "def_pos": [141, 9], "def_e... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.sub | [
96,
1
] | [
97,
98
] | [{"tactic": "simp_rw [Matrix.sub_apply, hM h, hN h, sub_zero]", "annotated_tactic": ["simp_rw [<a>Matrix.sub_apply</a>, hM h, hN h, <a>sub_zero</a>]", [{"full_name": "Matrix.sub_apply", "def_path": "Mathlib/Data/Matrix/Basic.lean", "def_pos": [306, 9], "def_end_pos": [306, 18]}, {"full_name": "sub_zero", "def_path": "M... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Congruence.lean | Con.lift_funext | [
953,
1
] | [
956,
28
] | [{"tactic": "rw [\u2190 lift_apply_mk' f, \u2190 lift_apply_mk' g]", "annotated_tactic": ["rw [\u2190 <a>lift_apply_mk'</a> f, \u2190 <a>lift_apply_mk'</a> g]", [{"full_name": "Con.lift_apply_mk'", "def_path": "Mathlib/GroupTheory/Congruence.lean", "def_pos": [943, 9], "def_end_pos": [943, 23]}, {"full_name": "Con.lift... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_modEq_two | [
553,
1
] | [
559,
88
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "a : \u2115\na1 : 1 < a\n\u22a2 yn a1 0 \u2261 0 [MOD 2]", "state_after": "no goals"}, {"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "a : \u2115\na1 : 1 < a\n\u22a2 yn a1 1 \u2261 1 [MOD 2]", "state_after": "no goals"}, {"tacti... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | UpperHalfPlane.dist_eq_iff_eq_sinh | [
100,
1
] | [
102,
68
] | [{"tactic": "rw [\u2190 div_left_inj' (two_ne_zero' \u211d), \u2190 sinh_inj, sinh_half_dist]", "annotated_tactic": ["rw [\u2190 <a>div_left_inj'</a> (<a>two_ne_zero'</a> \u211d), \u2190 <a>sinh_inj</a>, <a>sinh_half_dist</a>]", [{"full_name": "div_left_inj'", "def_path": "Mathlib/Algebra/GroupWithZero/Units/Lemmas.lea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.zero_nmem_multiset_map_X_sub_C | [
1578,
1
] | [
1581,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Cycle/Basic.lean | List.Nodup.isCycleOn_formPerm | [
1848,
1
] | [
1856,
16
] | [{"tactic": "refine' \u27e8l.formPerm.bijOn fun _ => List.formPerm_mem_iff_mem, fun a ha b hb => _\u27e9", "annotated_tactic": ["refine' \u27e8l.formPerm.bijOn fun _ => <a>List.formPerm_mem_iff_mem</a>, fun a ha b hb => _\u27e9", [{"full_name": "List.formPerm_mem_iff_mem", "def_path": "Mathlib/GroupTheory/Perm/List.lea... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_id | [
559,
1
] | [
560,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.eq_comp_toLinearMap_symm | [
429,
1
] | [
433,
47
] | [{"tactic": "constructor <;> intro H <;> ext", "annotated_tactic": ["constructor <;> intro H <;> ext", []], "state_before": "R : Type u_1\nR\u2081 : Type u_2\nR\u2082 : Type u_3\nR\u2083 : Type u_4\nk : Type u_5\nS : Type u_6\nM : Type u_7\nM\u2081 : Type u_8\nM\u2082 : Type u_9\nM\u2083 : Type u_10\nN\u2081 : Type u_1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/TypeTags.lean | ofAdd_toAdd | [
105,
1
] | [
106,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | EuclideanGeometry.oangle_add_cyc3 | [
304,
1
] | [
306,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RepresentationTheory/Action.lean | Action.leftUnitor_inv_hom | [
536,
1
] | [
538,
7
] | [{"tactic": "dsimp [Monoidal.induced_leftUnitor]", "annotated_tactic": ["dsimp [<a>Monoidal.induced_leftUnitor</a>]", [{"full_name": "CategoryTheory.Monoidal.induced_leftUnitor", "def_path": "Mathlib/CategoryTheory/Monoidal/Transport.lean", "def_pos": [115, 3], "def_end_pos": [115, 8]}]], "state_before": "V : Type (u +... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiff.sinh | [
1166,
1
] | [
1167,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WellFoundedSet.lean | Set.isWf_union | [
240,
9
] | [
240,
83
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_quadratic_le | [
1218,
1
] | [
1221,
71
] | [{"tactic": "simpa only [add_assoc] using\n degree_add_le_of_degree_le (degree_C_mul_X_pow_le 2 a)\n (le_trans degree_linear_le <| WithBot.coe_le_coe.mpr one_le_two)", "annotated_tactic": ["simpa only [<a>add_assoc</a>] using\n <a>degree_add_le_of_degree_le</a> (<a>degree_C_mul_X_pow_le</a> 2 a)\n (<a>le_tr... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Sups.lean | Finset.Nonempty.of_sups_left | [
121,
1
] | [
122,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Projection.lean | LinearMap.range_eq_of_proj | [
48,
1
] | [
49,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean | AlgebraicGeometry.QuasiCompact.affineProperty_stableUnderBaseChange | [
249,
1
] | [
256,
23
] | [{"tactic": "intro X Y S _ _ f g h", "annotated_tactic": ["intro X Y S _ _ f g h", []], "state_before": "X Y : Scheme\nf : X \u27f6 Y\n\u22a2 AffineTargetMorphismProperty.StableUnderBaseChange affineProperty", "state_after": "X\u271d Y\u271d : Scheme\nf\u271d : X\u271d \u27f6 Y\u271d\nX Y S : Scheme\ninst\u271d\u00b9 :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | Ico_mem_nhdsWithin_Ioi' | [
452,
1
] | [
453,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.eq_zero_iff | [
109,
1
] | [
111,
83
] | [{"tactic": "simp only [padicValNat, dite_eq_right_iff, PartENat.get_eq_iff_eq_coe, Nat.cast_zero,\n multiplicity_eq_zero, and_imp, pos_iff_ne_zero, Ne.def, \u2190 or_iff_not_imp_left]", "annotated_tactic": ["simp only [<a>padicValNat</a>, <a>dite_eq_right_iff</a>, <a>PartENat.get_eq_iff_eq_coe</a>, <a>Nat.cast_zero</... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Projection.lean | Submodule.prodEquivOfIsCompl_symm_apply_left | [
119,
1
] | [
121,
56
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R : Type u_1\ninst\u271d\u2079 : Ring R\nE : Type u_2\ninst\u271d\u2078 : AddCommGroup E\ninst\u271d\u2077 : Module R E\nF : Type u_3\ninst\u271d\u2076 : AddCommGroup F\ninst\u271d\u2075 : Module R F\nG : Type u_4\ninst\u271d\u2074 : AddCommGroup G\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Defs.lean | Finsupp.equivFunOnFinite_symm_single | [
517,
1
] | [
519,
57
] | [{"tactic": "rw [\u2190 equivFunOnFinite_single, Equiv.symm_apply_apply]", "annotated_tactic": ["rw [\u2190 <a>equivFunOnFinite_single</a>, <a>Equiv.symm_apply_apply</a>]", [{"full_name": "Finsupp.equivFunOnFinite_single", "def_path": "Mathlib/Data/Finsupp/Defs.lean", "def_pos": [510, 9], "def_end_pos": [510, 32]}, {"f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.flip | [
55,
1
] | [
56,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.succ_nth_convergent'_eq_squashGCF_nth_convergent' | [
227,
1
] | [
235,
17
] | [{"tactic": "cases n", "annotated_tactic": ["cases n", []], "state_before": "K : Type u_1\nn : \u2115\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst\u271d : DivisionRing K\n\u22a2 convergents' g (n + 1) = convergents' (squashGCF g n) n", "state_after": "case zero\nK : Type u_1\ng : GeneralizedConti... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Basic.lean | Set.mem_diff | [
1819,
1
] | [
1820,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/DedekindDomain/AdicValuation.lean | IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap | [
284,
1
] | [
285,
69
] | [{"tactic": "rw [valuation_def, Valuation.extendToLocalization_apply_map_apply]", "annotated_tactic": ["rw [<a>valuation_def</a>, <a>Valuation.extendToLocalization_apply_map_apply</a>]", [{"full_name": "IsDedekindDomain.HeightOneSpectrum.valuation_def", "def_path": "Mathlib/RingTheory/DedekindDomain/AdicValuation.lean"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | HasMFDerivAt.mdifferentiableAt | [
471,
1
] | [
473,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_zero | [
887,
1
] | [
889,
21
] | [{"tactic": "rw [\u2190 coe_bot, eq_bot_iff]", "annotated_tactic": ["rw [\u2190 <a>coe_bot</a>, <a>eq_bot_iff</a>]", [{"full_name": "MeasureTheory.OuterMeasure.coe_bot", "def_path": "Mathlib/MeasureTheory/Measure/OuterMeasure.lean", "def_pos": [363, 9], "def_end_pos": [363, 16]}, {"full_name": "eq_bot_iff", "def_path":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | LinearMap.finrank_le_finrank_of_injective | [
190,
1
] | [
192,
101
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.aroots_C_mul | [
965,
1
] | [
970,
52
] | [{"tactic": "rw [aroots_def, Polynomial.map_mul, map_C, roots_C_mul]", "annotated_tactic": ["rw [<a>aroots_def</a>, <a>Polynomial.map_mul</a>, <a>map_C</a>, <a>roots_C_mul</a>]", [{"full_name": "Polynomial.aroots_def", "def_path": "Mathlib/Data/Polynomial/RingDivision.lean", "def_pos": [920, 9], "def_end_pos": [920, 19... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.mul_refl | [
923,
1
] | [
924,
15
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.ext_iff | [
282,
11
] | [
283,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/CondCdf.lean | ProbabilityTheory.condCdf_nonneg | [
789,
1
] | [
790,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | AntitoneOn.convex_gt | [
410,
1
] | [
412,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Pointwise.lean | Finset.pow_mem_pow | [
874,
1
] | [
880,
44
] | [{"tactic": "rw [pow_zero]", "annotated_tactic": ["rw [<a>pow_zero</a>]", [{"full_name": "pow_zero", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [639, 9], "def_end_pos": [639, 17]}]], "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\ninst\u271d\u00b2 : DecidableEq \u0... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.trans_apply | [
364,
1
] | [
365,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.map_smul_eq_mul_coe | [
193,
1
] | [
198,
84
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9\u2074 : Ring \u03b1\ninst\u271d\u00b9\u00b3 : UniformSpace \u03b1\ninst\u271d\u00b9\u00b2 : TopologicalRing \u03b1\ninst\u271d\u00b9\u00b9 : UniformAddGroup \u03b1\n\u03b2 : Type u\ninst\u271d\u00b9\u2070 : Unif... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.le_card_falling_div_choose | [
181,
1
] | [
200,
31
] | [{"tactic": "induction' k with k ih", "annotated_tactic": ["induction' k with k ih", []], "state_before": "\ud835\udd5c : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : LinearOrderedField \ud835\udd5c\ninst\u271d\u00b9 : DecidableEq \u03b1\nk : \u2115\n\ud835\udc9c : Finset (Finset \u03b1)\ns : Finset \u03b1\ninst\u27... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_le_nadd | [
457,
1
] | [
458,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Prod.lean | Set.pi_congr | [
705,
1
] | [
706,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_mul | [
102,
1
] | [
103,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Bicategory/NaturalTransformation.lean | CategoryTheory.OplaxNatTrans.whiskerRight_naturality_naturality | [
119,
1
] | [
122,
87
] | [{"tactic": "rw [\u2190 comp_whiskerRight, naturality_naturality, comp_whiskerRight, whisker_assoc]", "annotated_tactic": ["rw [\u2190 <a>comp_whiskerRight</a>, <a>naturality_naturality</a>, <a>comp_whiskerRight</a>, <a>whisker_assoc</a>]", [{"full_name": "CategoryTheory.Bicategory.comp_whiskerRight", "def_path": "Math... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Basic.lean | Finset.Nonempty.eq_univ | [
96,
1
] | [
98,
68
] | [{"tactic": "rintro \u27e8x, hx\u27e9", "annotated_tactic": ["rintro \u27e8x, hx\u27e9", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ninst\u271d\u00b9 : Fintype \u03b1\ns t : Finset \u03b1\ninst\u271d : Subsingleton \u03b1\n\u22a2 Finset.Nonempty s \u2192 s = univ", "state_after": "cas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Gauge.lean | gauge_add_le | [
204,
1
] | [
215,
61
] | [{"tactic": "refine' le_of_forall_pos_lt_add fun \u03b5 h\u03b5 => _", "annotated_tactic": ["refine' <a>le_of_forall_pos_lt_add</a> fun \u03b5 h\u03b5 => _", [{"full_name": "le_of_forall_pos_lt_add", "def_path": "Mathlib/Algebra/Order/Group/Defs.lean", "def_pos": [1039, 3], "def_end_pos": [1039, 14]}]], "state_before":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_one | [
1030,
1
] | [
1032,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.unitsEquivAut_apply_symm | [
2462,
1
] | [
2463,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_one | [
53,
1
] | [
54,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.dotProduct_adjMatrix | [
205,
1
] | [
207,
76
] | [{"tactic": "simp [neighborFinset_eq_filter, dotProduct, sum_filter, Finset.sum_apply]", "annotated_tactic": ["simp [<a>neighborFinset_eq_filter</a>, <a>dotProduct</a>, <a>sum_filter</a>, <a>Finset.sum_apply</a>]", [{"full_name": "SimpleGraph.neighborFinset_eq_filter", "def_path": "Mathlib/Combinatorics/SimpleGraph/Bas... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Algebraic.lean | IsIntegralClosure.exists_smul_eq_mul | [
350,
1
] | [
362,
98
] | [{"tactic": "obtain \u27e8c, d, d_ne, hx\u27e9 :=\n exists_integral_multiple (h (algebraMap _ L a / algebraMap _ L b))\n ((injective_iff_map_eq_zero _).mp inj)", "annotated_tactic": ["obtain \u27e8c, d, d_ne, hx\u27e9 :=\n <a>exists_integral_multiple</a> (h (<a>algebraMap</a> _ L a / <a>algebraMap</a> _ L b))\n ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.add_const | [
436,
1
] | [
438,
46
] | [{"tactic": "simpa only [add_right_comm] using h (x + a)", "annotated_tactic": ["simpa only [<a>add_right_comm</a>] using h (x + a)", [{"full_name": "add_right_comm", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [101, 3], "def_end_pos": [101, 14]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order.lean | continuous_generateFrom | [
723,
1
] | [
726,
53
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.affineCombination_coord_eq_self | [
213,
1
] | [
221,
64
] | [{"tactic": "have hq : q \u2208 affineSpan k (range b) := by\n rw [b.tot]\n exact AffineSubspace.mem_top k V q", "annotated_tactic": ["have hq : q \u2208 <a>affineSpan</a> k (<a>range</a> b) := by\n rw [b.tot]\n exact <a>AffineSubspace.mem_top</a> k V q", [{"full_name": "affineSpan", "def_path": "Mathlib/Linear... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.extend_apply | [
361,
1
] | [
363,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.comap' | [
187,
1
] | [
190,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Abs.lean | abs_zero | [
128,
1
] | [
129,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | Real.multiset_prod_map_rpow | [
187,
1
] | [
191,
48
] | [{"tactic": "induction' s using Quotient.inductionOn with l", "annotated_tactic": ["induction' s using <a>Quotient.inductionOn</a> with l", [{"full_name": "Quotient.inductionOn", "def_path": "lake-packages/lean4/src/lean/Init/Core.lean", "def_pos": [1367, 19], "def_end_pos": [1367, 30]}]], "state_before": "\u03b9 : Typ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientEquivAlgOfEq_symm | [
610,
1
] | [
613,
6
] | [{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "R : Type u\nS : Type v\nF : Type w\ninst\u271d\u2078 : CommRing R\ninst\u271d\u2077 : CommRing S\nR\u2081 : Type u_1\nR\u2082 : Type u_2\nA : Type u_3\nB : Type u_4\ninst\u271d\u2076 : CommSemiring R\u2081\ninst\u271d\u2075 : CommSemiring R\u2082\nins... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Lattice.lean | Set.iUnion_iUnion_eq_or_left | [
950,
1
] | [
952,
69
] | [{"tactic": "simp only [iUnion_or, iUnion_union_distrib, iUnion_iUnion_eq_left]", "annotated_tactic": ["simp only [<a>iUnion_or</a>, <a>iUnion_union_distrib</a>, <a>iUnion_iUnion_eq_left</a>]", [{"full_name": "Set.iUnion_or", "def_path": "Mathlib/Data/Set/Lattice.lean", "def_pos": [879, 9], "def_end_pos": [879, 18]}, {... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_map | [
1595,
1
] | [
1595,
91
] | [{"tactic": "induction p <;> simp [*]", "annotated_tactic": ["induction p <;> simp [*]", []], "state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G \u2192g G'\nf' : G' \u2192g G''\nu v u' v' : V\np : Walk G u v\n\u22a2 darts (Walk.map f p) = List.ma... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_coord_change_source_mem_nhdsWithin' | [
1197,
1
] | [
1202,
39
] | [{"tactic": "apply extend_coord_change_source_mem_nhdsWithin", "annotated_tactic": ["apply <a>extend_coord_change_source_mem_nhdsWithin</a>", [{"full_name": "LocalHomeomorph.extend_coord_change_source_mem_nhdsWithin", "def_path": "Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean", "def_pos": [1188, 9], "def_end... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_le_snormEssSup | [
1113,
1
] | [
1115,
100
] | [{"tactic": "simp [measure_univ]", "annotated_tactic": ["simp [<a>measure_univ</a>]", [{"full_name": "MeasureTheory.IsProbabilityMeasure.measure_univ", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpace.lean", "def_pos": [3027, 3], "def_end_pos": [3027, 15]}]], "state_before": "\u03b1 : Type u_1\nE : Type u_2\nF :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_smul_left | [
168,
1
] | [
178,
38
] | [{"tactic": "rcases p.basisSets_iff.mp hU with \u27e8s, r, hr, hU\u27e9", "annotated_tactic": ["rcases p.basisSets_iff.mp hU with \u27e8s, r, hr, hU\u27e9", []], "state_before": "\ud835\udd5c : Type u_1\n\ud835\udd5c\u2082 : Type u_2\n\ud835\udd5d : Type u_3\n\ud835\udd5d\u2082 : Type u_4\nE : Type u_5\nF : Type u_6\nG... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.coe_mulLeft | [
64,
1
] | [
65,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nnnorm_const_eq | [
1027,
1
] | [
1028,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bases.lean | exists_countable_dense_bot_top | [
609,
1
] | [
612,
63
] | [{"tactic": "simpa using dense_univ.exists_countable_dense_subset_bot_top", "annotated_tactic": ["simpa using dense_univ.exists_countable_dense_subset_bot_top", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : TopologicalSpace \u03b1\ninst\u271d\u00b9 : SeparableSpace \u03b1\ninst\u271d : PartialOrder \u03b1... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Monotone/Basic.lean | StrictMono.injective | [
880,
1
] | [
881,
56
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_eq_zero_iff | [
424,
1
] | [
425,
82
] | [{"tactic": "rw [\u2190 cos_pi_div_two, \u2190 cos_coe, cos_eq_iff_eq_or_eq_neg, \u2190 coe_neg, \u2190 neg_div]", "annotated_tactic": ["rw [\u2190 <a>cos_pi_div_two</a>, \u2190 <a>cos_coe</a>, <a>cos_eq_iff_eq_or_eq_neg</a>, \u2190 <a>coe_neg</a>, \u2190 <a>neg_div</a>]", [{"full_name": "Real.cos_pi_div_two", "def_pat... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/Deriv/Basic.lean | Filter.EventuallyEq.deriv | [
643,
11
] | [
644,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Filter.sInter_comap_sets | [
2545,
1
] | [
2555,
27
] | [{"tactic": "ext x", "annotated_tactic": ["ext x", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\n\u03b4 : Type u_1\n\u03b9 : Sort x\nf\u271d f\u2081 f\u2082 : Filter \u03b1\ng g\u2081 g\u2082 : Filter \u03b2\nm : \u03b1 \u2192 \u03b2\nm' : \u03b2 \u2192 \u03b3\ns : Set \u03b1\nt : Set \u03b2\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.integral_deterministic | [
413,
1
] | [
416,
58
] | [{"tactic": "rw [kernel.deterministic_apply, integral_dirac _ (g a)]", "annotated_tactic": ["rw [<a>kernel.deterministic_apply</a>, <a>integral_dirac</a> _ (g a)]", [{"full_name": "ProbabilityTheory.kernel.deterministic_apply", "def_path": "Mathlib/Probability/Kernel/Basic.lean", "def_pos": [365, 9], "def_end_pos": [36... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Field/Basic.lean | div_lt_iff' | [
173,
1
] | [
173,
92
] | [{"tactic": "rw [mul_comm, div_lt_iff hc]", "annotated_tactic": ["rw [<a>mul_comm</a>, <a>div_lt_iff</a> hc]", [{"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [302, 9], "def_end_pos": [302, 17]}, {"full_name": "div_lt_iff", "def_path": "Mathlib/Algebra/Order/Field/Basic.lean", "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/LinearIndependent.lean | exists_of_linearIndependent_of_finite_span | [
1396,
1
] | [
1460,
39
] | [{"tactic": "classical\nhave :\n \u2200 t : Finset V,\n \u2200 s' : Finset V,\n \u2191s' \u2286 s \u2192\n s \u2229 \u2191t = \u2205 \u2192\n s \u2286 (span K \u2191(s' \u222a t) : Submodule K V) \u2192\n \u2203 t' : Finset V, \u2191t' \u2286 s \u222a \u2191t \u2227 s \u2286 \u2191t'... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.sum_le_one | [
165,
1
] | [
166,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_weightedVSubVSubWeights | [
695,
1
] | [
698,
16
] | [{"tactic": "simp_rw [weightedVSubVSubWeights, Pi.sub_apply, sum_sub_distrib]", "annotated_tactic": ["simp_rw [<a>weightedVSubVSubWeights</a>, <a>Pi.sub_apply</a>, <a>sum_sub_distrib</a>]", [{"full_name": "Finset.weightedVSubVSubWeights", "def_path": "Mathlib/LinearAlgebra/AffineSpace/Combination.lean", "def_pos": [670... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.add_le_add_left | [
781,
11
] | [
782,
58
] | [{"tactic": "rw [add_sub_add_left_eq_sub]", "annotated_tactic": ["rw [<a>add_sub_add_left_eq_sub</a>]", [{"full_name": "add_sub_add_left_eq_sub", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [894, 3], "def_end_pos": [894, 14]}]], "state_before": "d : \u2115\na b : \u2124\u221a\u2191d\nab : a \u2264 b\nc :... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Squarefree.lean | Squarefree.isRadical | [
197,
1
] | [
210,
83
] | [{"tactic": "by_cases gcd x y = 0", "annotated_tactic": ["by_cases <a>gcd</a> x y = 0", [{"full_name": "GCDMonoid.gcd", "def_path": "Mathlib/Algebra/GCDMonoid/Basic.lean", "def_pos": [274, 3], "def_end_pos": [274, 6]}]], "state_before": "R : Type u_1\ninst\u271d\u00b9 : CancelCommMonoidWithZero R\ninst\u271d : GCDMonoi... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo_iff | [
1156,
1
] | [
1165,
42
] | [{"tactic": "rcases exists_between h\u2081 with \u27e8x, xa, xb\u27e9", "annotated_tactic": ["rcases <a>exists_between</a> h\u2081 with \u27e8x, xa, xb\u27e9", [{"full_name": "exists_between", "def_path": "Mathlib/Order/Basic.lean", "def_pos": [1294, 9], "def_end_pos": [1294, 23]}]], "state_before": "\u03b1 : Type u_1\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/ConstantSpeed.lean | unique_unit_speed_on_Icc_zero | [
223,
1
] | [
236,
6
] | [{"tactic": "rw [\u2190 \u03c6st] at hf", "annotated_tactic": ["rw [\u2190 \u03c6st] at hf", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : LinearOrder \u03b1\nE : Type u_2\ninst\u271d : PseudoEMetricSpace E\nf : \u211d \u2192 E\ns\u271d : Set \u211d\nl : \u211d\u22650\ns t : \u211d\nhs : 0 \u2264 s\nht : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Num/Lemmas.lean | PosNum.to_nat_inj | [
529,
1
] | [
530,
91
] | [{"tactic": "rw [\u2190 PosNum.of_to_nat, \u2190 PosNum.of_to_nat, h]", "annotated_tactic": ["rw [\u2190 <a>PosNum.of_to_nat</a>, \u2190 <a>PosNum.of_to_nat</a>, h]", [{"full_name": "PosNum.of_to_nat", "def_path": "Mathlib/Data/Num/Lemmas.lean", "def_pos": [524, 9], "def_end_pos": [524, 18]}, {"full_name": "PosNum.of_t... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Fourier/FourierTransform.lean | Real.fourierIntegral_def | [
262,
1
] | [
264,
6
] | [] |
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