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/FieldTheory/Subfield.lean | RingHom.coe_rangeRestrictField | [
871,
1
] | [
872,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/Restrict.lean | AffineMap.restrict.injective | [
73,
1
] | [
78,
13
] | [{"tactic": "intro x y h", "annotated_tactic": ["intro x y h", []], "state_before": "k : Type u_1\nV\u2081 : Type u_2\nP\u2081 : Type u_3\nV\u2082 : Type u_4\nP\u2082 : Type u_5\ninst\u271d\u2078 : Ring k\ninst\u271d\u2077 : AddCommGroup V\u2081\ninst\u271d\u2076 : AddCommGroup V\u2082\ninst\u271d\u2075 : Module k V\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Bitwise.lean | Nat.xor_bit | [
124,
1
] | [
125,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_inf | [
661,
1
] | [
662,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/CompleteBooleanAlgebra.lean | iSup_iInf_le | [
117,
1
] | [
119,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_inf_dom_right₂ | [
1666,
1
] | [
1676,
75
] | [{"tactic": "haveI := ua2", "annotated_tactic": ["haveI := ua2", []], "state_before": "\u03b1\u271d : Type ua\n\u03b2\u271d : Type ub\n\u03b3\u271d : Type uc\n\u03b4 : Type ud\n\u03b9 : Sort u_1\ninst\u271d\u00b2 : UniformSpace \u03b1\u271d\ninst\u271d\u00b9 : UniformSpace \u03b2\u271d\ninst\u271d : UniformSpace \u03b3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_deriv_of_nonneg' | [
727,
1
] | [
730,
54
] | [{"tactic": "refine integrableOn_Ioi_deriv_of_nonneg (fun x hx \u21a6 ?_) (fun x hx => hderiv x hx.out.le) g'pos hg", "annotated_tactic": ["refine <a>integrableOn_Ioi_deriv_of_nonneg</a> (fun x hx \u21a6 ?_) (fun x hx => hderiv x hx.out.le) g'pos hg", [{"full_name": "MeasureTheory.integrableOn_Ioi_deriv_of_nonneg", "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.refl_symm | [
2186,
1
] | [
2187,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fin/Basic.lean | Fin.zero_mul' | [
1810,
11
] | [
1811,
29
] | [{"tactic": "simp [eq_iff_veq, mul_def]", "annotated_tactic": ["simp [<a>eq_iff_veq</a>, <a>mul_def</a>]", [{"full_name": "Fin.eq_iff_veq", "def_path": "Mathlib/Data/Fin/Basic.lean", "def_pos": [151, 9], "def_end_pos": [151, 19]}, {"full_name": "Fin.mul_def", "def_path": "lake-packages/std/Std/Data/Fin/Lemmas.lean", "d... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/Composition.lean | List.map_length_splitWrtCompositionAux | [
690,
1
] | [
698,
35
] | [{"tactic": "induction' ns with n ns IH <;> intro l h <;> simp at h", "annotated_tactic": ["induction' ns with n ns IH <;> intro l h <;> simp at h", []], "state_before": "n : \u2115\n\u03b1 : Type u_1\nns : List \u2115\n\u22a2 \u2200 {l : List \u03b1}, sum ns \u2264 length l \u2192 map length (splitWrtCompositionAux l ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.bounded_below | [
56,
1
] | [
67,
16
] | [{"tactic": "rcases coercive with \u27e8C, C_ge_0, coercivity\u27e9", "annotated_tactic": ["rcases coercive with \u27e8C, C_ge_0, coercivity\u27e9", []], "state_before": "V : Type u\ninst\u271d\u00b2 : NormedAddCommGroup V\ninst\u271d\u00b9 : InnerProductSpace \u211d V\ninst\u271d : CompleteSpace V\nB : V \u2192L[\u211... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Instances/RatLemmas.lean | Rat.not_countably_generated_nhds_infty_opc | [
65,
1
] | [
69,
47
] | [{"tactic": "intro", "annotated_tactic": ["intro", []], "state_before": "p q : \u211a\ns t : Set \u211a\n\u22a2 \u00acIsCountablyGenerated (\ud835\udcdd \u221e)", "state_after": "p q : \u211a\ns t : Set \u211a\na\u271d : IsCountablyGenerated (\ud835\udcdd \u221e)\n\u22a2 False"}, {"tactic": "have : IsCountablyGenerated... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/NNRat.lean | NNRat.toNNRat_sum_of_nonneg | [
276,
1
] | [
279,
78
] | [{"tactic": "rw [\u2190 coe_inj, coe_sum, Rat.coe_toNNRat _ (Finset.sum_nonneg hf)]", "annotated_tactic": ["rw [\u2190 <a>coe_inj</a>, <a>coe_sum</a>, <a>Rat.coe_toNNRat</a> _ (<a>Finset.sum_nonneg</a> hf)]", [{"full_name": "NNRat.coe_inj", "def_path": "Mathlib/Data/Rat/NNRat.lean", "def_pos": [78, 9], "def_end_pos": [... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/UniformGroup.lean | uniformGroup_inf | [
235,
1
] | [
239,
25
] | [{"tactic": "refine' uniformGroup_iInf fun b => _", "annotated_tactic": ["refine' <a>uniformGroup_iInf</a> fun b => _", [{"full_name": "uniformGroup_iInf", "def_path": "Mathlib/Topology/Algebra/UniformGroup.lean", "def_pos": [227, 9], "def_end_pos": [227, 26]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/DenseEmbedding.lean | isClosed_property3 | [
325,
1
] | [
330,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.pow_arith_mean_le_arith_mean_pow | [
120,
1
] | [
124,
62
] | [{"tactic": "exact_mod_cast\n Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)\n (by exact_mod_cast hw') (fun i _ => (z i).coe_nonneg) n", "annotated_tactic": ["exact_mod_cast\n <a>Real.pow_arith_mean_le_arith_mean_pow</a> s _ _ (fun i _ => (w i).<a>coe_nonneg</a>)\n (by exact_mod_c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_eq_zero_iff | [
168,
11
] | [
171,
28
] | [{"tactic": "simpa [h] using gcd_dvd a b", "annotated_tactic": ["simpa [h] using <a>gcd_dvd</a> a b", [{"full_name": "EuclideanDomain.gcd_dvd", "def_path": "Mathlib/Algebra/EuclideanDomain/Basic.lean", "def_pos": [150, 9], "def_end_pos": [150, 16]}]], "state_before": "R : Type u\ninst\u271d\u00b9 : EuclideanDomain R\ni... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/WittVector/Frobenius.lean | WittVector.ghostComponent_frobenius | [
278,
1
] | [
280,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_X_pow_sub | [
378,
1
] | [
379,
99
] | [{"tactic": "simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) \u2264 n by rwa [\u2190 degree_neg p] at H)", "annotated_tactic": ["simpa [<a>sub_eq_add_neg</a>] using <a>monic_X_pow_add</a> (show <a>degree</a> (-p) \u2264 n by rwa [\u2190 <a>degree_neg</a> p] at H)", [{"full_name": "sub_eq_add_neg", "def_p... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Fintype/Card.lean | Infinite.of_surjective_from_set | [
1014,
1
] | [
1016,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_lipschitz_aux1 | [
348,
9
] | [
374,
32
] | [{"tactic": "rcases (Real.isBounded_iff_bddBelow_bddAbove.1 g.isBounded_range).1 with \u27e8cg, hcg\u27e9", "annotated_tactic": ["rcases (<a>Real.isBounded_iff_bddBelow_bddAbove</a>.1 g.isBounded_range).1 with \u27e8cg, hcg\u27e9", [{"full_name": "Real.isBounded_iff_bddBelow_bddAbove", "def_path": "Mathlib/Topology/Ins... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_zero_le | [
1119,
1
] | [
1119,
94
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/TwoPointing.lean | TwoPointing.bool_snd | [
149,
1
] | [
149,
54
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.KernelFork.ι_ofι | [
102,
1
] | [
103,
43
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.ordered_iff | [
496,
1
] | [
515,
78
] | [{"tactic": "induction p with\n| root => simp\n| left _ _ x _ ih | right _ _ x _ ih => ?_", "annotated_tactic": ["induction p with\n | <a>root</a> => simp\n | <a>left</a> _ _ x _ ih | <a>right</a> _ _ x _ ih => ?_", [{"full_name": "Std.RBNode.Path.root", "def_path": "lake-packages/std/Std/Data/RBMap/Basic.lean", "def... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.pi_eq_bot_iff | [
1913,
1
] | [
1921,
63
] | [{"tactic": "simp only [eq_bot_iff_forall]", "annotated_tactic": ["simp only [<a>eq_bot_iff_forall</a>]", [{"full_name": "Subgroup.eq_bot_iff_forall", "def_path": "Mathlib/GroupTheory/Subgroup/Basic.lean", "def_pos": [901, 9], "def_end_pos": [901, 26]}]], "state_before": "G : Type u_1\nG' : Type u_2\nG'' : Type u_3\nin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext_ring_iff | [
547,
1
] | [
548,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.contDiffWithinAt | [
1438,
1
] | [
1439,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finsupp/Basic.lean | Finsupp.distribMulActionHom_ext | [
1662,
1
] | [
1664,
63
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/BigOperators/Lemmas.lean | Commute.list_sum_right | [
30,
1
] | [
35,
92
] | [{"tactic": "induction' l with x xs ih", "annotated_tactic": ["induction' l with x xs ih", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\nM : Type u_3\nN : Type u_4\nP : Type u_5\nM\u2080 : Type u_6\nG : Type u_7\nR : Type u_8\ninst\u271d : NonUnitalNonAssocSemiring R\na : R\nl : List R\nh : \u2200 (b : R)... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Finsupp.lean | mem_span_range_iff_exists_fun | [
1113,
1
] | [
1118,
94
] | [{"tactic": "rw [Finsupp.equivFunOnFinite.surjective.exists]", "annotated_tactic": ["rw [Finsupp.equivFunOnFinite.surjective.exists]", []], "state_before": "\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d\u2076 : Fintype \u03b1\ninst\u271d\u2075 : Semiring R\ninst\u271d\u2074 : AddCommMonoid M\ninst\u271d\u00... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean | UpperHalfPlane.ext_iff | [
70,
20
] | [
70,
86
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Monotone.lean | Antitone.Ico | [
131,
11
] | [
133,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Deprecated/Subgroup.lean | IsGroupHom.isNormalSubgroup_ker | [
441,
1
] | [
442,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/NNReal.lean | Real.le_coe_toNNReal | [
130,
1
] | [
131,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Homeomorph.lean | Homeomorph.image_symm | [
210,
1
] | [
211,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_eq_midpoint | [
231,
1
] | [
235,
82
] | [{"tactic": "refine' tendsto_nhds_unique (c.tendsto_approx_atTop x) ((tendsto_add_atTop_iff_nat 1).1 _)", "annotated_tactic": ["refine' <a>tendsto_nhds_unique</a> (c.tendsto_approx_atTop x) ((<a>tendsto_add_atTop_iff_nat</a> 1).1 _)", [{"full_name": "tendsto_nhds_unique", "def_path": "Mathlib/Topology/Separation.lean",... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | Convex.is_linear_preimage | [
208,
1
] | [
210,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/QPF/Univariate/Basic.lean | QPF.liftp_iff_of_isUniform | [
680,
1
] | [
692,
29
] | [{"tactic": "rw [liftp_iff, \u2190 abs_repr x]", "annotated_tactic": ["rw [<a>liftp_iff</a>, \u2190 <a>abs_repr</a> x]", [{"full_name": "QPF.liftp_iff", "def_path": "Mathlib/Data/QPF/Univariate/Basic.lean", "def_pos": [101, 9], "def_end_pos": [101, 18]}, {"full_name": "QPF.abs_repr", "def_path": "Mathlib/Data/QPF/Univa... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_iInf | [
254,
1
] | [
255,
51
] | [{"tactic": "simp only [iInf, mem_sInf, Set.forall_range_iff]", "annotated_tactic": ["simp only [<a>iInf</a>, <a>mem_sInf</a>, <a>Set.forall_range_iff</a>]", [{"full_name": "iInf", "def_path": "Mathlib/Order/CompleteLattice.lean", "def_pos": [83, 5], "def_end_pos": [83, 9]}, {"full_name": "Subsemigroup.mem_sInf", "def_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Monoid.lean | finprod_eventually_eq_prod | [
798,
1
] | [
802,
84
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finset/Prod.lean | Finset.product_eq_empty | [
214,
1
] | [
216,
31
] | [{"tactic": "rw [\u2190 not_nonempty_iff_eq_empty, nonempty_product, not_and_or, not_nonempty_iff_eq_empty,\n not_nonempty_iff_eq_empty]", "annotated_tactic": ["rw [\u2190 <a>not_nonempty_iff_eq_empty</a>, <a>nonempty_product</a>, <a>not_and_or</a>, <a>not_nonempty_iff_eq_empty</a>,\n <a>not_nonempty_iff_eq_empty</... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/AtTopBot.lean | Filter.Iic_mem_atBot | [
70,
1
] | [
71,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Basic.lean | InitialSeg.ordinal_type_le | [
364,
1
] | [
366,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_comp | [
798,
1
] | [
800,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ExtendFrom.lean | continuous_extendFrom | [
86,
1
] | [
89,
69
] | [{"tactic": "rw [continuous_iff_continuousOn_univ]", "annotated_tactic": ["rw [<a>continuous_iff_continuousOn_univ</a>]", [{"full_name": "continuous_iff_continuousOn_univ", "def_path": "Mathlib/Topology/ContinuousOn.lean", "def_pos": [546, 9], "def_end_pos": [546, 41]}]], "state_before": "X : Type u_1\nY : Type u_2\nin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_inj | [
398,
1
] | [
399,
59
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.of_d | [
968,
1
] | [
970,
36
] | [{"tactic": "dsimp [of]", "annotated_tactic": ["dsimp [<a>of</a>]", [{"full_name": "CochainComplex.of", "def_path": "Mathlib/Algebra/Homology/HomologicalComplex.lean", "def_pos": [943, 5], "def_end_pos": [943, 7]}]], "state_before": "\u03b9 : Type u_1\nV : Type u\ninst\u271d\u2074 : Category.{v, u} V\ninst\u271d\u00b3 ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_of_mul_lt_mul_left' | [
128,
1
] | [
131,
31
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Coset.lean | rightCoset_one | [
154,
1
] | [
155,
34
] | [{"tactic": "simp [rightCoset]", "annotated_tactic": ["simp [<a>rightCoset</a>]", [{"full_name": "rightCoset", "def_path": "Mathlib/GroupTheory/Coset.lean", "def_pos": [56, 5], "def_end_pos": [56, 15]}]], "state_before": "\u03b1 : Type u_1\ninst\u271d : Monoid \u03b1\ns : Set \u03b1\n\u22a2 \u2200 (x : \u03b1), x \u220... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Basic.lean | Convex.mapsTo_lineMap | [
510,
1
] | [
512,
78
] | [{"tactic": "simpa only [mapsTo', segment_eq_image_lineMap] using h.segment_subset hx hy", "annotated_tactic": ["simpa only [<a>mapsTo'</a>, <a>segment_eq_image_lineMap</a>] using h.segment_subset hx hy", [{"full_name": "Set.mapsTo'", "def_path": "Mathlib/Data/Set/Function.lean", "def_pos": [396, 9], "def_end_pos": [39... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.get!_cons_zero | [
588,
1
] | [
588,
85
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Stream/Init.lean | Stream'.tail_iterate | [
275,
1
] | [
280,
50
] | [{"tactic": "ext n", "annotated_tactic": ["ext n", []], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b4 : Type w\nf : \u03b1 \u2192 \u03b1\na : \u03b1\n\u22a2 tail (iterate f a) = iterate f (f a)", "state_after": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b4 : Type w\nf : \u03b1 \u2192 \u03b1\na : \u03b1\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Num/Lemmas.lean | Num.mod_to_nat | [
1655,
1
] | [
1659,
43
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u22a2 \u2191(0 % 0) = \u21910 % \u21910", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/BumpFunction.lean | SmoothBumpFunction.smooth_smul | [
333,
1
] | [
343,
100
] | [{"tactic": "refine contMDiff_of_support fun x hx => ?_", "annotated_tactic": ["refine <a>contMDiff_of_support</a> fun x hx => ?_", [{"full_name": "contMDiff_of_support", "def_path": "Mathlib/Geometry/Manifold/ContMDiff.lean", "def_pos": [1298, 9], "def_end_pos": [1298, 29]}]], "state_before": "E : Type uE\ninst\u271d\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Rotate.lean | List.isRotated_append | [
511,
1
] | [
512,
22
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u03b1 : Type u\nl l' : List \u03b1\n\u22a2 rotate (l ++ l') (length l) = l' ++ l", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_trans | [
335,
1
] | [
336,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Image.lean | Set.rangeFactorization_eq | [
1064,
1
] | [
1065,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set_inter | [
515,
1
] | [
517,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Iic | [
157,
1
] | [
161,
35
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Nat/Lemmas.lean | Nat.mul_mod_right | [
724,
9
] | [
725,
63
] | [{"tactic": "rw [\u2190 Nat.zero_add (m * n), add_mul_mod_self_left, zero_mod]", "annotated_tactic": ["rw [\u2190 <a>Nat.zero_add</a> (m * n), <a>add_mul_mod_self_left</a>, <a>zero_mod</a>]", [{"full_name": "Nat.zero_add", "def_path": "lake-packages/lean4/src/lean/Init/Data/Nat/Basic.lean", "def_pos": [114, 27], "def_e... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Order/Basic.lean | Int.lt_succ_self | [
100,
1
] | [
101,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Sqrt.lean | Real.sqrt_zero | [
253,
1
] | [
253,
49
] | [{"tactic": "simp [sqrt]", "annotated_tactic": ["simp [<a>sqrt</a>]", [{"full_name": "Real.sqrt", "def_path": "Mathlib/Data/Real/Sqrt.lean", "def_pos": [166, 19], "def_end_pos": [166, 23]}]], "state_before": "x y : \u211d\n\u22a2 sqrt 0 = 0", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineBasis.finite | [
776,
11
] | [
777,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/ContMDiff.lean | ContMDiff.prod_map | [
1713,
1
] | [
1716,
36
] | [{"tactic": "intro p", "annotated_tactic": ["intro p", []], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b3\u2077 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u00b3\u2076 : NormedAddCommGroup E\ninst\u271d\u00b3\u2075 : NormedSpace \ud835\udd5c E\nH : Type u_3\ninst\u271d\u00b3\u2074 : To... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/ContinuousOn.lean | continuousAt_prod_of_discrete_right | [
590,
1
] | [
592,
87
] | [{"tactic": "simp_rw [\u2190 continuousWithinAt_univ]", "annotated_tactic": ["simp_rw [\u2190 <a>continuousWithinAt_univ</a>]", [{"full_name": "continuousWithinAt_univ", "def_path": "Mathlib/Topology/ContinuousOn.lean", "def_pos": [541, 9], "def_end_pos": [541, 32]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Lift.lean | Filter.lift_lift_same_eq_lift | [
158,
1
] | [
164,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.sum_moebius_mul_log_eq | [
142,
1
] | [
158,
51
] | [{"tactic": "simp only [\u2190 log_mul_moebius_eq_vonMangoldt, mul_comm log, mul_apply, log_apply, intCoe_apply, \u2190\n Finset.sum_neg_distrib, neg_mul_eq_mul_neg]", "annotated_tactic": ["simp only [\u2190 <a>log_mul_moebius_eq_vonMangoldt</a>, <a>mul_comm</a> <a>log</a>, <a>mul_apply</a>, <a>log_apply</a>, <a>intCo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Init/Logic.lean | true_iff_iff | [
198,
1
] | [
198,
64
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.trans | [
71,
1
] | [
72,
42
] | [{"tactic": "simp [add_smul, \u2190 hm, \u2190 hn]", "annotated_tactic": ["simp [<a>add_smul</a>, \u2190 hm, \u2190 hn]", [{"full_name": "add_smul", "def_path": "Mathlib/Algebra/Module/Basic.lean", "def_pos": [91, 9], "def_end_pos": [91, 17]}]], "state_before": "\u03b1 : Type u_1\ninst\u271d : AddCommGroup \u03b1\np a ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.toCone_π_app | [
183,
1
] | [
183,
90
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Between.lean | wbtw_vadd_const_iff | [
192,
1
] | [
194,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.Adhesive.mono_of_isPushout_of_mono_right | [
251,
1
] | [
253,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/KummerDedekind.lean | prod_mem_ideal_map_of_mem_conductor | [
97,
1
] | [
126,
52
] | [{"tactic": "rw [Ideal.map, Ideal.span, Finsupp.mem_span_image_iff_total] at hz'", "annotated_tactic": ["rw [<a>Ideal.map</a>, <a>Ideal.span</a>, <a>Finsupp.mem_span_image_iff_total</a>] at hz'", [{"full_name": "Ideal.map", "def_path": "Mathlib/RingTheory/Ideal/Operations.lean", "def_pos": [1367, 5], "def_end_pos": [13... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.lipschitz_apply | [
490,
1
] | [
491,
92
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_iUnion | [
336,
1
] | [
338,
20
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Lemmas.lean | List.zipWith_map_left | [
186,
1
] | [
188,
57
] | [{"tactic": "induction l\u2081 generalizing l\u2082 <;> cases l\u2082 <;> simp_all", "annotated_tactic": ["induction l\u2081 generalizing l\u2082 <;> cases l\u2082 <;> simp_all", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b1' : Type u_3\n\u03b3 : Type u_4\nl\u2081 : List \u03b1\nl\u2082 : List \u03... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_id | [
382,
1
] | [
383,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_induced | [
131,
1
] | [
133,
18
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Invertible/Defs.lean | mul_left_inj_of_invertible | [
248,
1
] | [
250,
68
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Init/Lemmas.lean | List.append_right_inj | [
79,
1
] | [
80,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Lifts.lean | Polynomial.monomial_mem_lifts | [
120,
1
] | [
124,
18
] | [{"tactic": "obtain \u27e8r, rfl\u27e9 := Set.mem_range.1 h", "annotated_tactic": ["obtain \u27e8r, rfl\u27e9 := <a>Set.mem_range</a>.1 h", [{"full_name": "Set.mem_range", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [673, 9], "def_end_pos": [673, 18]}]], "state_before": "R : Type u\ninst\u271d\u00b9 : Semirin... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/VectorBundle/Constructions.lean | Trivialization.continuousLinearEquivAt_prod | [
151,
1
] | [
159,
64
] | [{"tactic": "ext v : 2", "annotated_tactic": ["ext v : 2", []], "state_before": "\ud835\udd5c : Type u_1\nB : Type u_2\ninst\u271d\u00b9\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b9\u2076 : TopologicalSpace B\nF\u2081 : Type u_3\ninst\u271d\u00b9\u2075 : NormedAddCommGroup F\u2081\ninst\u271d\u00b9\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.ext | [
458,
1
] | [
459,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/MinMax.lean | max_inv_inv' | [
44,
1
] | [
47,
34
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | Differentiable.restrictScalars | [
85,
1
] | [
86,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/LocallyFinite.lean | LocallyFinite.nhdsWithin_iUnion | [
77,
11
] | [
88,
86
] | [{"tactic": "rcases hf a with \u27e8U, haU, hfin\u27e9", "annotated_tactic": ["rcases hf a with \u27e8U, haU, hfin\u27e9", []], "state_before": "\u03b9 : Type u_1\n\u03b9' : Type u_2\n\u03b1 : Type u_3\nX : Type u_4\nY : Type u_5\ninst\u271d\u00b9 : TopologicalSpace X\ninst\u271d : TopologicalSpace Y\nf g : \u03b9 \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Module.lean | Complex.nonempty_linearEquiv_real | [
573,
1
] | [
574,
56
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\u22a2 Module.rank \u211a \u2102 = Module.rank \u211a \u211d", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.IsEquivalence.fun_inv_map | [
601,
1
] | [
604,
6
] | [{"tactic": "erw [NatIso.naturality_2]", "annotated_tactic": ["erw [<a>NatIso.naturality_2</a>]", [{"full_name": "CategoryTheory.NatIso.naturality_2", "def_path": "Mathlib/CategoryTheory/NatIso.lean", "def_pos": [172, 9], "def_end_pos": [172, 21]}]], "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u20... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Martingale/Upcrossing.lean | MeasureTheory.upperCrossingTime_stabilize | [
274,
1
] | [
276,
94
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Compactness/LocallyCompact.lean | exists_compact_subset | [
154,
1
] | [
157,
55
] | [{"tactic": "rcases LocallyCompactSpace.local_compact_nhds x U (hU.mem_nhds hx) with \u27e8K, h1K, h2K, h3K\u27e9", "annotated_tactic": ["rcases <a>LocallyCompactSpace.local_compact_nhds</a> x U (hU.mem_nhds hx) with \u27e8K, h1K, h2K, h3K\u27e9", [{"full_name": "LocallyCompactSpace.local_compact_nhds", "def_path": "Ma... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Array/Lemmas.lean | Array.swapAt_def | [
126,
9
] | [
127,
46
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.lcompₛₗ_apply | [
298,
1
] | [
299,
41
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_image | [
1201,
1
] | [
1207,
29
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Basic.lean | continuous_def | [
1602,
1
] | [
1604,
33
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.symm_neg | [
2179,
1
] | [
2180,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/Irrational.lean | Irrational.ne_nat | [
168,
1
] | [
169,
13
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_eq_iSup_eapprox_lintegral | [
451,
1
] | [
462,
62
] | [{"tactic": "congr", "annotated_tactic": ["congr", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\nm : MeasurableSpace \u03b1\n\u03bc \u03bd : Measure \u03b1\nf : \u03b1 \u2192 \u211d\u22650\u221e\nhf : Measurable f\n\u22a2 \u222b\u207b (a : \u03b1), f a \u2202\u03bc = ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean | MeasureTheory.condexpL1_measure_zero | [
532,
1
] | [
533,
30
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean | CategoryTheory.Subgroupoid.isWide_iff_objs_eq_univ | [
315,
1
] | [
323,
29
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "C : Type u\ninst\u271d : Groupoid C\nS : Subgroupoid C\n\u22a2 IsWide S \u2194 objs S = univ", "state_after": "case mp\nC : Type u\ninst\u271d : Groupoid C\nS : Subgroupoid C\n\u22a2 IsWide S \u2192 objs S = univ\n\ncase mpr\nC : Type ... |
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