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/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_union | [
1018,
1
] | [
1019,
30
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Sum/Lemmas.lean | Sum.elim_inl_inr | [
105,
9
] | [
106,
60
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/Algebra/Monoid.lean | SmoothWithinAt.div_const | [
503,
8
] | [
505,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/Integral.lean | MeasureTheory.Integrable.comp_div_right | [
126,
1
] | [
129,
30
] | [{"tactic": "simp_rw [div_eq_mul_inv]", "annotated_tactic": ["simp_rw [<a>div_eq_mul_inv</a>]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}]], "state_before": "\ud835\udd5c : Type u_1\nM : Type u_2\n\u03b1 : Type u_3\nG : Type u_4\nE : T... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.compatiblePreservingOfFlat | [
124,
1
] | [
156,
83
] | [{"tactic": "constructor", "annotated_tactic": ["constructor", []], "state_before": "C\u271d : Type u\u2081\ninst\u271d\u2075 : Category.{v\u2081, u\u2081} C\u271d\nD\u271d : Type u\u2082\ninst\u271d\u2074 : Category.{v\u2082, u\u2082} D\u271d\nA : Type u\u2083\ninst\u271d\u00b3 : Category.{v\u2083, u\u2083} A\nJ : Gro... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr'_trans | [
554,
9
] | [
557,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_int_mod | [
533,
1
] | [
534,
66
] | [{"tactic": "induction s using Multiset.induction <;> simp [Int.add_emod, *]", "annotated_tactic": ["induction s using <a>Multiset.induction</a> <;> simp [<a>Int.add_emod</a>, *]", [{"full_name": "Multiset.induction", "def_path": "Mathlib/Data/Multiset/Basic.lean", "def_pos": [154, 19], "def_end_pos": [154, 28]}, {"ful... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MatrixExponential.lean | Matrix.exp_conj | [
194,
1
] | [
197,
71
] | [{"tactic": "simpa only [Matrix.coe_units_inv] using exp_units_conj \ud835\udd42 u A", "annotated_tactic": ["simpa only [<a>Matrix.coe_units_inv</a>] using <a>exp_units_conj</a> \ud835\udd42 u A", [{"full_name": "Matrix.coe_units_inv", "def_path": "Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean", "def_pos": [228,... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.toSpanSingleton_homothety | [
229,
1
] | [
232,
22
] | [{"tactic": "rw [mul_comm]", "annotated_tactic": ["rw [<a>mul_comm</a>]", [{"full_name": "mul_comm", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [302, 9], "def_end_pos": [302, 17]}]], "state_before": "\ud835\udd5c : Type u_1\n\ud835\udd5c\u2082 : Type u_2\nE : Type u_3\nF : Type u_4\nG : Type u_5\ninst\u2... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.lmul'_apply_tmul | [
955,
1
] | [
956,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingFaceMapComplex.d_squared | [
74,
1
] | [
116,
53
] | [{"tactic": "dsimp", "annotated_tactic": ["dsimp", []], "state_before": "C : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\ninst\u271d : Preadditive C\nX Y : SimplicialObject C\nn : \u2115\n\u22a2 objD X (n + 1) \u226b objD X n = 0", "state_after": "C : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\ninst\u271... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Logic.lean | not_forall_of_exists_not | [
447,
1
] | [
448,
27
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | Metric.isBounded_iff | [
702,
1
] | [
705,
17
] | [{"tactic": "rw [isBounded_def, \u2190 Filter.mem_sets, @PseudoMetricSpace.cobounded_sets \u03b1, mem_setOf_eq,\n compl_compl]", "annotated_tactic": ["rw [<a>isBounded_def</a>, \u2190 <a>Filter.mem_sets</a>, @<a>PseudoMetricSpace.cobounded_sets</a> \u03b1, <a>mem_setOf_eq</a>,\n <a>compl_compl</a>]", [{"full_name":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Disjoint.lean | isComplemented_bot | [
656,
1
] | [
657,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/BumpFunction.lean | SmoothBumpFunction.tsupport_mem_nhds | [
182,
1
] | [
183,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean | Real.BohrMollerup.f_add_nat_le | [
227,
1
] | [
234,
96
] | [{"tactic": "have hn' : 0 < (n : \u211d) := Nat.cast_pos.mpr (Nat.pos_of_ne_zero hn)", "annotated_tactic": ["have hn' : 0 < (n : \u211d) := Nat.cast_pos.mpr (<a>Nat.pos_of_ne_zero</a> hn)", [{"full_name": "Nat.pos_of_ne_zero", "def_path": "lake-packages/std/Std/Data/Nat/Init/Lemmas.lean", "def_pos": [25, 19], "def_end_... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.surjOn | [
193,
11
] | [
194,
17
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convolution.lean | contDiffOn_convolution_right_with_param_aux | [
1349,
1
] | [
1392,
28
] | [{"tactic": "induction' n using ENat.nat_induction with n ih ih generalizing g E' F", "annotated_tactic": ["induction' n using <a>ENat.nat_induction</a> with n ih ih generalizing g E' F", [{"full_name": "ENat.nat_induction", "def_path": "Mathlib/Data/ENat/Basic.lean", "def_pos": [213, 9], "def_end_pos": [213, 22]}]], "... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ioi_iff_exists_Ioc_subset | [
1733,
1
] | [
1741,
55
] | [{"tactic": "rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]", "annotated_tactic": ["rw [<a>mem_nhdsWithin_Ioi_iff_exists_Ioo_subset</a>]", [{"full_name": "mem_nhdsWithin_Ioi_iff_exists_Ioo_subset", "def_path": "Mathlib/Topology/Order/Basic.lean", "def_pos": [1712, 9], "def_end_pos": [1712, 49]}]], "state_before": "\u03b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq_of_equiv_aux | [
325,
9
] | [
345,
25
] | [{"tactic": "have hpn : 0 < padicNorm p (f (stationaryPoint hf)) - padicNorm p (g (stationaryPoint hg)) :=\n sub_pos_of_lt hlt", "annotated_tactic": ["have hpn : 0 < <a>padicNorm</a> p (f (<a>stationaryPoint</a> hf)) - <a>padicNorm</a> p (g (<a>stationaryPoint</a> hg)) :=\n <a>sub_pos_of_lt</a> hlt", [{"full_name":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.toPlus_mk | [
178,
1
] | [
191,
6
] | [{"tactic": "dsimp [mk, toPlus]", "annotated_tactic": ["dsimp [<a>mk</a>, <a>toPlus</a>]", [{"full_name": "CategoryTheory.GrothendieckTopology.Plus.mk", "def_path": "Mathlib/CategoryTheory/Sites/Sheafification.lean", "def_pos": [159, 5], "def_end_pos": [159, 7]}, {"full_name": "CategoryTheory.GrothendieckTopology.toPlu... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.end_hom_mk_of_mk | [
302,
1
] | [
306,
57
] | [{"tactic": "rw [\u2190 sec h, hs]", "annotated_tactic": ["rw [\u2190 sec h, hs]", []], "state_before": "V : Type u\nG : SimpleGraph V\nK\u271d L\u271d L' M : Set V\ns : (j : (Finset V)\u1d52\u1d56) \u2192 (componentComplFunctor G).obj j\nsec : s \u2208 SimpleGraph.end G\nK L : (Finset V)\u1d52\u1d56\nh : L \u27f6 K\nv... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/MellinTransform.lean | MellinConvergent.comp_mul_left | [
76,
1
] | [
87,
56
] | [{"tactic": "have := integrableOn_Ioi_comp_mul_left_iff (fun t : \u211d => (t : \u2102) ^ (s - 1) \u2022 f t) 0 ha", "annotated_tactic": ["have := <a>integrableOn_Ioi_comp_mul_left_iff</a> (fun t : \u211d => (t : \u2102) ^ (s - 1) \u2022 f t) 0 ha", [{"full_name": "MeasureTheory.integrableOn_Ioi_comp_mul_left_iff", "de... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_empty | [
1268,
1
] | [
1269,
21
] | [{"tactic": "simp [deleteVerts]", "annotated_tactic": ["simp [<a>deleteVerts</a>]", [{"full_name": "SimpleGraph.Subgraph.deleteVerts", "def_path": "Mathlib/Combinatorics/SimpleGraph/Subgraph.lean", "def_pos": [1244, 5], "def_end_pos": [1244, 16]}]], "state_before": "\u03b9 : Sort u_1\nV : Type u\nW : Type v\nG : Simple... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_right_eq_zero_iff | [
465,
1
] | [
466,
57
] | [{"tactic": "by_cases hq : q = 0 <;> simp [h.mul_right_ne_zero, hq]", "annotated_tactic": ["by_cases hq : q = 0 <;> simp [h.mul_right_ne_zero, hq]", []], "state_before": "R : Type u\nS : Type v\na b : R\nm n : \u2115\n\u03b9 : Type y\ninst\u271d : Semiring R\np : R[X]\nh : Monic p\nq : R[X]\n\u22a2 p * q = 0 \u2194 q =... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.square_to_iso_invert | [
256,
1
] | [
258,
87
] | [{"tactic": "simpa only [Category.assoc] using (Iso.comp_inv_eq p).mpr (Arrow.w_mk_right sq).symm", "annotated_tactic": ["simpa only [<a>Category.assoc</a>] using (<a>Iso.comp_inv_eq</a> p).<a>mpr</a> (<a>Arrow.w_mk_right</a> sq).<a>symm</a>", [{"full_name": "CategoryTheory.Category.assoc", "def_path": "Mathlib/Categor... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.top_ne_coe | [
305,
9
] | [
305,
66
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_finset_prod | [
662,
1
] | [
664,
37
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Prod.lean | Set.univ_pi_update | [
841,
1
] | [
844,
62
] | [{"tactic": "rw [compl_eq_univ_diff, \u2190 pi_update_of_mem (mem_univ _)]", "annotated_tactic": ["rw [<a>compl_eq_univ_diff</a>, \u2190 <a>pi_update_of_mem</a> (<a>mem_univ</a> _)]", [{"full_name": "Set.compl_eq_univ_diff", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [1916, 9], "def_end_pos": [1916, 27]}, {"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/Slope.lean | ConvexOn.secant_mono_aux2 | [
250,
1
] | [
255,
52
] | [{"tactic": "have hxy' : 0 < y - x := by linarith", "annotated_tactic": ["have hxy' : 0 < y - x := by linarith", []], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d : LinearOrderedField \ud835\udd5c\ns : Set \ud835\udd5c\nf : \ud835\udd5c \u2192 \ud835\udd5c\nhf : ConvexOn \ud835\udd5c s f\nx y z : \ud835\udd5c\n... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Choose/Vandermonde.lean | Nat.add_choose_eq | [
29,
1
] | [
36,
83
] | [{"tactic": "calc\n (m + n).choose k = ((X + 1) ^ (m + n)).coeff k := by rw [coeff_X_add_one_pow, Nat.cast_id]\n _ = ((X + 1) ^ m * (X + 1) ^ n).coeff k := by rw [pow_add]\n _ = \u2211 ij : \u2115 \u00d7 \u2115 in antidiagonal k, m.choose ij.1 * n.choose ij.2 := by\n rw [coeff_mul, Finset.sum_congr rfl]\n simp... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.toBlock_inverse_eq_zero | [
310,
1
] | [
327,
40
] | [{"tactic": "let p i := b i < k", "annotated_tactic": ["let p i := b i < k", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nm : Type u_3\nn : Type u_4\no : Type u_5\nm' : \u03b1 \u2192 Type u_6\nn' : \u03b1 \u2192 Type u_7\nR : Type v\ninst\u271d\u2076 : CommRing R\nM N : Matrix m m R\nb : m \u2192 \u03b1\... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Convex/StoneSeparation.lean | exists_convex_convex_compl_subset | [
83,
1
] | [
111,
29
] | [{"tactic": "let S : Set (Set E) := { C | Convex \ud835\udd5c C \u2227 Disjoint C t }", "annotated_tactic": ["let S : <a>Set</a> (<a>Set</a> E) := { C | <a>Convex</a> \ud835\udd5c C \u2227 <a>Disjoint</a> C t }", [{"full_name": "Set", "def_path": "Mathlib/Init/Set.lean", "def_pos": [38, 5], "def_end_pos": [38, 8]}, {"f... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/MetricSpace/Basic.lean | nhds_comap_dist | [
1845,
1
] | [
1847,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.setAverage_eq' | [
303,
1
] | [
305,
47
] | [{"tactic": "simp only [average_eq', restrict_apply_univ]", "annotated_tactic": ["simp only [<a>average_eq'</a>, <a>restrict_apply_univ</a>]", [{"full_name": "MeasureTheory.average_eq'", "def_path": "Mathlib/MeasureTheory/Integral/Average.lean", "def_pos": [277, 9], "def_end_pos": [277, 20]}, {"full_name": "MeasureTheo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_map | [
734,
1
] | [
736,
20
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/MeanValue.lean | concaveOn_of_deriv2_nonpos' | [
1240,
1
] | [
1244,
79
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Quot.lean | Quotient.induction_on_pi | [
435,
1
] | [
439,
10
] | [{"tactic": "rw [\u2190 (funext fun i \u21a6 Quotient.out_eq (f i) : (fun i \u21a6 \u27e6(f i).out\u27e7) = f)]", "annotated_tactic": ["rw [\u2190 (<a>funext</a> fun i \u21a6 <a>Quotient.out_eq</a> (f i) : (fun i \u21a6 \u27e6(f i).<a>out</a>\u27e7) = f)]", [{"full_name": "funext", "def_path": "lake-packages/lean4/src/... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_add | [
138,
1
] | [
146,
47
] | [{"tactic": "simp_rw [degrees_def]", "annotated_tactic": ["simp_rw [<a>degrees_def</a>]", [{"full_name": "MvPolynomial.degrees_def", "def_path": "Mathlib/Data/MvPolynomial/Variables.lean", "def_pos": [92, 9], "def_end_pos": [92, 20]}]], "state_before": "R : Type u\nS : Type v\n\u03c3 : Type u_1\n\u03c4 : Type u_2\nr : ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one | [
396,
1
] | [
398,
45
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/CategoryTheory/Limits/Preserves/Shapes/Products.lean | CategoryTheory.Limits.PreservesCoproduct.inv_hom | [
171,
1
] | [
171,
99
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Fin/Lemmas.lean | Fin.castLE_castLE | [
288,
9
] | [
290,
38
] | [{"tactic": "simp only [coe_castLE]", "annotated_tactic": ["simp only [<a>coe_castLE</a>]", [{"full_name": "Fin.coe_castLE", "def_path": "lake-packages/std/Std/Data/Fin/Lemmas.lean", "def_pos": [278, 17], "def_end_pos": [278, 27]}]], "state_before": "k m n : Nat\nkm : k \u2264 m\nmn : m \u2264 n\ni : Fin k\n\u22a2 \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_succ_iff_deriv | [
2195,
1
] | [
2198,
27
] | [{"tactic": "simp only [\u2190 contDiffOn_univ, contDiffOn_succ_iff_deriv_of_open, isOpen_univ,\n differentiableOn_univ]", "annotated_tactic": ["simp only [\u2190 <a>contDiffOn_univ</a>, <a>contDiffOn_succ_iff_deriv_of_open</a>, <a>isOpen_univ</a>,\n <a>differentiableOn_univ</a>]", [{"full_name": "contDiffOn_univ",... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_smul | [
363,
1
] | [
365,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.not_mem_of_not_mem_closure | [
270,
1
] | [
271,
24
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/Int/DivMod.lean | Int.dvd_zero | [
594,
11
] | [
594,
75
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Geometry/Manifold/MFDeriv.lean | mdifferentiableAt_iff_of_mem_source | [
642,
1
] | [
650,
70
] | [{"tactic": "rw [continuousWithinAt_univ, Set.preimage_univ, Set.univ_inter]", "annotated_tactic": ["rw [<a>continuousWithinAt_univ</a>, <a>Set.preimage_univ</a>, <a>Set.univ_inter</a>]", [{"full_name": "continuousWithinAt_univ", "def_path": "Mathlib/Topology/ContinuousOn.lean", "def_pos": [541, 9], "def_end_pos": [541... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Basic.lean | le_of_eq_of_le' | [
199,
1
] | [
200,
22
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Group/Defs.lean | Right.self_lt_inv | [
503,
1
] | [
504,
42
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Module/PID.lean | Submodule.isInternal_prime_power_torsion_of_pid | [
70,
1
] | [
79,
36
] | [{"tactic": "convert isInternal_prime_power_torsion hM", "annotated_tactic": ["convert <a>isInternal_prime_power_torsion</a> hM", [{"full_name": "Submodule.isInternal_prime_power_torsion", "def_path": "Mathlib/Algebra/Module/DedekindDomain.lean", "def_pos": [67, 9], "def_end_pos": [67, 39]}]], "state_before": "R : Type... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/EReal.lean | EReal.sign_bot | [
1122,
1
] | [
1122,
48
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_neg | [
514,
1
] | [
522,
65
] | [{"tactic": "cases' x with x", "annotated_tactic": ["cases' x with x", []], "state_before": "x : \u211d\u22650\u221e\ny : \u211d\n\u22a2 x ^ (-y) = (x ^ y)\u207b\u00b9", "state_after": "case none\ny : \u211d\n\u22a2 none ^ (-y) = (none ^ y)\u207b\u00b9\n\ncase some\ny : \u211d\nx : \u211d\u22650\n\u22a2 Option.some x ^... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Group/LIntegral.lean | MeasureTheory.lintegral_mul_right_eq_self | [
46,
1
] | [
49,
35
] | [{"tactic": "convert (lintegral_map_equiv f <| MeasurableEquiv.mulRight g).symm using 1", "annotated_tactic": ["convert (<a>lintegral_map_equiv</a> f <| <a>MeasurableEquiv.mulRight</a> g).<a>symm</a> using 1", [{"full_name": "MeasureTheory.lintegral_map_equiv", "def_path": "Mathlib/MeasureTheory/Integral/Lebesgue.lean"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Game/PGame.lean | SetTheory.PGame.relabel_moveLeft' | [
1182,
1
] | [
1184,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.apply_one | [
692,
1
] | [
694,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.pow_eq_on_of_mem_support | [
382,
1
] | [
388,
81
] | [{"tactic": "induction' k with k hk", "annotated_tactic": ["induction' k with k hk", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : Fintype \u03b1\nf g : Perm \u03b1\nh : \u2200 (x : \u03b1), x \u2208 support f \u2229 support g \u2192 \u2191f x = \u2191g x\nk : \u2115\n\u22... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/TypeVec.lean | TypeVec.snd_diag | [
577,
1
] | [
580,
33
] | [{"tactic": "funext i", "annotated_tactic": ["funext i", []], "state_before": "n : \u2115\n\u03b1 : TypeVec.{u_1} n\n\u22a2 prod.snd \u229a prod.diag = id", "state_after": "case h\nn : \u2115\n\u03b1 : TypeVec.{u_1} n\ni : Fin2 n\n\u22a2 (prod.snd \u229a prod.diag) i = id i"}, {"tactic": "induction i", "annotated_tacti... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ioc_of_Ioo | [
658,
1
] | [
659,
24
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/WellFoundedSet.lean | Set.IsWf.isPwo | [
551,
11
] | [
556,
39
] | [{"tactic": "intro f hf", "annotated_tactic": ["intro f hf", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\n\u03b3 : Type u_4\n\u03c0 : \u03b9 \u2192 Type u_5\ninst\u271d : LinearOrder \u03b1\ns : Set \u03b1\nhs : IsWf s\n\u22a2 IsPwo s", "state_after": "\u03b9 : Type u_1\n\u03b1 : Type ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Order/Ring/Defs.lean | neg_one_lt_zero | [
1126,
1
] | [
1127,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Div.lean | Polynomial.degree_divByMonic_lt | [
322,
1
] | [
335,
64
] | [{"tactic": "haveI := Nontrivial.of_polynomial_ne hp0", "annotated_tactic": ["haveI := <a>Nontrivial.of_polynomial_ne</a> hp0", [{"full_name": "Polynomial.Nontrivial.of_polynomial_ne", "def_path": "Mathlib/Data/Polynomial/Basic.lean", "def_pos": [817, 9], "def_end_pos": [817, 36]}]], "state_before": "R : Type u\nS : Ty... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_monomial_same | [
1398,
1
] | [
1399,
40
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_isLimit | [
300,
1
] | [
303,
55
] | [{"tactic": "simpa using ho\u2082", "annotated_tactic": ["simpa using ho\u2082", []], "state_before": "o : Ordinal.{u}\nho\u2082 : 2 < o\nho : Principal (fun x x_1 => x * x_1) o\n\u22a2 succ 1 < o", "state_after": "no goals"}] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Real/ENNReal.lean | ENNReal.orderIsoIicOneBirational_symm_apply | [
1836,
1
] | [
1838,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.coe_zero | [
227,
1
] | [
228,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Star/NonUnitalSubalgebra.lean | StarAlgEquiv.ofLeftInverse'_symm_apply | [
499,
1
] | [
501,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | OneHom.coe_coe | [
249,
1
] | [
249,
91
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_lt | [
132,
1
] | [
133,
28
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_mul | [
295,
1
] | [
328,
27
] | [{"tactic": "rw [mul_eq_sum_sum, derivative_sum]", "annotated_tactic": ["rw [<a>mul_eq_sum_sum</a>, <a>derivative_sum</a>]", [{"full_name": "Polynomial.mul_eq_sum_sum", "def_path": "Mathlib/Data/Polynomial/Basic.lean", "def_pos": [989, 9], "def_end_pos": [989, 23]}, {"full_name": "Polynomial.derivative_sum", "def_path"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Probability/Kernel/IntegralCompProd.lean | ProbabilityTheory.integrable_compProd_iff | [
124,
1
] | [
129,
59
] | [{"tactic": "simp only [Integrable, hasFiniteIntegral_compProd_iff' hf, hf.norm.integral_kernel_compProd,\n hf, hf.compProd_mk_left, eventually_and, true_and_iff]", "annotated_tactic": ["simp only [<a>Integrable</a>, <a>hasFiniteIntegral_compProd_iff'</a> hf, hf.norm.integral_kernel_compProd,\n hf, hf.compProd_mk_l... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.integrable | [
101,
1
] | [
102,
4
] | [] |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/List/Basic.lean | List.erase_eq_eraseTR | [
41,
10
] | [
50,
35
] | [{"tactic": "funext \u03b1 _ l a", "annotated_tactic": ["funext \u03b1 _ l a", []], "state_before": "\u22a2 @List.erase = @eraseTR", "state_after": "case h.h.h.h\n\u03b1 : Type u_1\nx\u271d : BEq \u03b1\nl : List \u03b1\na : \u03b1\n\u22a2 List.erase l a = eraseTR l a"}, {"tactic": "simp [eraseTR]", "annotated_tactic":... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_smul_set | [
318,
1
] | [
319,
10
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/List/Count.lean | List.prod_eq_pow_single | [
178,
1
] | [
180,
64
] | [{"tactic": "rw [map_id]", "annotated_tactic": ["rw [<a>map_id</a>]", [{"full_name": "List.map_id", "def_path": "lake-packages/std/Std/Data/List/Init/Lemmas.lean", "def_pos": [94, 17], "def_end_pos": [94, 23]}]], "state_before": "\u03b1 : Type u_1\nl : List \u03b1\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : Mo... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Complex/Exponential.lean | Real.cosh_sub | [
1387,
1
] | [
1388,
54
] | [{"tactic": "simp [sub_eq_add_neg, cosh_add, sinh_neg, cosh_neg]", "annotated_tactic": ["simp [<a>sub_eq_add_neg</a>, <a>cosh_add</a>, <a>sinh_neg</a>, <a>cosh_neg</a>]", [{"full_name": "sub_eq_add_neg", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [975, 3], "def_end_pos": [975, 14]}, {"full_name": "Real.c... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Sups.lean | Set.singleton_infs_singleton | [
319,
1
] | [
320,
19
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Finmap.lean | Finmap.induction_on | [
142,
1
] | [
143,
41
] | [{"tactic": "rcases s with \u27e8\u27e8a\u27e9, h\u27e9", "annotated_tactic": ["rcases s with \u27e8\u27e8a\u27e9, h\u27e9", []], "state_before": "\u03b1 : Type u\n\u03b2 : \u03b1 \u2192 Type v\nC : Finmap \u03b2 \u2192 Prop\ns : Finmap \u03b2\nH : \u2200 (a : AList \u03b2), C \u27e6a\u27e7\n\u22a2 C s", "state_after":... |
https://github.com/leanprover/std4 | 869c615eb10130c0637a7bc038e2b80253559913 | lake-packages/std/Std/Data/String/Lemmas.lean | String.extract_zero_endPos | [
451,
1
] | [
455,
35
] | [{"tactic": "simp [extract, Nat.ne_of_gt add_csize_pos]", "annotated_tactic": ["simp [<a>extract</a>, <a>Nat.ne_of_gt</a> <a>add_csize_pos</a>]", [{"full_name": "String.extract", "def_path": "lake-packages/lean4/src/lean/Init/Data/String/Basic.lean", "def_pos": [220, 5], "def_end_pos": [220, 12]}, {"full_name": "Nat.ne... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.map_natDegree_eq_sub | [
274,
1
] | [
280,
18
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "R : Type u_1\ninst\u271d\u00b2 : Semiring R\nf : R[X]\nS : Type u_2\nF : Type u_3\ninst\u271d\u00b9 : Semiring S\ninst\u271d : AddMonoidHomClass F R[X] S[X]\n\u03c6 : F\np : R[X]\nk : \u2115\n\u03c6_k : \u2200 (f : R[X]), natDegree f < k \u2192 \u21... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/NumberTheory/LegendreSymbol/AddCharacter.lean | AddChar.map_nsmul_pow | [
143,
1
] | [
144,
68
] | [{"tactic": "rw [coe_to_fun_apply, coe_to_fun_apply _ x, ofAdd_nsmul, map_pow]", "annotated_tactic": ["rw [<a>coe_to_fun_apply</a>, <a>coe_to_fun_apply</a> _ x, <a>ofAdd_nsmul</a>, <a>map_pow</a>]", [{"full_name": "AddChar.coe_to_fun_apply", "def_path": "Mathlib/NumberTheory/LegendreSymbol/AddCharacter.lean", "def_pos"... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Rat/Cast/Defs.lean | Rat.commute_cast | [
69,
1
] | [
70,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/Partrec.lean | Computable.vector_length | [
375,
1
] | [
376,
32
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_head | [
555,
1
] | [
556,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.comap_exp_comap_abs_atTop | [
423,
1
] | [
427,
55
] | [{"tactic": "rw [Real.comap_exp_atTop]", "annotated_tactic": ["rw [<a>Real.comap_exp_atTop</a>]", [{"full_name": "Real.comap_exp_atTop", "def_path": "Mathlib/Analysis/SpecialFunctions/Exp.lean", "def_pos": [303, 9], "def_end_pos": [303, 24]}]], "state_before": "\u22a2 comap re (comap Real.exp atTop) = comap re atTop", ... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Order/Filter/Basic.lean | Function.Commute.filter_comap | [
2205,
1
] | [
2207,
26
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.unit_le_op_norm | [
386,
1
] | [
387,
55
] | [{"tactic": "simp", "annotated_tactic": ["simp", []], "state_before": "\ud835\udd5c : Type u\n\u03b9 : Type v\n\u03b9' : Type v'\nn : \u2115\nE : \u03b9 \u2192 Type wE\nE\u2081 : \u03b9 \u2192 Type wE\u2081\nE' : \u03b9' \u2192 Type wE'\nEi : Fin (Nat.succ n) \u2192 Type wEi\nG : Type wG\nG' : Type wG'\ninst\u271d\u00b... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/UnorderedInterval.lean | Set.uIcc_prod_uIcc | [
145,
1
] | [
147,
23
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_zero | [
1242,
1
] | [
1243,
52
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Nat/Size.lean | Nat.size_le_size | [
158,
1
] | [
159,
49
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Analysis/InnerProductSpace/OfNorm.lean | InnerProductSpaceable.add_left_aux5 | [
199,
9
] | [
206,
68
] | [{"tactic": "rw [eq_sub_iff_add_eq, eq_div_iff (two_ne_zero' \u211d), mul_comm _ (2 : \u211d), eq_comm]", "annotated_tactic": ["rw [<a>eq_sub_iff_add_eq</a>, <a>eq_div_iff</a> (<a>two_ne_zero'</a> \u211d), <a>mul_comm</a> _ (2 : \u211d), <a>eq_comm</a>]", [{"full_name": "eq_sub_iff_add_eq", "def_path": "Mathlib/Algebra... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AdjoinSimple.algebraMap_gen | [
511,
1
] | [
512,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_injective | [
1133,
1
] | [
1134,
38
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Group/Conj.lean | IsConj.conjugatesOf_eq | [
290,
1
] | [
291,
71
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Hom/Group/Defs.lean | MonoidHom.map_inv | [
1431,
11
] | [
1432,
14
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_eq' | [
166,
1
] | [
167,
43
] | [{"tactic": "simpa only [sub_eq_neg_add] using h (-x)", "annotated_tactic": ["simpa only [<a>sub_eq_neg_add</a>] using h (-x)", [{"full_name": "sub_eq_neg_add", "def_path": "Mathlib/Algebra/Group/Basic.lean", "def_pos": [491, 3], "def_end_pos": [491, 14]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Data/Setoid/Basic.lean | Setoid.ker_eq_lift_of_injective | [
315,
1
] | [
320,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/Separation.lean | SeparatedNhds.union_right | [
165,
1
] | [
166,
36
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Topology/OmegaCompletePartialOrder.lean | notBelow_isOpen | [
98,
1
] | [
102,
49
] | [{"tactic": "have h : Monotone (notBelow y) := fun x z hle \u21a6 mt hle.trans", "annotated_tactic": ["have h : <a>Monotone</a> (<a>notBelow</a> y) := fun x z hle \u21a6 <a>mt</a> hle.trans", [{"full_name": "Monotone", "def_path": "Mathlib/Order/Monotone/Basic.lean", "def_pos": [77, 5], "def_end_pos": [77, 13]}, {"full... |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/Algebra/Associated.lean | Associates.one_eq_mk_one | [
798,
1
] | [
799,
6
] | [] |
https://github.com/leanprover-community/mathlib4 | 3ce43c18f614b76e161f911b75a3e1ef641620ff | Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq_iff_exists | [
587,
1
] | [
588,
63
] | [] |
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