file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Std/Data/List/Lemmas.lean | List.get?_append | [
{
"state_after": "α : Type u_1\nl₁ l₂ : List α\nn : Nat\nhn : n < length l₁\nhn' : n < length (l₁ ++ l₂)\n⊢ get? (l₁ ++ l₂) n = get? l₁ n",
"state_before": "α : Type u_1\nl₁ l₂ : List α\nn : Nat\nhn : n < length l₁\n⊢ get? (l₁ ++ l₂) n = get? l₁ n",
"tactic": "have hn' : n < (l₁ ++ l₂).length := Nat.lt_... | [
623,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
619,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_const | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nhu : u ~[l] const α 0\n⊢ Tendsto u l (𝓝 0)\n\ncase inr\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nc : β\nhu : u ~[l] const α c\nh : ¬c = 0\n⊢ Tendsto u... | [
150,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.complete | [] | [
338,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.left_le_of_le_right' | [] | [
726,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.algHom_C | [] | [
500,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAtFilter_iff_tendsto | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.101028\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.101123\... | [
307,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.mk_coe | [] | [
779,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.elim_inl_inr | [] | [
198,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two | [] | [
489,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
8
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.apply_inv_self | [] | [
231,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.inf | [] | [
1558,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Data/List/Basic.lean | List.tail_append_of_ne_nil | [
{
"state_after": "case nil\nι : Type ?u.45132\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l' : List α\nh : [] ≠ []\n⊢ tail ([] ++ l') = tail [] ++ l'\n\ncase cons\nι : Type ?u.45132\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l' : List α\nhead✝ : α\ntail✝ : List α\nh : head✝ :: tail✝ ≠ []\... | [
939,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.dvdNotUnit_iff_normalizedFactors_lt_normalizedFactors | [
{
"state_after": "case mp\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\nx y : α\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ DvdNotUnit x y → normalizedFactors x < normalizedFactors y\n\ncase mpr\nα : Type u_1\ninst✝³ : CancelCommM... | [
802,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.mul_listTransvecRow_last_col | [
{
"state_after": "n : Type ?u.185522\np : Type ?u.185525\nR : Type u₂\n𝕜 : Type u_1\ninst✝³ : Field 𝕜\ninst✝² : DecidableEq n\ninst✝¹ : DecidableEq p\ninst✝ : CommRing R\nr : ℕ\nM : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\ni : Fin r ⊕ Unit\nA : List.length (listTransvecRow M) = r\n⊢ (M ⬝ List.prod (listTransv... | [
449,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos | [
{
"state_after": "case h.e'_5.h.e'_3\nc : ℝ≥0∞\nhc : c ≠ ⊤\ny : ℝ\nhy : 0 < y\n⊢ 0 = c * 0 ^ y\n\ncase convert_3\nc : ℝ≥0∞\nhc : c ≠ ⊤\ny : ℝ\nhy : 0 < y\n⊢ 0 ^ y ≠ 0 ∨ c ≠ ⊤",
"state_before": "c : ℝ≥0∞\nhc : c ≠ ⊤\ny : ℝ\nhy : 0 < y\n⊢ Tendsto (fun x => c * x ^ y) (𝓝 0) (𝓝 0)",
"tactic": "convert ENN... | [
532,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_fg | [] | [
874,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_zero | [] | [
513,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
11
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_le_iff_le_add | [] | [
468,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
467,
11
] |
Mathlib/Topology/Category/TopCat/OpenNhds.lean | TopologicalSpace.OpenNhds.inclusionMapIso_inv | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsTerminal.hom_ext | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y : C\nt : IsTerminal X\nf g : Y ⟶ X\n⊢ ∀ (j : Discrete PEmpty), f ≫ (asEmptyCone X).π.app j = g ≫ (asEmptyCone X).π.app j",
"tactic": "aesop_cat"
}
] | [
138,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | innerSL_apply_coe | [] | [
1776,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1775,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.zero_limZero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nε : α\nε0 : ε > 0\nj : ℕ\nx✝ : j ≥ 0\n⊢ abv (↑0 j) < ε",
"tactic": "simpa [abv_zero abv] using ε0"
}
] | [
455,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.mem_range | [] | [
2598,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2597,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.Infinite.mul | [] | [
900,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.le_toNNRat_iff_coe_le' | [
{
"state_after": "no goals",
"state_before": "p q✝ : ℚ\nq : ℚ≥0\nhq : 0 < q\nhp : p < 0\n⊢ q ≤ toNNRat p ↔ ↑q ≤ p",
"tactic": "simp only [(hp.trans_le q.coe_nonneg).not_le, toNNRat_eq_zero.2 hp.le, hq.not_le]"
}
] | [
396,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapDomain_smul_of_injective | [] | [
1624,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1621,
1
] |
Mathlib/Analysis/Convex/StrictConvexBetween.lean | Collinear.sbtw_of_dist_eq_of_dist_lt | [
{
"state_after": "case refine'_1\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : StrictConvexSpace ℝ V\np p₁ p₂ p₃ : P\nr : ℝ\nh : Collinear ℝ {p₁, p₂, p₃}\nhp₁ : dist p₁ p = r\nhp₂ : dist p₂ p < r\nhp₃ : d... | [
82,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.eq | [] | [
157,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_lt_mul_of_pos_right | [] | [
453,
72
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
452,
11
] |
Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | TopCat.Sheaf.extend_hom_app | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : TopCat\nι : Type u_1\nB : ι → Opens ↑X\nF : Presheaf C X\nF' : Sheaf C X\nh : Opens.IsBasis (Set.range B)\nα : Functor.op (inducedFunctor B) ⋙ F ⟶ Functor.op (inducedFunctor B) ⋙ F'.val\ni : ι\n⊢ (↑(restrictHomEquivHom F F' h) α).app (B i).op =\n (Equiv.i... | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_dedup_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19437\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\ninst✝ : DecidableEq α\nhi : IsIdempotent α op\ns : Multiset α\nb : α\n⊢ fold op b (dedup 0) = fold op b 0",
"tactic": "simp"
},
{
"state_after": "case ... | [
123,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_filter_eq_of_maps_to | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.521487\ninst✝¹ : DecidableEq β\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : α → Finset β\ninst✝ : DecidableEq α\ns : Finset α\nt : Finset β\nf : α → β\nh : ∀ (x : α), x ∈ s → f x ∈ t\n⊢ (Finset.biUnion t fun a => filter (fun c => f c ... | [
3650,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3648,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mod_self | [] | [
66,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.List.two_step_induction | [
{
"state_after": "no goals",
"state_before": "motive : List Nat → Sort u\nl : List Nat\nempty : motive []\nsingle : (a : Nat) → motive [a]\nstep : (a b : Nat) → (l : List Nat) → motive (b :: l) → motive (a :: b :: l)\n⊢ motive l",
"tactic": "induction l with\n| nil => assumption\n| cons a l => cases l; ... | [
116,
62
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
107,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.preserves_seq | [] | [
149,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.moveLeft_mk_left | [
{
"state_after": "no goals",
"state_before": "xl : Type u_1\ni : xl\nxr : Type u_1\nxR : xr → PGame\nxL : xl → PGame\nj : LeftMoves (xL i)\n⊢ Subsequent (PGame.moveLeft (xL i) j) (mk xl xr xL xR)",
"tactic": "pgame_wf_tac"
}
] | [
317,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
9
] |
Mathlib/Order/Lattice.lean | Prod.mk_sup_mk | [] | [
1258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | MulAction.exists_smul_eq | [] | [
156,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | mul_dvd_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommSemigroup α\na✝ b c✝ a c e f : α\n⊢ a * e * (c * f) = a * c * (e * f)",
"tactic": "simp"
}
] | [
180,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.comp_le_comp_left | [] | [
318,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.mk'_mk_eq_div | [] | [
160,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_singleton | [] | [
398,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | sum_Ico_pow | [
{
"state_after": "A : Type ?u.1099012\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn p : ℕ\n⊢ ∑ k in Ico 1 (n + 1), ↑k ^ p =\n ∑ i in range (p + 1), bernoulli' i * ↑(Nat.choose (p + 1) i) * ↑n ^ (p + 1 - i) / ↑(succ p)",
"state_before": "A : Type ?u.1099012\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn p : ... | [
428,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.ret_mem | [] | [
372,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_assoc | [] | [
153,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.eq_endpoints_or_mem_Ioo_of_mem_Icc | [] | [
949,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/RingTheory/FiniteType.lean | AlgHom.FiniteType.comp | [] | [
304,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Algebra/Field/Basic.lean | Commute.one_div_add_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14282\nK : Type ?u.14285\ninst✝ : DivisionSemiring α\na b c d : α\nhab : _root_.Commute a b\nha : a ≠ 0\nhb : b ≠ 0\n⊢ 1 / a + 1 / b = (a + b) / (a * b)",
"tactic": "rw [(Commute.one_right a).div_add_div hab ha hb, one_mul, mul_one,... | [
81,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.coeFn_ofInjective | [] | [
679,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.smul_integral_comp_mul_sub | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14916038\n𝕜 : Type ?u.14916041\nE : Type u_1\nF : Type ?u.14916047\nA : Type ?u.14916050\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d✝ : ℝ\nf : ℝ → E\nc d : ℝ\n⊢ (c • ∫ (x : ℝ) in a..b, f (c * x - d)) =... | [
809,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_map | [
{
"state_after": "case zero\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace ℝ F\nφ : E ≃ₗᵢ[ℝ] F\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\ninst✝ : Fact (finrank ℝ F = Nat.zero)\nx ... | [
334,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.ext | [] | [
261,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.norm_nat | [] | [
163,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Group/Pi.lean | Function.update_one | [] | [
617,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.exists_unique_congr_left' | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nβ : Sort v\nγ : Sort w\np : α → Prop\nf : α ≃ β\nx✝ : α\n⊢ p x✝ ↔ p (↑f.symm (↑f x✝))",
"tactic": "simp"
}
] | [
862,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
11
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | Convex.quasiconcaveOn_of_convex_ge | [] | [
90,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/RingTheory/Adjoin/FG.lean | Algebra.fg_trans | [
{
"state_after": "case intro.intro\nR : Type u\nA : Type v\nB : Type w\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\ns t : Set A\nh1 : FG (↑Subalgebra.toSubmodule (adjoin R s))\nh2 : FG (↑Subalgebra.toSubmodule (adjoin { x // x ∈ adjoin R s } t))\np : Set A\nhp : Set.Finite p\nhp' : sp... | [
83,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | isCyclic_of_subgroup_isDomain | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nG : Type u_1\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : Group G\ninst✝ : Finite G\nf : G →* R\nhf : Injective ↑f\n⊢ IsCyclic G",
"tactic": "classical\n cases nonempty_fintype G\n apply isCyclic_of_card_pow_eq_one_le\n intro n hn\n ... | [
145,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.preimageHomeomorph_apply | [] | [
468,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivCongrLeft_symm | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_symm_X | [] | [
84,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_inf | [] | [
380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | add_sq' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.88727\nM : Type ?u.88730\ninst✝ : CommSemiring R\na b : R\n⊢ (a + b) ^ 2 = a ^ 2 + b ^ 2 + 2 * a * b",
"tactic": "rw [add_sq, add_assoc, add_comm _ (b ^ 2), add_assoc]"
}
] | [
178,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_le_one | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.48906\nt : Finset α\nf : α → β\nn : ℕ\n⊢ card ∅ ≤ 1 ↔ ∀ (a : α), a ∈ ∅ → ∀ (b : α), b ∈ ∅ → a = b\n\ncase inr.intro\nα : Type u_1\nβ : Type ?u.48906\ns t : Finset α\nf : α → β\nn : ℕ\nx : α\nhx : x ∈ s\n⊢ card s ≤ 1 ↔ ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a ... | [
536,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12108\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ 𝓝ˢ ∅ = ⊥",
"tactic": "rw [isOpen_empty.nhdsSet_eq, principal_empty]"
}
] | [
111,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_atTop_of_degree_gt' | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhdeg : degree Q < degree P\nhpos : 0 < leadingCoeff P / leadingCoeff Q\nhQ : Q ≠ 0\n⊢ Tendsto (fun x => eval x P / eval x Q) atTop atTop",
"state_before": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrdere... | [
185,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | zero_mem_ℓp' | [] | [
147,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.of_injective | [] | [
109,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_le_lf_neg_iff | [
{
"state_after": "xl xr : Type u\nxL : xl → PGame\nxR : xr → PGame\nyl yr : Type u\nyL : yl → PGame\nyR : yr → PGame\n⊢ (((∀ (i : yr), -yR i ⧏ -mk xl xr (fun i => xL i) fun j => xR j) ∧\n ∀ (j : xl), (-mk yl yr (fun i => yL i) fun j => yR j) ⧏ -xL j) ↔\n (∀ (i : xl), xL i ⧏ mk yl yr yL yR) ∧ ∀ (j : ... | [
1318,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
9
] |
Mathlib/Order/BoundedOrder.lean | subsingleton_of_top_le_bot | [] | [
679,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.pow_multiplicity_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nh : Finite a b\n⊢ ↑(Part.get (multiplicity a b) h) ≤ multiplicity a b",
"tactic": "rw [PartENat.natCast_get]"
}
] | [
113,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.neg_iff | [] | [
260,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f | [] | [
169,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_le_pi_div_two | [] | [
52,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.tsum_comp_le_tsum_of_inj | [] | [
1162,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_inv_le_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.99475\ninst✝³ : LinearOrderedField k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nh : c < 0\n⊢ a ≤ c⁻¹ • b ↔ b ≤ c • a",
"tactic": "rw [← smul_le_smul_iff_of_neg h, smu... | [
175,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Std/Data/List/Lemmas.lean | List.range_eq_range' | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ range' 0 (0 + n) = range' 0 n",
"tactic": "rw [Nat.zero_add]"
}
] | [
1891,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1890,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.eqLocusS_same | [] | [
1198,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_of_add_le_add_left | [] | [
3150,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3149,
1
] |
Mathlib/Logic/Relation.lean | Relation.ReflTransGen.symmetric | [
{
"state_after": "α : Type u_1\nβ : Type ?u.16745\nγ : Type ?u.16748\nδ : Type ?u.16751\nr : α → α → Prop\na b c d : α\nh✝ : Symmetric r\nx y : α\nh : ReflTransGen r x y\n⊢ ReflTransGen r y x",
"state_before": "α : Type u_1\nβ : Type ?u.16745\nγ : Type ?u.16748\nδ : Type ?u.16751\nr : α → α → Prop\na b c d ... | [
290,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_coe | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
11
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_conjTranspose | [
{
"state_after": "l : Type ?u.1228403\nm : Type u_1\nn : Type u_2\no : Type ?u.1228412\nm' : o → Type ?u.1228417\nn' : o → Type ?u.1228422\nR : Type ?u.1228425\nS : Type ?u.1228428\nα : Type v\nβ : Type w\nγ : Type ?u.1228435\nM : Matrix m n α\ni : m\nj : n\nb : n → α\nc : m → α\ninst✝¹ : DecidableEq m\ninst✝ :... | [
2838,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2834,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_iff_reflTransGen | [
{
"state_after": "case mp\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\n⊢ Reachable G u v → Relation.ReflTransGen G.Adj u v\n\ncase mpr\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V... | [
1900,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1890,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasStrictFDerivAt.clm_apply | [] | [
119,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | LinearIsometryEquiv.piLpCongrLeft_single | [
{
"state_after": "case h\np : ℝ≥0∞\n𝕜 : Type u_4\n𝕜' : Type ?u.391376\nι : Type u_1\nα : ι → Type ?u.391384\nβ : ι → Type ?u.391389\ninst✝¹⁰ : Fintype ι\ninst✝⁹ : Fact (1 ≤ p)\ninst✝⁸ : NormedField 𝕜\ninst✝⁷ : NormedField 𝕜'\ninst✝⁶ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝⁵ : (i : ι) → NormedSpace 𝕜... | [
765,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Data/Set/Basic.lean | SetCoe.ext_iff | [] | [
217,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime_mul_X_sub_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\np : ℕ\nhn : Fact (Nat.Prime p)\n⊢ cyclotomic p R * (X - 1) = X ^ p - 1",
"tactic": "rw [cyclotomic_prime, geom_sum_mul]"
}
] | [
409,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.denseRange_denseSeq | [] | [
339,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.infsep_anti | [] | [
447,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Std/Data/Int/DivMod.lean | Int.div_mul_cancel | [] | [
701,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
700,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.exists_ball_subset_ball | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.44914\nι : Type ?u.44917\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nh : y ∈ ball x ε\n⊢ dist y x ≤ ε - (ε - dist y x)",
"tactic": "rw [sub_sub_self]"
}
] | [
670,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.next_prev | [] | [
890,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
8
] |
Mathlib/Data/Set/Basic.lean | Set.mem_powerset_iff | [] | [
2142,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2141,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_eq_self_of_mem_closed | [] | [
182,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.15034\nr : α → α → Prop\ns✝ t✝ : Multiset α\na : α\ns : Multiset α\nt : α → Multiset β\nh₁ : ∀ (a : α), ∃ l, t a = ↑l\nt' : α → List β\nh' : ∀ (x : α), t x = ↑(t' x)\nthis : t = fun a => ↑(t' a)\nhd : Symmetric fun a b => ... | [
233,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.induction_on | [
{
"state_after": "case h.e'_1\nα : Type u\nC : FreeCommRing α → Prop\nz : FreeCommRing α\nhn1 : C (-1)\nhb : ∀ (b : α), C (of b)\nha : ∀ (x y : FreeCommRing α), C x → C y → C (x + y)\nhm : ∀ (x y : FreeCommRing α), C x → C y → C (x * y)\nhn : ∀ (x : FreeCommRing α), C x → C (-x)\nh1 : C 1\nm✝ : Multiplicative (... | [
111,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
11
] |
Std/Data/String/Lemmas.lean | String.Pos.addChar_byteIdx | [] | [
105,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
105,
9
] |
Std/Data/List/Lemmas.lean | List.replaceF_nil | [] | [
1302,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1302,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.le_of_lt_add | [] | [
242,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_cons_succ | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
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