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 |
|---|---|---|---|---|---|---|
Mathlib/Topology/SubsetProperties.lean | isClopen_biUnion | [] | [
1592,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1590,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.isCountablyGenerated_pure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.111166\nγ : Type ?u.111169\nι : Type ?u.111172\nι' : Sort ?u.111175\na : α\n⊢ IsCountablyGenerated (𝓟 {a})",
"state_before": "α : Type u_1\nβ : Type ?u.111166\nγ : Type ?u.111169\nι : Type ?u.111172\nι' : Sort ?u.111175\na : α\n⊢ IsCountablyGenerated (pure a)",
... | [
1183,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | lp.inner_eq_tsum | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderComposition.isomorphisms | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.62388\ninst✝ : Category D\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhf : IsIso f\nhg : IsIso g\n⊢ IsIso (f ≫ g)",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.62388\ninst✝ : Category D\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhf : MorphismProp... | [
458,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | convexOn_of_deriv2_nonneg' | [] | [
1220,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_inter | [] | [
334,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Set/Basic.lean | Set.disjoint_compl_right_iff_subset | [] | [
1751,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero | [] | [
296,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_mem_Icc' | [] | [
2590,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2588,
1
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.inv_apply_self | [] | [
236,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioo.one_minus_pos | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.65525\ninst✝¹ : StrictOrderedSemiring α\nβ : Type u_1\ninst✝ : OrderedRing β\nx : ↑(Ioo 0 1)\n⊢ 0 < 1 - ↑x",
"tactic": "simpa using x.2.2"
}
] | [
383,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateRow_reindex | [] | [
2906,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2903,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [
{
"state_after": "case a\nσ : Type u_1\nτ : Type ?u.360896\nR : Type u_2\nS : Type ?u.360902\ninst✝ : CommSemiring R\nn : ℕ\nφ ψ : MvPolynomial σ R\nd : σ →₀ ℕ\n⊢ coeff d (∑ i in range (totalDegree φ + 1), ↑(homogeneousComponent i) φ) = coeff d φ",
"state_before": "σ : Type u_1\nτ : Type ?u.360896\nR : Type... | [
313,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftl_eq_mul_pow | [] | [
435,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_copy | [] | [
273,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_same | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i : ι\nb : β i\n⊢ ↑(single i b) i = b",
"tactic": "simp only [single_apply, dite_eq_ite, ite... | [
654,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.minpolyGen_eq | [
{
"state_after": "R : Type ?u.135537\nS : Type u_2\nT : Type ?u.135543\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring S\ninst✝⁶ : Algebra R S\nA : Type u_1\nB : Type ?u.135849\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : IsDomain B\ninst✝² : Algebra A B\nK : Type ?u.136271\ninst✝¹ : Field K\ninst✝ : Algebra A S\npb... | [
208,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.sub | [
{
"state_after": "R₁ : Type ?u.151370\nR₂ : Type ?u.151373\nR₃ : Type ?u.151376\nR₄ : Type ?u.151379\ninst✝¹² : Semiring R₁\ninst✝¹¹ : Semiring R₂\ninst✝¹⁰ : CommSemiring R₃\ninst✝⁹ : CommSemiring R₄\nσ₁₂ : R₁ →+* R₂\nσ₁₄ : R₁ →+* R₄\nσ₃₄ : R₃ →+* R₄\nM₁ : Type u_2\nM₂ : Type ?u.151847\nM₃ : Type ?u.151850\nM₄ ... | [
235,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_le_iff | [] | [
165,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.ext | [] | [
583,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_two | [
{
"state_after": "a b : Ordinal\nha : a < 2\nhb : b < 2\nh₂ : succ 1 = 2\n⊢ (fun x x_1 => x * x_1) a b < 2",
"state_before": "a b : Ordinal\nha : a < 2\nhb : b < 2\n⊢ (fun x x_1 => x * x_1) a b < 2",
"tactic": "have h₂ : succ (1 : Ordinal) = 2 := by simp"
},
{
"state_after": "a b : Ordinal\nha :... | [
291,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | LinearIsometry.angle_map | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.9920\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\nx y : V\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : InnerProductSpace ℝ F\nf : E →ₗᵢ[ℝ] F\nu v... | [
69,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.edist_map | [] | [
986,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_comp_equiv_symm | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.147461\nm : Type u_2\nn : Type u_1\no : Type ?u.147470\nm' : o → Type ?u.147475\nn' : o → Type ?u.147480\nR : Type ?u.147483\nS : Type ?u.147486\nα : Type v\nβ : Type w\nγ : Type ?u.147493\ninst✝² : Fintype m\ninst✝¹ : Fintype n\ninst✝ : NonUnitalNon... | [
791,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_zero | [] | [
133,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_biUnion | [] | [
1206,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | isUnit_iff_dvd_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommMonoid α\nx : α\nx✝ : x ∣ 1\ny : α\nh : 1 = x * y\n⊢ y * x = 1",
"tactic": "rw [h, mul_comm]"
}
] | [
128,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ rtakeWhile p [] = []",
"tactic": "simp [rtakeWhile, takeWhile]"
}
] | [
197,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.255042\nβ : Type ?u.255045\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a⁻¹ ≠ ⊤ ↔ a ≠ 0",
"tactic": "simp"
}
] | [
1406,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans_tendsto | [] | [
1429,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Mathlib/Init/Function.lean | Function.surjective_id | [] | [
125,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mapDomain_algebraMap | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.2773678\nA : Type u_1\nH : Type u_2\nF : Type u_3\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Semiring A\ninst✝³ : Algebra k A\ninst✝² : AddMonoid G\ninst✝¹ : AddMonoid H\ninst✝ : AddMonoidHomClass F G H\nf : F\nr : k\n⊢ mapDomain (↑... | [
2038,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2035,
1
] |
Mathlib/Topology/ContinuousFunction/Polynomial.lean | Polynomial.aeval_continuousMap_apply | [
{
"state_after": "case refine'_1\nR : Type u_1\nα : Type u_2\ninst✝³ : TopologicalSpace α\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : TopologicalSemiring R\ng : R[X]\nf : C(α, R)\nx : α\n⊢ ∀ (p q : R[X]),\n ↑(↑(aeval f) p) x = eval (↑f x) p →\n ↑(↑(aeval f) q) x = eval (↑f x) q → ↑(↑(... | [
74,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Finsupp/WellFounded.lean | Finsupp.Lex.wellFoundedLT_of_finite | [] | [
72,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_updateRow_smul | [] | [
404,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain_zero | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type u_1\ninst✝ : (i : ι) → Zero (β i)\nh : κ → ι\nhh : Function.Injective h\ni✝ : κ\n⊢ ↑(comapDomain h hh 0) i✝ = ↑0 i✝",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ... | [
1325,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_toDual | [] | [
2310,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2309,
1
] |
Mathlib/Topology/Algebra/Algebra.lean | Subalgebra.topologicalClosure_minimal | [] | [
126,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_append | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.470224\nγ : Type ?u.470227\ninst✝ : DecidableEq α\nl l' : List α\na : α\n⊢ toFinset ([] ++ l') = toFinset [] ∪ toFinset l'\n\ncase cons\nα : Type u_1\nβ : Type ?u.470224\nγ : Type ?u.470227\ninst✝ : DecidableEq α\nl l' : List α\na hd : α\ntl : List α\nhl : t... | [
3306,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3303,
1
] |
Mathlib/Data/PFun.lean | PFun.core_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.50828\nδ : Type ?u.50831\nε : Type ?u.50834\nι : Type ?u.50837\nf✝ f : α →. β\ns : Set β\n⊢ core f s = preimage f s ∪ Dom fᶜ",
"tactic": "rw [preimage_eq, Set.union_distrib_right, Set.union_comm (Dom f), Set.compl_unio... | [
523,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_subset_iff | [] | [
98,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_inv | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns✝ : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulLeftInvariant μ\ns : Set G\nhsm : MeasurableSet s\nhμs : ↑↑μ s = 0\n⊢ ↑↑(map Inv.inv μ) s =... | [
172,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.degree_list_prod | [] | [
300,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.multinomial_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\n⊢ multinomial {a} f = 1",
"tactic": "simp [multinomial, Nat.div_self (factorial_pos (f a))]"
}
] | [
68,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.locally_compact | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹ : TopologicalSpace H\nI✝ : ModelWithCorners 𝕜 E H\ninst✝ : LocallyCompactSpace E\nI : ModelWithCorners 𝕜 E H\nthis :\n ∀ (x : H), HasBasis (𝓝 x) ... | [
359,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
11
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | invOn_arg_expMapCircle | [] | [
81,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_update_of_mem | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_3\nβ : ι → Type u_2\ns s₁ s₂ : Set ι\nt✝ t₁ t₂ : (i : ι) → Set (α i)\ni : ι\ninst✝ : DecidableEq ι\nhi : i ∈ s\nf : (j : ι) → α j\na : α i\nt : (j : ι) → α j → Set (β j)\n⊢ (pi s fun j => t j (update f i a j)) = pi ({i} ∪ s \\ {i}) f... | [
784,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ioi | [] | [
156,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.coe_copy | [] | [
413,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.mem_pointwise_smul_iff_inv_smul_mem₀ | [] | [
158,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Combinatorics/Catalan.lean | Tree.mem_treesOfNumNodesEq_numNodes | [] | [
203,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Order/Basic.lean | Prod.mk_lt_mk_iff_left | [] | [
1229,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.abs_diff_coe_le_dist | [
{
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1034,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_zero_mono | [] | [
316,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_smul | [] | [
375,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.T_sub | [
{
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"tactic": "rw [← T_add, sub_eq_add_neg]"
}
] | [
184,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
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Mathlib/Analysis/Convex/Hull.lean | segment_subset_convexHull | [] | [
126,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.compares | [] | [
827,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
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Mathlib/RingTheory/Nakayama.lean | Submodule.eq_bot_of_le_smul_of_le_jacobson_bot | [
{
"state_after": "no goals",
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"tactic": "rw [eq_smul_of_le_smul_of_le_jacobson hN hIN hIjac, Submodu... | [
73,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Ioc | [
{
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359,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
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Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.zeta_mul_vonMangoldt | [
{
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},
{
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] | [
132,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.add_rpow_le_one_of_add_le_one | [
{
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181,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.update_eq_sub_add_single | [
{
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867,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
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Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.leftUnitor_inv_app | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/RingTheory/IsTensorProduct.lean | Algebra.pushoutDesc_apply | [
{
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481,
78
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474,
1
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_add | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.triangle_assoc_comp_left_inv | [
{
"state_after": "no goals",
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"tactic": "simp [← cancel_mono ((ρ_ f).hom ▷ g)]"
}
] | [
340,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.bisim | [
{
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313,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_norm_pow_id | [
{
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2043,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2039,
1
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Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.CostructuredArrow.lift_projectQuotient | [
{
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194,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.MonoOver.factors_congr | [
{
"state_after": "no goals",
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48,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Std/Data/Array/Lemmas.lean | getElem_fin | [] | [
15,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
14,
9
] |
Mathlib/Order/Max.lean | Subsingleton.isBot | [] | [
363,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
11
] |
Mathlib/Algebra/Lie/OfAssociative.lean | AlgHom.to_lieHom_id | [] | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.quotientiInfEmbedding_apply_mk | [] | [
778,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.subset_congr_right | [] | [
107,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_eq_iff | [] | [
182,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.ideal_eq_span_pow_irreducible | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\ns : Ideal R\nhs : s ≠ ⊥\nϖ : R\nhirr : Irreducible ϖ\ngen_ne_zero : generator s ≠ 0\n⊢ ∃ n, s = span {ϖ ^ n}",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteV... | [
366,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.one_lt_iff_ne_zero_and_ne_one | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ 1 < 0 ↔ 0 ≠ 0 ∧ 0 ≠ 1",
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},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ 1 < 1 ↔ 1 ≠ 0 ∧ 1 ≠ 1",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "m n✝ k l n : ℕ\n... | [
93,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.odd_of_ne_two | [] | [
509,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.iSup_mul | [
{
"state_after": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (⨆ (i : ι), a * f i) = ⨆ (i : ι), f i * a",
"state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (⨆ (i : ι), f i) * a = ⨆ (i : ι), f i * a",
"tactic": "rw [mul_comm, mul_iSup]"
},
{
"state_after": "no goals",
"state_before": "ι ... | [
969,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Deprecated/Subring.lean | Ring.subset_closure | [] | [
192,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.not_eq_true_eq_eq_false | [
{
"state_after": "no goals",
"state_before": "a : Bool\n⊢ ((!a) = true) = (a = false)",
"tactic": "cases a <;> simp"
}
] | [
94,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.toAddSubmonoid_mono | [] | [
173,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.bit_true | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.mk'_surjective | [] | [
868,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | Subalgebra.SeparatesPoints.strongly | [
{
"state_after": "case pos\nα : Type u_2\ninst✝¹² : TopologicalSpace α\nR : Type ?u.1508154\ninst✝¹¹ : CommSemiring R\nA : Type ?u.1508160\ninst✝¹⁰ : TopologicalSpace A\ninst✝⁹ : Semiring A\ninst✝⁸ : Algebra R A\ninst✝⁷ : TopologicalSemiring A\nA₂ : Type ?u.1508332\ninst✝⁶ : TopologicalSpace A₂\ninst✝⁵ : Semiri... | [
842,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.mk_lf_of_le | [] | [
498,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Topology/Order/Basic.lean | continuousWithinAt_Ioc_iff_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderClosedTopology α\na✝ b✝ : α\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace β\na b : α\nf : α → β\nh : a < b\n⊢ ContinuousWithinAt f (Ioc a b) a ↔ Conti... | [
445,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.addHom_ext' | [] | [
819,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/CategoryTheory/Balanced.lean | CategoryTheory.isIso_of_mono_of_epi | [] | [
43,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.encode_lt_rfind' | [
{
"state_after": "cf : Code\n⊢ encodeCode cf < 2 * (2 * encodeCode cf + 1) + 1 + 4",
"state_before": "cf : Code\n⊢ encode cf < encode (rfind' cf)",
"tactic": "simp [encodeCode_eq, encodeCode]"
},
{
"state_after": "cf : Code\nthis : 1 * encodeCode cf ≤ 2 * 2 * encodeCode cf\n⊢ encodeCode cf < 2 *... | [
232,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist.triangle_inequality | [
{
"state_after": "n m k : ℕ\nthis : dist n m + dist m k = n - m + (m - k) + (k - m + (m - n))\n⊢ dist n k ≤ dist n m + dist m k",
"state_before": "n m k : ℕ\n⊢ dist n k ≤ dist n m + dist m k",
"tactic": "have : dist n m + dist m k = n - m + (m - k) + (k - m + (m - n)) := by\n simp [dist.def, add_comm, ... | [
100,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Associated.lean | Associated.mul_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.181036\nγ : Type ?u.181039\nδ : Type ?u.181042\ninst✝ : CommMonoid α\na₁ a₂ b₁ b₂ : α\nc₁ : αˣ\nh₁ : a₁ * ↑c₁ = b₁\nc₂ : αˣ\nh₂ : a₂ * ↑c₂ = b₂\n⊢ a₁ * a₂ * ↑(c₁ * c₂) = b₁ * b₂",
"tactic": "simp [h₁.symm, h₂.symm, mul_assoc, mul_co... | [
521,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_subtype_subset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.135552\nγ : Type ?u.135555\nt : Set α\ns : Finset ↑t\na : α\nha : a ∈ ↑(map (Embedding.subtype fun x => x ∈ t) s)\n⊢ a ∈ t",
"state_before": "α : Type u_1\nβ : Type ?u.135552\nγ : Type ?u.135555\nt : Set α\ns : Finset ↑t\n⊢ ↑(map (Embedding.subtype fun x => x ∈ t)... | [
716,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.refl | [] | [
342,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasStrictDerivAt.add | [
{
"state_after": "no goals",
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61,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
8
] |
Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Iio | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Iio b) = Iio ↑b",
"tactic": "simp [Iio_eq_finset_subtype, Finset.fin, Finset.map_map]"
}
] | [
171,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Sigma/Basic.lean | PSigma.ext_iff | [
{
"state_after": "case mk\nα : Sort u_1\nβ : α → Sort u_2\nx₁ : PSigma β\nfst✝ : α\nsnd✝ : β fst✝\n⊢ { fst := fst✝, snd := snd✝ } = x₁ ↔\n { fst := fst✝, snd := snd✝ }.fst = x₁.fst ∧ HEq { fst := fst✝, snd := snd✝ }.snd x₁.snd",
"state_before": "α : Sort u_1\nβ : α → Sort u_2\nx₀ x₁ : PSigma β\n⊢ x₀ = x₁... | [
240,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/List/Nodup.lean | List.nthLe_eq_of_ne_imp_not_nodup | [
{
"state_after": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr : α → α → Prop\na b : α\nxs : List α\nn m : ℕ\nhn : n < length xs\nhm : m < length xs\nh : nthLe xs n hn = nthLe xs m hm\nhne : n ≠ m\n⊢ ¬∀ (i j : ℕ) (h₁ : i < length xs) (h₂ : j < length xs), nthLe xs i h₁ = nthLe xs j h₂ → i = j",
"state_before... | [
164,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
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