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/UniformSpace/UniformEmbedding.lean | UniformInducing.basis_uniformity | [] | [
79,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.fractional_div_of_nonzero | [] | [
1092,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_iff_multifork | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nA : Type u₂\ninst✝ : Category A\nJ : GrothendieckTopology C\nU : C\nR : Presieve U\nP : Cᵒᵖ ⥤ A\n⊢ (∀ (X : C) (S : GrothendieckTopology.Cover J X), Nonempty (IsLimit (GrothendieckTopology.Cover.multifork S P))) →\n IsSheaf J P",
"state_before": "C : Typ... | [
507,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospan_map_id | [] | [
251,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Order/GameAdd.lean | WellFounded.prod_gameAdd | [] | [
117,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo | [] | [
436,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_linear | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | NormedSpace.image_isVonNBounded_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\n𝕜' : Type ?u.256544\nE : Type u_3\nE' : Type u_1\nF : Type ?u.256553\nι : Type ?u.256556\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : E' → E\ns : Set E'\n⊢ Bornology.IsVonNBounded 𝕜 (f ''... | [
307,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_vsub_eq_affineCombination_vsub | [
{
"state_after": "k : Type u_3\nV : Type u_1\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.340261\ns₂ : Finset ι₂\nw : ι → k\np₁ p₂ : ι → P\n⊢ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) =\n ↑(weightedVSubOfPoint s p₁ (Classical.... | [
518,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_iff_exists_injective | [] | [
55,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
11
] |
Mathlib/Algebra/Order/WithZero.lean | lt_of_mul_lt_mul_of_le₀ | [
{
"state_after": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nh : a * b < c * d\nhc : 0 < c\nhh : c ≤ a\nha : a ≠ 0\n⊢ b < d",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nh : a * b < c * d\nhc : 0 < c\nhh : c ≤ a\n⊢ b < d",
"... | [
228,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_mul_succ_self | [
{
"state_after": "no goals",
"state_before": "m n✝ n : ℤ\n⊢ Even (n * (n + 1))",
"tactic": "simpa [even_mul, parity_simps] using n.even_or_odd"
}
] | [
197,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.neg_mul | [
{
"state_after": "u : Lean.Level\nR✝ : Type ?u.204257\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\na₁ : R\na₂ : ℕ\na₃ : R\n⊢ -(a₁ ^ a₂ * a₃) = a₁ ^ a₂ * -a₃",
"state_before": "u : Lean.Level\nR✝ : Type ?u.204257\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\... | [
530,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.empty_ne_coe | [] | [
147,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.inv_apply_self | [] | [
80,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.mul_inv_of_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c u : αˣ\na : α\nh : ↑u = a\n⊢ a * ↑u⁻¹ = 1",
"tactic": "rw [← h, u.mul_inv]"
}
] | [
279,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | singleton_div_closedBall | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ {x} / closedBall y δ = closedBall (x / y) δ",
"tactic": "simp_rw [div_eq_mul_inv, inv_closedBall, singleton_mul_closedBall]"
}
] | [
164,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.zpow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.46017\ninst✝¹ : DivisionSemiring R\ninst✝ : StarRing R\nx : R\nhx : IsSelfAdjoint x\nn : ℤ\n⊢ IsSelfAdjoint (x ^ n)",
"tactic": "simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]"
}
] | [
238,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Sign.lean | SignType.neg_one_lt_iff | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ -1 < a ↔ 0 ≤ a",
"tactic": "cases a <;> decide"
}
] | [
174,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convexHull_ediam | [
{
"state_after": "ι : Type ?u.38573\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns✝ t s : Set E\nx : E\nhx : x ∈ ↑(convexHull ℝ).toOrderHom s\ny : E\nhy : y ∈ ↑(convexHull ℝ).toOrderHom s\n⊢ edist x y ≤ EMetric.diam s",
"state_before": "ι : Type ?u.38573\nE : Type u_1\ninst✝¹ :... | [
111,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Nat.cast_pred | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\nh : 0 < 0\n⊢ ↑(0 - 1) = ↑0 - 1",
"tactic": "cases h"
},
{
"state_after": "R : Type u\ninst✝ : AddGroupWithOne R\nn : ℕ\nx✝ : 0 < n + 1\n⊢ ↑(n + 1 - 1) = ↑n",
"state_before": "R : Type u\ninst✝ : AddGroupWith... | [
43,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Data/List/Join.lean | List.length_join | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4048\nL : List (List α)\n⊢ length (join L) = sum (map length L)",
"tactic": "induction L <;> [rfl; simp only [*, join, map, sum_cons, length_append]]"
}
] | [
74,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.not_mem_commonNeighbors_left | [] | [
1025,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prod_prime_factors_dvd | [
{
"state_after": "case pos\nn : ℕ\nhn : n = 0\n⊢ ∏ p in toFinset (factors n), p ∣ n\n\ncase neg\nn : ℕ\nhn : ¬n = 0\n⊢ ∏ p in toFinset (factors n), p ∣ n",
"state_before": "n : ℕ\n⊢ ∏ p in toFinset (factors n), p ∣ n",
"tactic": "by_cases hn : n = 0"
},
{
"state_after": "no goals",
"state_be... | [
664,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.pnatDen_zero | [] | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.insert_sigma | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.9903\nα : ι → Type u_2\nβ : ι → Type ?u.9913\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni j : ι\na : α i\n⊢ α i",
"state_before": "ι : Type u_1\nι' : Type ?u.9903\nα : ι → Type u_2\nβ : ι → Type ?u.9913\ns s₁ s₂ :... | [
151,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/DualNumber.lean | DualNumber.snd_mul | [] | [
80,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_of_ne_of_not_mem_of_mem_of_mem | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.468482\ns : AffineSubspace k P\np₁ p₂ p₃ : P\nhp₂p₃ : p₂ ≠ p₃\nhp₁ : ¬p₁ ∈ s\nhp₂ : p₂ ∈ s\nhp₃ : p₃ ∈ s\n⊢ AffineIndependent k (![p₁, p₂, p₃] ∘... | [
715,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | eventually_liminf_le | [] | [
279,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.inf | [] | [
611,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Order/WithBot.lean | WithBot.unbot'_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4491\nγ : Type ?u.4494\nδ : Type ?u.4497\na b d : α\nx : WithBot α\n⊢ unbot' d x = d ↔ x = ↑d ∨ x = ⊥",
"tactic": "simp [unbot'_eq_iff]"
}
] | [
139,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
9
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.mk_out'_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\ng : α\n⊢ Quotient.out' ↑g = g * ↑{ val := g⁻¹ * Quotient.out' ↑g, property := (_ : g⁻¹ * Quotient.out' ↑g ∈ s) }",
"tactic": "rw [mul_inv_cancel_left]"
}
] | [
542,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBounded.isCobounded_ge | [] | [
208,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Ico_iff_integrableOn_Ioo | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4224895\nE : Type u_2\nF : Type ?u.4224901\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ 0 ≠ ⊤",
"state_before": "α : ... | [
689,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.Stable.inter_left | [] | [
425,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_irrefl | [] | [
341,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.leftInverse_bijInv | [] | [
1146,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.169453\nι : Type ?u.169456\ninst✝ : CompleteBooleanAlgebra α\nf : Filter β\nu : β → α\n⊢ limsup u fᶜ = liminf (compl ∘ u) f",
"tactic": "simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Func... | [
1020,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.coe_nil | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_zero | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_iInf | [] | [
948,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_apply_inter_support | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.28546\nγ : Type ?u.28549\np : Pmf α\ns t : Set α\n⊢ ↑(toOuterMeasure p) (s ∩ support p) = ↑(toOuterMeasure p) s",
"tactic": "simp only [toOuterMeasure_apply, Pmf.support, Set.indicator_inter_support]"
}
] | [
216,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.le_div_iff_mul_le' | [] | [
608,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_int_add_iff | [] | [
538,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coeToPowerSeries.ringHom_apply | [] | [
2646,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2645,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_integral_symm | [] | [
495,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | MulAction.pow_smul_mod_minimalPeriod | [] | [
623,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₂Γ₂_inv_app_f_f | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nX : Karoubi (ChainComplex C ℕ)\nn : ℕ\n⊢ HomologicalComplex.Hom.f (N₂Γ₂.inv.app X).f n =\n HomologicalComplex.Hom.f X.p n ≫ Splitting.ιSummand (Γ₀.splitting X.X) (Splitt... | [
164,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_one_eq_lintegral_nnnorm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.526534\nF : Type u_2\nG : Type ?u.526540\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\n⊢ snorm f 1 μ = ∫⁻ (x : α), ↑‖f... | [
102,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.mem_so | [
{
"state_after": "n : Type u_1\np : Type ?u.30314\nq : Type ?u.30317\nl : Type ?u.30320\nR : Type u₂\ninst✝⁵ : DecidableEq n\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : DecidableEq l\ninst✝¹ : CommRing R\ninst✝ : Fintype n\nA : Matrix n n R\n⊢ IsSkewAdjoint 1 A ↔ Aᵀ = -A",
"state_before": "n :... | [
162,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.disjoint_map_inl_map_inr | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ns : Finset α\nt : Finset β\n⊢ ∀ ⦃a : α ⊕ β⦄, (∃ a_1, a_1 ∈ s ∧ ↑Embedding.inl a_1 = a) → ¬∃ a_2, a_2 ∈ t ∧ ↑Embedding.inr a_2 = a",
"state_before": "α : Type u_2\nβ : Type u_1\ns : Finset α\nt : Finset β\n⊢ _root_.Disjoint (map Embedding.inl s) (map Embedding.in... | [
59,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/Coset.lean | mem_rightCoset_rightCoset | [
{
"state_after": "α : Type u_1\ninst✝ : Monoid α\ns : Submonoid α\na : α\nha : ↑s *r a = ↑s\n⊢ a ∈ ↑s *r a",
"state_before": "α : Type u_1\ninst✝ : Monoid α\ns : Submonoid α\na : α\nha : ↑s *r a = ↑s\n⊢ a ∈ s",
"tactic": "rw [← SetLike.mem_coe, ← ha]"
},
{
"state_after": "no goals",
"state_b... | [
192,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_one_lt_of_lt_of_pos | [] | [
887,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_sup_closure_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Sort ?u.9446\nκ : ι → Sort ?u.9451\ninst✝ : SemilatticeSup α\nc : ClosureOperator α\nx y : α\n⊢ ↑c.toOrderHom (x ⊔ ↑c.toOrderHom y) = ↑c.toOrderHom (x ⊔ y)",
"tactic": "rw [sup_comm, closure_sup_closure_left, sup_comm]"
}
] | [
263,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_inr_pushoutAssoc_inv | [
{
"state_after": "C : Type u\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nW X Y Z X₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl)\n⊢ pu... | [
2630,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2622,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfLocalizations_symm_eq_mulEquivOfLocalizations | [] | [
1387,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1386,
1
] |
Mathlib/Topology/List.lean | List.continuous_cons | [] | [
100,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/Support.lean | subset_mulTSupport | [] | [
53,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_id_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1269380\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1269386\ninst✝¹² : Semiring R''\nM : Type u_3\nN : Type u_2\nP : Type ?u.1269398\nQ : Type ?u.1269401\nS : Type ?u.1269404\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddC... | [
1111,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.d_of_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.287176\nF : Type ?u.287179\nK : Type ?u.287182\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nh : toPoly P = toPoly Q\n⊢ P.d = Q.d",
"tactic": "rw [← coeff_eq_d, h, coeff_eq_d]"
}
] | [
133,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.add_left_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm0 : MeasurableSpace α\nμ μ₁ μ₂ ν ν₁ ν₂ : Measure α\n⊢ μ₁ + μ₂ ⟂ₘ ν ↔ μ₁ ⟂ₘ ν ∧ μ₂ ⟂ₘ ν",
"tactic": "rw [← sum_cond, sum_left, Bool.forall_bool, cond, cond, and_comm]"
}
] | [
105,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_sub | [] | [
550,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.flip_inj | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝³² : Semiring R\nS : Type u_6\ninst✝³¹ : Semiring S\nR₂ : Type u_2\ninst✝³⁰ : Semiring R₂\nS₂ : Type u_7\ninst✝²⁹ : Semiring S₂\nM : Type u_3\nN : Type u_5\nP : Type u_4\nM₂ : Type ?u.174405\nN₂ : Type ?u.174408\nP₂ : Type ?u.174411\nNₗ : Type... | [
155,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.def | [] | [
91,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/List/Lemmas.lean | List.insert_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nh : ¬a ∈ l\n⊢ List.insert a l = a :: l",
"tactic": "simp only [List.insert, if_neg h]"
}
] | [
896,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
895,
9
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_disjoint_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2824\nA : Type ?u.2827\nB : Type ?u.2830\nM : Type u_2\nN : Type ?u.2836\nP : Type ?u.2839\nR : Type ?u.2842\nS : Type ?u.2845\nG : Type ?u.2848\nM₀ : Type ?u.2851\nG₀ : Type ?u.2854\nι : Sort ?u.2857\ninst✝² : One M\ninst✝¹ : One N\nin... | [
99,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_zero_iff | [
{
"state_after": "α : Type ?u.312782\nβ : Type ?u.312785\nγ : Type ?u.312788\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nh : bsup o f = 0\ni : Ordinal\nhi : i < o\n⊢ f i hi = 0",
"state_before": "α : Type ?u.312782\nβ : Type ?u.312785\nγ : Type ?u... | [
1535,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/Algebra/GroupWithZero/Divisibility.lean | mul_dvd_mul_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelMonoidWithZero α\na b c : α\nha : a ≠ 0\nd : α\n⊢ a * c = a * b * d ↔ c = b * d",
"tactic": "rw [mul_assoc, mul_right_inj' ha]"
}
] | [
53,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_union_congr | [
{
"state_after": "α : Type u_1\nβ : Type ?u.307809\nγ : Type ?u.307812\nδ : Type ?u.307815\nι : Type ?u.307818\nR : Type ?u.307821\nR' : Type ?u.307824\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\n⊢ restrict μ s = restrict ν s... | [
1835,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
1
] |
Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Finsupp.linearIndependent_single | [
{
"state_after": "case hindep\nR : Type u_2\nM : Type u_3\nι : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nφ : ι → Type u_1\nf : (ι : ι) → φ ι → M\nhf : ∀ (i : ι), LinearIndependent R (f i)\n⊢ ∀ (j : ι), LinearIndependent R fun x => single j (f j x)\n\ncase hd\nR : Type u_2\nM : Type... | [
57,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | StrictMonoOn.continuousWithinAt_right_of_image_mem_nhdsWithin | [] | [
123,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/Convex/Star.lean | starConvex_sInter | [] | [
115,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_bot | [] | [
335,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
9
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_inr | [] | [
589,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Set/Function.lean | Set.restrict_extend_compl_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Sort ?u.3746\nπ : α → Type ?u.3751\nf : α → β\ng : α → γ\ng' : β → γ\n⊢ restrict (range fᶜ) (extend f g g') = g' ∘ Subtype.val",
"tactic": "classical\nexact restrict_dite_compl _ _"
},
{
"state_after": "n... | [
130,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_one | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.subsingleton_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\n⊢ Subsingleton ↑↑⊥",
"tactic": "simp"
}
... | [
577,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.leftUnitor_hom_apply | [] | [
225,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | isCycle_finRotate_of_le | [
{
"state_after": "case intro\nm : ℕ\nh : 2 ≤ 2 + m\n⊢ IsCycle (finRotate (2 + m))",
"state_before": "n : ℕ\nh : 2 ≤ n\n⊢ IsCycle (finRotate n)",
"tactic": "obtain ⟨m, rfl⟩ := exists_add_of_le h"
},
{
"state_after": "case intro\nm : ℕ\nh : 2 ≤ 2 + m\n⊢ IsCycle (finRotate (m + 2))",
"state_bef... | [
139,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_def | [] | [
334,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Basic.lean | Dense.denseRange_val | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.174734\nγ : Type ?u.174737\nδ : Type ?u.174740\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nκ : Type ?u.174752\nι : Type ?u.174755\nf : κ → β\ng : β → γ\ns : Set α\nh : Dense s\n⊢ DenseRange Sub... | [
1815,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.isConjugateExponent_one_div | [
{
"state_after": "a b : ℝ\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\n⊢ a < 1",
"state_before": "a b : ℝ\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\n⊢ 1 < 1 / a",
"tactic": "rw [lt_div_iff ha, one_mul]"
},
{
"state_after": "no goals",
"state_before": "a b : ℝ\nha : 0 < a\nhb : 0 < b\nhab : a + b... | [
133,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.smul | [
{
"state_after": "R : Type u_1\ninst✝⁴ : Ring R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nU U₁ U₂ : Submodule R M\nx x₁ x₂ y y₁ y₂ z z₁ z₂ : M\nN : Type ?u.60443\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nV V₁ V₂ : Submodule R N\nhxy : Submodule.Quotient.mk x = Submodule.Quotient.mk y\nc :... | [
95,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.divInt_sub_divInt | [
{
"state_after": "no goals",
"state_before": "n₁ n₂ d₁ d₂ : Int\nz₁ : d₁ ≠ 0\nz₂ : d₂ ≠ 0\n⊢ n₁ /. d₁ - n₂ /. d₂ = (n₁ * d₂ - n₂ * d₁) /. (d₁ * d₂)",
"tactic": "simp only [Rat.sub_eq_add_neg, neg_divInt,\n divInt_add_divInt _ _ z₁ z₂, Int.neg_mul, Int.sub_eq_add_neg]"
}
] | [
242,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
239,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.comp_id | [] | [
479,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicoequalizer.multicofork_π | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.inv_mul_of_unit | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na : ZMod n\nh : IsUnit a\n⊢ a⁻¹ * a = 1",
"tactic": "rw [mul_comm, mul_inv_of_unit a h]"
}
] | [
724,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_surjective | [] | [
781,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.close_isClosed | [] | [
107,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_eq_empty | [] | [
123,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_eq_singleton | [
{
"state_after": "G : Type u_1\nG' : Type ?u.169479\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.169488\ninst✝ : AddGroup A\nH✝ K H : Subgroup G\nx✝ : ∃ g, ↑H = {g}\ng : G\nhg : ↑H = {g}\n⊢ Subsingleton ↑{g}",
"state_before": "G : Type u_1\nG' : Type ?u.169479\ninst✝² : Group G\ninst✝¹ : Group G'\nA : ... | [
929,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.Subobject.inf_eq_of_isDetecting | [] | [
336,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀ | [
{
"state_after": "C : Type u_2\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ✝ Δ'✝ Δ''✝ : SimplexCategory\ninst✝² : HasFiniteCoproducts C\nΔ Δ' : SimplexCategoryᵒᵖ\nA : Splitting.IndexSet Δ\nθ : Δ ⟶ Δ'\nΔ'' : SimplexCategory\ne : Δ'.unop ⟶ Δ''\ni : Δ'' ⟶ A.fst.unop\ninst✝¹ ... | [
202,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_add_pi | [] | [
1208,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.eq_zpow_of_nonzero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nq : ℚ\nhq : q ≠ 0\n⊢ padicNorm p q = ↑p ^ (-padicValRat p q)",
"tactic": "simp [hq, padicNorm]"
}
] | [
62,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_inter | [
{
"state_after": "α : Type u_1\nM : Type u_2\nN : Type ?u.113043\nP : Type ?u.113046\nR : Type u_3\nS : Type ?u.113052\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\ns t : Set ... | [
310,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.nonempty | [] | [
80,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualCopairing_nondegenerate | [
{
"state_after": "case left\nK : Type u\ninst✝⁴ : Field K\nV₁ : Type v'\nV₂ : Type v''\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nW : Subspace K V₁\n⊢ LinearMap.SeparatingLeft (dualCopairing W)\n\ncase right\nK : Type u\ninst✝⁴ : Field K\nV₁ : Type v'\nV₂ : T... | [
1411,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.MonoidalFunctor.μ_hom_inv_id | [] | [
251,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Set/Basic.lean | Set.powerset_mono | [] | [
2151,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2150,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.