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/LinearAlgebra/TensorProduct.lean | TensorProduct.lift.equiv_apply | [] | [
556,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.sigmaFinite_map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.799057\nδ : Type ?u.799060\nι : Type ?u.799063\nR : Type ?u.799066\nR' : Type ?u.799069\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\nμ : Measure α\nf : α ≃ᵐ β\nh : Sig... | [
3857,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3854,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.Pi.reindex_hom_π | [
{
"state_after": "β : Type w\nC : Type u\ninst✝² : Category C\nγ : Type v\nε : β ≃ γ\nf : γ → C\ninst✝¹ : HasProduct f\ninst✝ : HasProduct (f ∘ ↑ε)\nb : β\n⊢ (HasLimit.isoOfEquivalence (Discrete.equivalence ε)\n (Discrete.natIso fun x =>\n Iso.refl ((Discrete.functor f).obj ((Discrete.functo... | [
411,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.const_inv_mul | [] | [
140,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.reApplyInnerSelf_smul | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.4189796\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nT : E →L[𝕜] E\nx : E\nc : 𝕜\n⊢ reApplyInn... | [
2309,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2305,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.left_distrib | [
{
"state_after": "case c\nR : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\ny z : OreLocalization R S\nr₁ : R\ns₁ : { x // x ∈ S }\n⊢ r₁ /ₒ s₁ * (y + z) = r₁ /ₒ s₁ * y + r₁ /ₒ s₁ * z",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nx y z : OreLocal... | [
731,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
11
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43189\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : card s = k\nhz : 0 < k\n⊢ ↑(orderEmbOfFin s h) { val := 0, isLt := hz } = min' s (_ : Finset.Nonempty s)",
"tactic": "simp only [orderEmbOfFin_apply, Fin.val_mk, sorted_zero_eq_... | [
197,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iSup_eq_zero | [] | [
2480,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2479,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Ici | [] | [
438,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/Group/Units.lean | divp_eq_divp_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : CommMonoid α\nx y : α\nux uy : αˣ\n⊢ x /ₚ ux = y /ₚ uy ↔ x * ↑uy = y * ↑ux",
"tactic": "rw [divp_eq_iff_mul_eq, divp_mul_eq_mul_divp, divp_eq_iff_mul_eq]"
}
] | [
543,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | deriv_inner_apply | [] | [
154,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.mul_apply | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.dedup | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : DecidableEq α\nl₁ l₂ : List α\np : l₁ ~ l₂\na : α\nh : a ∈ l₁\n⊢ count a (List.dedup l₁) = count a (List.dedup l₂)",
"tactic": "simp [nodup_dedup, h, p.subset h]"
},
{
"state_after": "no goals",
... | [
959,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | max_mul_mul_le_max_mul_max | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.218570\ninst✝ : LinearOrderedCommRing α\na b✝ c✝ d b c : α\nha : 0 ≤ a\nhd : 0 ≤ d\nba : b * a ≤ max d b * max c a\ncd : c * d ≤ max a c * max b d\n⊢ a * b ≤ max a c * max d b",
"tactic": "simpa [mul_comm, max_comm] using ba"
},
{... | [
1244,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | coe_starₗᵢ | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_sup | [
{
"state_after": "case h.mk.mk\nι : Sort ?u.70414\n𝕜 : Type ?u.70417\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\nx✝ : Sym2 V\nx y : V\n⊢ Quot.mk Setoid.r (x, y) ∈ edgeSet (G₁ ⊔ G₂) ↔ Quot.mk Setoid.r (x, y) ∈ edgeSet G₁ ∪ edgeS... | [
525,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Order/Monotone/Basic.lean | AntitoneOn.reflect_lt | [] | [
770,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMaxOn.fderivWithin_nonpos | [
{
"state_after": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMaxOn f s a\ny : E\nhy : y ∈ posTangentConeAt s a\nhf : ¬DifferentiableWithinAt ℝ f s a\n⊢ ↑0 y ≤ 0",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst... | [
134,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_iUnion_le_sum_mk | [] | [
2037,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2034,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_eq | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nX Y : SimplicialObject C\ns : Splitting X\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\n⊢ ιCoprod s.N A ≫ (iso s Δ).hom = ι s (len A.fst.unop) ≫ X.map (IndexSet.e A).op",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ :... | [
278,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq | [] | [
297,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.bijOn_iff | [] | [
966,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.eq | [] | [
382,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_singleton | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_count_iff_replicate_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.395888\nγ : Type ?u.395891\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nn : ℕ\n_l : List α\n⊢ n ≤ List.count a _l ↔ replicate n a ≤ ↑_l",
"state_before": "α : Type u_1\nβ : Type ?u.395888\nγ : Type ?u.395891\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nn : ℕ\n... | [
2480,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2476,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.eqLocus_eq_ker_sub | [] | [
1485,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1484,
1
] |
Mathlib/Data/Nat/Units.lean | Nat.units_eq_one | [] | [
20,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
19,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\n⊢ ↑sign (f.trans g) = ↑sign g * ↑sign f",
"tactic": "rw [← mul_def, sign_mul]"
}
] | [
555,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Logic/Function/Basic.lean | eq_rec_inj | [] | [
1024,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_atTop_finset_prod_le_of_prod_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.355390\nι' : Type ?u.355393\nα : Type u_1\nβ : Type u_3\nγ : Type u_2\ninst✝ : CommMonoid α\nf : β → α\ng : γ → α\nh_eq : ∀ (u : Finset γ), ∃ v, ∀ (v' : Finset β), v ⊆ v' → ∃ u', u ⊆ u' ∧ ∏ x in u', g x = ∏ b in v', f b\n⊢ map (fun s => ∏ b in s, f b... | [
1759,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sq_sqrt | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : 0 ≤ x\n⊢ sqrt x ^ 2 = x",
"tactic": "rw [sq, mul_self_sqrt h]"
}
] | [
235,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.HasFiniteIntegral.tendsto_set_integral_nhds_zero | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF : Type ?u.973542\n𝕜 : Type ?u.973545\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
966,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousOn.mono | [] | [
155,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.compl | [] | [
91,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Std/Data/Int/Lemmas.lean | Int.not_lt | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ ¬a < b ↔ b ≤ a",
"tactic": "rw [← Int.not_le, Decidable.not_not]"
}
] | [
667,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
666,
11
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.mem_map_equiv | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.2247631\nR₂ : Type u_2\nR₃ : Type ?u.2247637\nR₄ : Type ?u.2247640\nS : Type ?u.2247643\nK : Type ?u.2247646\nK₂ : Type ?u.2247649\nM : Type u_3\nM' : Type ?u.2247655\nM₁ : Type ?u.2247658\nM₂ : Type u_4\nM₃ : Type ?u.2247664\nM₄ : Type ?u.2247667\nN : Type ?u.224767... | [
2503,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2497,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictMono_int_of_lt_succ | [] | [
1064,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.num_dvd | [
{
"state_after": "case mk'\na b : ℤ\nb0 : b ≠ 0\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : Nat.coprime (Int.natAbs n) d\ne : a /. b = mk' n d\n⊢ (mk' n d).num ∣ a",
"state_before": "a b : ℤ\nb0 : b ≠ 0\n⊢ (a /. b).num ∣ a",
"tactic": "cases' e : a /. b with n d h c"
},
{
"state_after": "case mk'\na b : ℤ\nb0... | [
31,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.ne_top_iff_one | [] | [
101,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_congr | [] | [
511,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.fac | [
{
"state_after": "C : Type u_1\ninst✝¹ : Category C\nW : MorphismProperty C\nD : Type u_3\ninst✝ : Category D\nG : C ⥤ D\nhG : MorphismProperty.IsInvertedBy W G\nX Y : C\nf : X ⟶ Y\n⊢ (MorphismProperty.Q W ⋙ lift G hG).map f =\n eqToHom (_ : (MorphismProperty.Q W ⋙ lift G hG).obj X = (MorphismProperty.Q W ⋙ ... | [
190,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.component.of | [] | [
230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | MeasureTheory.tendsto_measure_Iic_atTop | [
{
"state_after": "case inl\nα : Type u_1\nmα : MeasurableSpace α\ninst✝¹ : SemilatticeSup α\ninst✝ : IsCountablyGenerated atTop\nμ : Measure α\nh✝ : IsEmpty α\n⊢ Tendsto (fun x => ↑↑μ (Iic x)) atTop (𝓝 (↑↑μ univ))\n\ncase inr\nα : Type u_1\nmα : MeasurableSpace α\ninst✝¹ : SemilatticeSup α\ninst✝ : IsCountably... | [
181,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.deriv_add | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.range_familyOfBFamily | [] | [
1196,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/Analysis/Calculus/Deriv/Support.lean | HasCompactSupport.deriv | [] | [
50,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.add_const | [] | [
194,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
8
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.orderOf_a_one | [
{
"state_after": "case inl\nn : ℕ\nhn : n = 0\n⊢ orderOf (a 1) = 2 * n\n\ncase inr\nn : ℕ\nhn : NeZero n\n⊢ orderOf (a 1) = 2 * n",
"state_before": "n : ℕ\n⊢ orderOf (a 1) = 2 * n",
"tactic": "cases' eq_zero_or_neZero n with hn hn"
},
{
"state_after": "case inr\nn : ℕ\nhn : NeZero n\n⊢ ¬orderOf ... | [
255,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.wSameSide | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.C_injective | [
{
"state_after": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonAssocSemiring R\nr s : R\nrs : ↑C r = ↑C s\n⊢ r = s",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonAssocSemiring R\n⊢ Injective ↑C",
"tactic": "intro r s rs"
... | [
980,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.leLT_apply | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\ninst✝¹ : IsWellOrder β s\ninst✝ : IsTrans γ t\nf : r ≼i s\ng : s ≺i t\na : α\n⊢ ↑(match ltOrEq f with\n | Sum.inl f' => PrincipalSeg.trans f' g\n | Sum.inr f' => PrincipalSeg.equiv... | [
494,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_finset_sum | [] | [
170,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Lp.lean | MeasureTheory.Integrable.aefinStronglyMeasurable | [] | [
71,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.epi_snd_of_isLimit | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : Abelian C\ninst✝¹ : HasPullbacks C\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : Epi f\ns : PullbackCone f g\nhs : IsLimit s\nthis : Epi ((limit.cone (cospan f g)).π.app WalkingCospan.right)\n⊢ Epi (PullbackCone.snd s)",
"state_before": "C : Type u\n... | [
688,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_add_pos_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x = 0 ∨ y ≠ 0\n⊢ ‖x‖ / Real.sqrt (‖x‖ * ‖x‖ + ‖y‖ * ‖y‖) < 1",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = ... | [
119,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_eq_sdiff_iff_inter_eq_inter | [] | [
2335,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2333,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.le_top | [] | [
340,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_nonempty_iff | [] | [
163,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.mul_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : MulZeroClass α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nhb : 0 < b\n⊢ 0 < a * b",
"tactic": "simpa only [mul_zero] using mul_lt_mul_of_pos_left hb ha"
}
] | [
341,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_const | [] | [
192,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.zero_power_le | [
{
"state_after": "case pos\nα β : Type u\nc : Cardinal\nh : c = 0\n⊢ 0 ^ c ≤ 1\n\ncase neg\nα β : Type u\nc : Cardinal\nh : ¬c = 0\n⊢ 0 ^ c ≤ 1",
"state_before": "α β : Type u\nc : Cardinal\n⊢ 0 ^ c ≤ 1",
"tactic": "by_cases h : c = 0"
},
{
"state_after": "no goals",
"state_before": "case po... | [
715,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_eq_U_sub_X_mul_U | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.21238\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\n⊢ T R (n + 1) = U R (n + 1) - X * U R n",
"tactic": "rw [U_eq_X_mul_U_add_T, add_comm (X * U R n), add_sub_cancel]"
}
] | [
139,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rdropWhile_last_not | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nhl : rdropWhile p l ≠ []\n⊢ ¬p (getLast (reverse (dropWhile p (reverse l))) (_ : reverse (dropWhile p (reverse l)) ≠ [])) = true",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nhl : rdropWhile p l ≠ []\n⊢ ¬p (getLast (rdropWh... | [
130,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/CategoryTheory/Category/Preorder.lean | CategoryTheory.le_of_op_hom | [] | [
116,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformGroup.uniformContinuous_iff_open_ker | [
{
"state_after": "case refine'_1\nα : Type u_3\nβ : Type u_2\ninst✝⁷ : UniformSpace α\ninst✝⁶ : Group α\ninst✝⁵ : UniformGroup α\nhom : Type u_1\ninst✝⁴ : UniformSpace β\ninst✝³ : DiscreteTopology β\ninst✝² : Group β\ninst✝¹ : UniformGroup β\ninst✝ : MonoidHomClass hom α β\nf : hom\nhf : UniformContinuous ↑f\n⊢... | [
426,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | multiplesHom_symm_apply | [] | [
876,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_eq_iff_exists_eq | [] | [
137,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | MultilinearMap.alternatization_coe | [] | [
886,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.mem_restrictDegree_iff_sup | [
{
"state_after": "σ : Type u\nR : Type v\ninst✝¹ : CommRing R\np✝ m : ℕ\ninst✝ : DecidableEq σ\np : MvPolynomial σ R\nn : ℕ\n⊢ (∀ (s : σ →₀ ℕ), s ∈ support p → ∀ (i : σ), ↑s i ≤ n) ↔ ∀ (i : σ) (b : σ →₀ ℕ), b ∈ support p → ↑b i ≤ n",
"state_before": "σ : Type u\nR : Type v\ninst✝¹ : CommRing R\np✝ m : ℕ\nin... | [
106,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualAnnihilator_dualAnnihilator_eq | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁶ : Field K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nW✝ : Subspace K V\nV₁ : Type ?u.1312004\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : FiniteDimensional K V\ninst✝ : FiniteDimensional K V₁\nW : Subspace K V\nthis : dualCoannihilator (dualAnnih... | [
1104,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isFractional_of_fg | [
{
"state_after": "case intro\nR : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type ?u.669844\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.670297\ninst✝¹ : CommRing P''\ninst✝ : ... | [
862,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.mul_val | [
{
"state_after": "case h\nι : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁵ : AddCommMonoid ι\ninst✝⁴ : DecidableEq ι\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : Submonoid A\ny2 : HomogeneousLocalization 𝒜 x\na✝ : NumDenSameDeg 𝒜 x\n⊢ v... | [
429,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_zero_eq_zero | [] | [
554,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.161008\nι : Sort x\nf : Filter α\nP : α → Prop\n⊢ (∀ {q : α → Prop}, (∀ᶠ (x : α) in f, q x) → ∃ x, q x ∧ P x) ↔ ∀ {U : Set α}, U ∈ f → ∃ x, x ∈ U ∧ P x",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.161008\nι : Sort x\nf :... | [
1312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finiteDimensional_of_rank_eq_one | [] | [
649,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.supp_inj | [] | [
58,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_inf' | [] | [
933,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.complete_of_convergent_controlled_sequences | [] | [
1334,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Units.mulRight_bijective | [] | [
107,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_of_mul_le_mul_left' | [] | [
62,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.bitwise'_comm | [
{
"state_after": "no goals",
"state_before": "f : Bool → Bool → Bool\nhf : ∀ (b b' : Bool), f b b' = f b' b\nhf' : f false false = false\nn m : ℕ\nthis : bitwise' f = swap (bitwise' f)\n⊢ bitwise' f n m = bitwise' f m n",
"tactic": "conv_lhs => rw [this]"
}
] | [
173,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffAt.congr_of_eventuallyEq | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
1345,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftRingHom_injective | [] | [
787,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_inf_principal_pi_eq_bot | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\ninst✝ : ∀ (i : ι), NeBot (f i)\nI : Set ι\n⊢ (∃ i, f i ⊓ 𝓟 (piecewise I s (fun x => univ) i) = ⊥) ↔ ∃ i, i ∈ I ∧ f i ⊓ 𝓟 (s i) = ⊥",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ... | [
136,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_sUnion_null_iff | [] | [
291,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.isBigO | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\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.381155\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
694,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
8
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.IsSplitEpi.id | [] | [
138,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Real.nnnorm_of_nonneg | [] | [
1747,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.toDual_sup' | [] | [
1058,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Right.one_lt_inv_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ 1 < a⁻¹ ↔ a < 1",
"tactic": "rw [← mul_lt_mul_iff_right a, inv_mul_self, one_mul]"
}
] | [
291,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_simple_toSubalgebra_of_integral | [
{
"state_after": "case hS\nF : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nhα : IsIntegral F α\n⊢ ∀ (x : E), x ∈ Insert.insert ∅ α → IsAlgebraic F x",
"state_before": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\n... | [
528,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_succ_of_isLimit | [] | [
265,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Algebra/Support.lean | Function.support_mul_subset_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.84556\nA : Type ?u.84559\nB : Type ?u.84562\nM : Type ?u.84565\nN : Type ?u.84568\nP : Type ?u.84571\nR : Type u_1\nS : Type ?u.84577\nG : Type ?u.84580\nM₀ : Type ?u.84583\nG₀ : Type ?u.84586\nι : Sort ?u.84589\ninst✝ : MulZeroClass R\... | [
361,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_add | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.24395\nT : Type ?u.24398\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ ↑(x + y) = ↑x + ↑y",
"tactic": "ext <;> simp"
}
] | [
237,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.isInt_lcm | [] | [
88,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.nhds_basis_closed_eball | [] | [
640,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Int.norm_cast_rat | [
{
"state_after": "𝓕 : Type ?u.1114918\n𝕜 : Type ?u.1114921\nα : Type ?u.1114924\nι : Type ?u.1114927\nκ : Type ?u.1114930\nE : Type ?u.1114933\nF : Type ?u.1114936\nG : Type ?u.1114939\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nm : ℤ\n⊢ ‖↑↑m‖ = ‖↑m‖",
... | [
1827,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1826,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.inv_hom_id_apply | [] | [
90,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.inter_bijOn | [] | [
939,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | skewAdjoint.isStarNormal_of_mem | [
{
"state_after": "R : Type u_1\nA : Type ?u.113647\ninst✝¹ : Ring R\ninst✝ : StarRing R\nx : R\nhx : star x = -x\n⊢ Commute (star x) x",
"state_before": "R : Type u_1\nA : Type ?u.113647\ninst✝¹ : Ring R\ninst✝ : StarRing R\nx : R\nhx : x ∈ skewAdjoint R\n⊢ Commute (star x) x",
"tactic": "simp only [mem... | [
501,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.