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/Data/Finset/Lattice.lean | List.foldr_inf_eq_inf_toFinset | [
{
"state_after": "F : Type ?u.129296\nα : Type u_1\nβ : Type ?u.129302\nγ : Type ?u.129305\nι : Type ?u.129308\nκ : Type ?u.129311\ninst✝² : SemilatticeInf α\ninst✝¹ : OrderTop α\ns s₁ s₂ : Finset β\nf g : β → α\na : α\ninst✝ : DecidableEq α\nl : List α\n⊢ Multiset.fold (fun x x_1 => x ⊓ x_1) ⊤ (dedup ↑l) = Mul... | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | mul_sub_le_image_sub_of_le_deriv | [] | [
840,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.fderivWithin | [] | [
957,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.one_cpow | [
{
"state_after": "x : ℂ\n⊢ (if 1 = 0 then if x = 0 then 1 else 0 else exp (log 1 * x)) = 1",
"state_before": "x : ℂ\n⊢ 1 ^ x = 1",
"tactic": "rw [cpow_def]"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ (if 1 = 0 then if x = 0 then 1 else 0 else exp (log 1 * x)) = 1",
"tactic... | [
91,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | OpenEmbedding.singleton_hasGroupoid | [] | [
1042,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.coe_star_mul_self | [] | [
87,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Coloring.valid | [] | [
75,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.center_le_centralizer | [] | [
536,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lid_tmul | [] | [
633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.lowerCentralSeries_succ | [] | [
93,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_iSup | [] | [
1671,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_smul | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : Monoid γ\ninst✝¹ : (i : ι) → AddMonoid (β i)\ninst✝ : (i : ι) → DistribMulAction γ (β i)\ni✝ : ι\nc : γ\nx : β i✝\ni : ι\n⊢ (if h : i✝ = i then (_ : i✝ = i) ▸ (c • x) else 0) = c • if h : ... | [
1083,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_sUnion_of_directed | [
{
"state_after": "ι : Type u'\nι' : Type ?u.216784\nR : Type u_2\nK : Type ?u.216790\nM : Type u_1\nM' : Type ?u.216796\nM'' : Type ?u.216799\nV : Type u\nV' : Type ?u.216804\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\nin... | [
451,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.funMulInvSnorm_rpow | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nhp0 : 0 < p\nf : α → ℝ≥0∞\na : α\n⊢ f a ^ p * ((∫⁻ (c : α), f c ^ p ∂μ) ^ (1 / p))⁻¹ ^ p = f a ^ p * (∫⁻ (c : α), f c ^ p ∂μ)⁻¹",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure... | [
96,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Lie/CartanSubalgebra.lean | LieSubalgebra.ucs_eq_self_of_isCartanSubalgebra | [
{
"state_after": "case zero\nR : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\nH✝ H : LieSubalgebra R L\ninst✝ : IsCartanSubalgebra H\n⊢ LieSubmodule.ucs Nat.zero (toLieSubmodule H) = toLieSubmodule H\n\ncase succ\nR : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : Lie... | [
71,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpTo_top_iff | [
{
"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\... | [
1272,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
] |
Mathlib/Data/List/Sigma.lean | List.sizeOf_dedupKeys | [
{
"state_after": "α✝ : Type u\nβ✝ : α✝ → Type v\nl l₁ l₂ : List (Sigma β✝)\ninst✝² : DecidableEq α✝\nα : Type u_1\nβ : α → Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf (Sigma β)\nxs : List (Sigma β)\n⊢ rec 1 (fun head tail tail_ih => 1 + sizeOf head + tail_ih) (dedupKeys xs) ≤\n rec 1 (fun head tail tail... | [
671,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.prod_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.796690\ninst✝³ : AddCommMonoid α\ninst✝² : TopologicalSpace α\ninst✝¹ : AddCommMonoid γ\ninst✝ : TopologicalSpace γ\nf : β → α\ng : β → γ\na : α\nb : γ\nhf : HasSum f a\nhg : HasSum g b\n⊢ HasSum (fun x => (f... | [
1303,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.stopPos | [] | [
810,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
809,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Relation.map_snd | [] | [
556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.app_one_eq_π | [] | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_cons | [] | [
650,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Logic/IsEmpty.lean | Function.isEmpty | [] | [
44,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
11
] |
Mathlib/Topology/UniformSpace/Separation.lean | separationRel_iff_inseparable | [] | [
122,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.obj_μ_zero_app | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nm₁ m₂ : M\nX : C\n⊢ (LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor (𝟙_ M) m₂).app ((F.obj m₁).obj X) ≫\n (LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor m₁ (𝟙_ M ⊗ m... | [
298,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.mem_map_C_iff | [
{
"state_after": "case mp\nR : Type u\nS : Type ?u.979377\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nf : MvPolynomial σ R\n⊢ f ∈ Ideal.map C I → ∀ (m : σ →₀ ℕ), coeff m f ∈ I\n\ncase mpr\nR : Type u\nS : Type ?u.979377\nσ : Type v... | [
1190,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.homEquiv_naturality_left | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : F.obj X ⟶ Y\n⊢ F.map f ≫ g = ↑(homEquiv adj X' Y).symm (f ≫ ↑(homEquiv adj X Y) g)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\nins... | [
161,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAt.add_const | [] | [
103,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
8
] |
Mathlib/Analysis/Convex/Slope.lean | ConvexOn.secant_mono_aux1 | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : ConvexOn 𝕜 s f\nx y z : 𝕜\nhx : x ∈ s\nhz : z ∈ s\nhxy : x < y\nhyz : y < z\nhxy' : 0 < y - x\n⊢ (z - x) * f y ≤ (z - y) * f x + (y - x) * f z",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : ... | [
258,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_one_of_card_eq_zero | [] | [
114,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.le_pointwise_smul_iff | [] | [
438,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Order/Filter/Bases.lean | Pairwise.exists_mem_filter_basis_of_disjoint | [
{
"state_after": "case intro.intro\nα : Type u_2\nβ : Type ?u.53092\nγ : Type ?u.53095\nι✝ : Sort ?u.53098\nι' : Sort ?u.53101\nl✝ l' : Filter α\np✝ : ι✝ → Prop\ns✝ : ι✝ → Set α\nt✝ : Set α\ni : ι✝\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nI : Type u_1\ninst✝ : Finite I\nl : I → Filter α\nι : I → Sort u_3\np :... | [
665,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.leftRel_eq | [
{
"state_after": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ ∀ (a b : α), Setoid.r a b ↔ a⁻¹ * b ∈ s",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ ∀ (a b : α), Setoid.r a b = (a⁻¹ * b ∈ s)",
"tactic": "simp only [eq_iff_iff]"
},
{
"state_after": "no goals",
"state... | [
340,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.rel_get_of_le | [
{
"state_after": "case inl\nα : Type uu\nr : α → α → Prop\na✝ : α\nl✝ : List α\ninst✝ : IsRefl α r\nl : List α\nh : Sorted r l\na : Fin (length l)\nhab : a ≤ a\n⊢ r (get l a) (get l a)\n\ncase inr\nα : Type uu\nr : α → α → Prop\na✝ : α\nl✝ : List α\ninst✝ : IsRefl α r\nl : List α\nh : Sorted r l\na b : Fin (len... | [
125,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_pow_count_factors_of_dvd_pow | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\np a : Associates α\nhp : Irreducible p\nn : ℕ\nh : a ∣ p ^ n\n✝ : Nontrivial α\n⊢ a = p ^ co... | [
1852,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.ne_zero | [] | [
66,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Order/Interval.lean | Interval.bot_ne_pure | [] | [
410,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.insert_WF | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nk : α\nv : β\nh : Bucket.WF m.buckets\n⊢ Bucket.WF\n (match\n AssocList.contains k\n m.buckets.val[USize.toNat (mkIdx (_ : 0 < Array.size m.buckets.val) (UInt64.toUSize (hash k))).val] with\n |... | [
239,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
221,
1
] |
Mathlib/Topology/SubsetProperties.lean | Finset.isCompact_biUnion | [] | [
417,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.min_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : PseudoEMetricSpace α\nf g : α → ℝ\nKf Kg : ℝ≥0\nhf : LipschitzWith Kf f\na : ℝ\n⊢ LipschitzWith Kf fun x => min (f x) a",
"tactic": "simpa only [max_eq_left (zero_le Kf)] using hf.min (LipschitzWith.con... | [
460,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.strictMono_iff_injective | [] | [
880,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.destruct_eq_nil | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ Option.map (fun a' => (a', tail s)) (get? s 0) = none → s = nil",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ destruct s = none → s = nil",
"tactic": "dsimp [destruct]"
},
{
"state_after": "case none\nα : Ty... | [
220,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Set/Function.lean | Set.maps_univ_to | [] | [
528,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.univ_nonempty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1860\nγ : Type ?u.1863\ninst✝ : Fintype α\ns t : Finset α\n⊢ Finset.Nonempty univ ↔ Nonempty α",
"tactic": "rw [← coe_nonempty, coe_univ, Set.nonempty_iff_univ_nonempty]"
}
] | [
105,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Set/Function.lean | Function.Surjective.surjOn | [] | [
1600,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1599,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_measure_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.951145\nF : Type u_2\nG : Type ?u.951151\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : MeasurableSpace α\nf : α → F\n⊢ s... | [
242,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneEquiv.symm | [] | [
170,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.sumArrowLequivProdArrow_symm_apply_inl | [] | [
464,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.dist_conj_conj | [] | [
331,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Order/LocallyFinite.lean | Multiset.mem_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33793\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\na x : α\n⊢ x ∈ Ioi a ↔ a < x",
"tactic": "rw [Ioi, ← Finset.mem_def, Finset.mem_Ioi]"
}
] | [
592,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_transpose | [
{
"state_after": "case a.mk.h.mk\nl : Type ?u.198919\nm : Type ?u.198922\nn : Type ?u.198925\no : Type u_4\np : Type ?u.198931\nq : Type ?u.198934\nm' : o → Type u_1\nn' : o → Type u_2\np' : o → Type ?u.198949\nR : Type ?u.198952\nS : Type ?u.198955\nα : Type u_3\nβ : Type ?u.198961\ninst✝² : DecidableEq o\nins... | [
684,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.subset | [] | [
250,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.coprodMap_apply | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Connected.set_univ_walk_nonempty | [] | [
2209,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2207,
1
] |
Mathlib/Order/Disjointed.lean | disjointed_le_id | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1032\ninst✝ : GeneralizedBooleanAlgebra α\nf : ℕ → α\nn : ℕ\n⊢ disjointed f n ≤ id f n",
"state_before": "α : Type u_1\nβ : Type ?u.1032\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ disjointed ≤ id",
"tactic": "rintro f n"
},
{
"state_after": "case zero\nα ... | [
70,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioi_self | [] | [
533,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Topology/Order.lean | continuous_inf_dom_left | [] | [
779,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.pointwise_smul_subset_iff | [] | [
358,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_eq_top | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.378850\nγ : Type ?u.378853\nδ : Type ?u.378856\nι : Type ?u.378859\nR : Type ?u.378862\nR' : Type ?u.378865\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝¹ : Measurabl... | [
2254,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2250,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.symm_piecewise | [] | [
1009,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_anti | [] | [
1383,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1382,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.sinh_log | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\nhx : 0 < x\n⊢ sinh (log x) = (x - x⁻¹) / 2",
"tactic": "rw [sinh_eq, exp_neg, exp_log hx]"
}
] | [
118,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_range_add_rank_ker | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.580352\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V'\ninst✝² : Module K V'\ninst✝¹ : AddCommGroup V₁\ninst✝ : Module K V... | [
1093,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.to_continuousMap_injective | [
{
"state_after": "case h\nR : Type u_1\nV : Type u_2\nW : Type u_3\nP : Type u_4\nQ : Type u_5\ninst✝⁸ : Ring R\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module R V\ninst✝⁵ : TopologicalSpace P\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup W\ninst✝² : Module R W\ninst✝¹ : TopologicalSpace Q\ninst✝ : AddTorsor W Q\nf ... | [
119,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_curry | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.65130\nβ : Type u_2\nβ' : Type ?u.65136\nγ : Type u_3\nγ' : Type ?u.65142\nδ : Type ?u.65145\nδ' : Type ?u.65148\nε : Type ?u.65151\nε' : Type ?u.65154\nζ : Type ?u.65157\nζ' : Type ?u.65160\nν : Type ?u.65163\ninst✝⁷ : DecidableEq α'\... | [
342,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_singleton_iff' | [] | [
793,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_eval | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nP : R[X]\nr : R\nf g : R[X]\nhf : eval r (↑(expand R p) f) = eval (r ^ p) f\nhg : eval r (↑(expand R p) g) = eval (r ^ p) g\n⊢ eval r (↑(expand R p) (f + g)) = eval (r ^ p) (f + g)",
"state_before": "R : T... | [
193,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Topology/Separation.lean | Set.EqOn.closure | [] | [
1191,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1189,
11
] |
Mathlib/Topology/Sober.lean | IsGenericPoint.specializes | [] | [
67,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | lipschitzWith_circleMap | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.27048\ninst✝ : NormedAddCommGroup E\nc : ℂ\nR θ : ℝ\n⊢ ↑‖deriv (circleMap c R) θ‖₊ ≤ ↑(↑Real.nnabs R)",
"tactic": "simp"
}
] | [
213,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.apply_single | [] | [
124,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.symm_mk | [] | [
747,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Std/Logic.lean | and_iff_right_iff_imp | [] | [
212,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
211,
9
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.bilinearComp_apply | [] | [
1364,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.isCycle_of_prime_order'' | [
{
"state_after": "α : Type u_1\ninst✝ : Fintype α\nσ : Perm α\nh1 : Nat.Prime (Fintype.card α)\nh2 : orderOf σ = Fintype.card α\n⊢ 1 < 2",
"state_before": "α : Type u_1\ninst✝ : Fintype α\nσ : Perm α\nh1 : Nat.Prime (Fintype.card α)\nh2 : orderOf σ = Fintype.card α\n⊢ Fintype.card α < 2 * orderOf σ",
"t... | [
365,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.ediam_image | [] | [
669,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Std/Data/Fin/Lemmas.lean | USize.le_def | [] | [
26,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
26,
9
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_int | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nn : ℤ\n⊢ F⟮↑n⟯ = ⊥",
"tactic": "refine' adjoin_simple_eq_bot_iff.mpr (coe_int_mem ⊥ n)"
}
] | [
697,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.of_denote_eq_cancel | [
{
"state_after": "ctx : Context\nm₁ m₂ : Poly\nh : denote_eq ctx (cancel m₁ m₂)\n⊢ denote_eq ctx (m₁, m₂)",
"state_before": "ctx : Context\nm₁ m₂ : Poly\nh : denote_eq ctx (cancel m₁ m₂)\n⊢ denote_eq ctx (m₁, m₂)",
"tactic": "simp at h"
},
{
"state_after": "ctx : Context\nm₁ m₂ : Poly\nh : denot... | [
422,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
418,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean | Complex.volume_preserving_equiv_pi | [] | [
48,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.compl₁₂_inj | [
{
"state_after": "case mp\nR : Type u_1\ninst✝²³ : CommSemiring R\nR₂ : Type ?u.489611\ninst✝²² : CommSemiring R₂\nR₃ : Type ?u.489617\ninst✝²¹ : CommSemiring R₃\nR₄ : Type ?u.489623\ninst✝²⁰ : CommSemiring R₄\nM : Type ?u.489629\nN : Type ?u.489632\nP : Type ?u.489635\nQ : Type ?u.489638\nMₗ : Type u_2\nNₗ : T... | [
373,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneDegree.add_le | [
{
"state_after": "case h\nα : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : Type v\ninst✝³ : Primcodable β\ninst✝² : Inhabited β\nγ : Type w\ninst✝¹ : Primcodable γ\ninst✝ : Inhabited γ\nd₂ d₃ : ManyOneDegree\np✝ : Set ℕ\n⊢ of p✝ + d₂ ≤ d₃ ↔ of p✝ ≤ d₃ ∧ d₂ ≤ d₃",
"state_before": "α : Type u\nin... | [
495,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.mul_const | [
{
"state_after": "case h.e'_10\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type ?u.934607\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type ?u.934702\ninst✝⁷ : NormedAddCommGroup G\ninst✝⁶ : NormedSpace 𝕜 ... | [
420,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.pow_antitone_exp | [] | [
726,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_zero | [] | [
226,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
8
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.lowerBound?_least_lb | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\ncmp : α → α → Ordering\ncut : α → Ordering\nx y : α\ninst✝¹ : TransCmp cmp\ninst✝ : IsCut cmp cut\nlb : Option α\nh : Ordered cmp nil\nhlb : ∀ {x : α}, x ∈ lb → All (fun x_1 => cmpLT cmp x x_1) nil\n⊢ x ∈ lowerBound? cut nil lb → y ∈ nil ... | [
291,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
271,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_empty | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.liftRight_inv_mul | [
{
"state_after": "F : Type ?u.44210\nG : Type ?u.44213\nα : Type ?u.44216\nM : Type u_1\nN : Type u_2\ninst✝¹ : Monoid M\ninst✝ : Monoid N\nf : M →* N\nh : ∀ (x : M), IsUnit (↑f x)\nx x✝ : M\n⊢ ↑(IsUnit.unit (_ : IsUnit (↑f x✝))) = ↑f x✝",
"state_before": "F : Type ?u.44210\nG : Type ?u.44213\nα : Type ?u.4... | [
266,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.nonempty_coe_sort | [] | [
497,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.le_closure_iff | [] | [
166,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.strictMono | [] | [
417,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atBot_of_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.227494\nι' : Type ?u.227497\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.227506\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x => f x * r) l atBot ↔ Tendsto f l atBot",
"tactic": "simpa only [mul_comm] usi... | [
1086,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_comp_castSucc | [
{
"state_after": "no goals",
"state_before": "m n✝ : ℕ\nα✝ : Fin (n✝ + 1) → Type u\nx : α✝ (last n✝)\nq : (i : Fin (n✝ + 1)) → α✝ i\np : (i : Fin n✝) → α✝ (↑castSucc i)\ni✝ : Fin n✝\ny : α✝ (↑castSucc i✝)\nz : α✝ (last n✝)\nn : ℕ\nα : Type u_1\na : α\nf : Fin n → α\ni : Fin n\n⊢ (snoc f a ∘ ↑castSucc) i = f... | [
467,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_add | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cos (x + y)) = ↑(cos x * cos y - sin x * sin y)",
"tactic": "simp [cos_add]"
}
] | [
1202,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
8
] |
Mathlib/Data/Set/Accumulate.lean | Set.subset_accumulate | [] | [
39,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_add_mul_right_right | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime x (y + x * z)\n⊢ IsCoprime x y",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime x (y + z * x)\n⊢ IsCoprime x y",
"tactic": "rw [mul_comm] at h"
},
{
"state_after": "no goals",
"state... | [
201,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.81289\ninst✝¹... | [
132,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to0.tr_eval | [
{
"state_after": "Γ : Type u_1\ninst✝² : Inhabited Γ\nΛ : Type u_2\ninst✝¹ : Inhabited Λ\nσ : Type u_3\ninst✝ : Inhabited σ\nM : Λ → Stmt₁\nl : List Γ\n⊢ Part.map ((fun c => Tape.right₀ c.Tape) ∘ fun a => trCfg M a)\n (eval (TM1.step M) { l := some default, var := default, Tape := Tape.mk₁ l }) =\n Part... | [
1523,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/Topology/Instances/Matrix.lean | continuousAt_matrix_inv | [] | [
237,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsBigO.antisymm | [] | [
58,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.