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/Order/Monotone/Basic.lean | Int.exists_strictMono | [
{
"state_after": "ι : Type ?u.44185\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.44194\nπ : ι → Type ?u.44199\nr : α → α → Prop\ninst✝⁴ inst✝³ : Preorder α\ninst✝² : Nonempty α\ninst✝¹ : NoMinOrder α\ninst✝ : NoMaxOrder α\ninhabited_h : Inhabited α\n⊢ ∃ f, StrictMono f",
"state_before": "ι : Type ?u.441... | [
1087,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.IsPushout.IsVanKampen.isPullback_of_mono_right | [
{
"state_after": "no goals",
"state_before": "J : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝ : Mono g\nH : IsPushout f g h i\nH' : IsVanKampen H\n⊢ f ≫ 𝟙 X = 𝟙 W ≫ f",
"tactic": "simp"
},
{
"state_after": "no go... | [
205,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.unique_diff_preimage_source | [] | [
333,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.extendWith_some | [] | [
1643,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.degree_sum_eq_of_disjoint | [
{
"state_after": "case empty\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nf : S → R[X]\ns : Finset S\nh✝ : Set.Pairwise {i | i ∈ s ∧ f i ≠ 0} (Ne on degree ∘ f)\nh : Set.Pairwise {i | i ∈ ∅ ∧ f i ≠ 0} (Ne on degree ∘ f)\n⊢ degree (Finset.sum ∅ f) = sup ∅ fun i => degr... | [
219,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.coe_zero | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isClosed_iff_of_not_mem | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nh : ¬∞ ∈ s\n⊢ IsClosed s ↔ IsClosed (some ⁻¹' s) ∧ IsCompact (some ⁻¹' s)",
"tactic": "rw [← isOpen_compl_iff, isOpen_iff_of_mem (mem_compl h), ← preimage_compl, compl_compl]"
}
] | [
235,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.isCompactElement_iff | [
{
"state_after": "ι : Type ?u.43879\nα : Type u_1\nβ : Type ?u.43885\nγ : Type ?u.43888\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Opens α\n⊢ (∀ (ι : Type u_1) (s_1 : ι → Opens α), s ≤ iSup s_1 → ∃ t, s ≤ Finset.sup t s_1) ↔\n ∀ {ι : Type u_1} (U : ι → Set α),\... | [
355,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.sum_divisors_filter_squarefree | [
{
"state_after": "n : ℕ\nh0 : n ≠ 0\nα : Type u_1\ninst✝ : AddCommMonoid α\nf : ℕ → α\n⊢ Multiset.sum\n (Multiset.map ((fun i => f i) ∘ fun x => Multiset.prod x.val)\n (Finset.powerset (Multiset.toFinset (normalizedFactors n))).val) =\n Multiset.sum\n (Multiset.map (fun i => f (Multiset.prod... | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.add_union_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.187191\nγ : Type ?u.187194\ninst✝ : DecidableEq α\ns✝ t✝ u✝ : Multiset α\na b : α\ns t u : Multiset α\n⊢ s + (t ∪ u) = s + t ∪ (s + u)",
"tactic": "rw [add_comm, union_add_distrib, add_comm s, add_comm s]"
}
] | [
1852,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1851,
1
] |
Mathlib/Logic/Relation.lean | Relation.ReflTransGen.head_induction_on | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.16998\nγ : Type ?u.17001\nδ : Type ?u.17004\nr : α → α → Prop\na✝ b c d a : α\nP : (a_1 : α) → ReflTransGen r a_1 a → Prop\nrefl : P a (_ : ReflTransGen r a a)\nhead : ∀ {a_1 c : α} (h' : r a_1 c) (h : ReflTransGen r c a), P c h → P a_1 (_ : ReflTransGen r ... | [
307,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Order/Chain.lean | ChainClosure.succ_fixpoint | [
{
"state_after": "case succ\nα : Type u_1\nβ : Type ?u.13163\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\nhc₂ : ChainClosure r c₂\nhc : SuccChain r c₂ = c₂\ns✝ : Set α\na✝ : ChainClosure r s✝\na_ih✝ : s✝ ⊆ c₂\n⊢ SuccChain r s✝ ⊆ c₂\n\ncase union\nα : Type u_1\nβ : Type ?u.13163\nr : α → α → Prop\nc c... | [
255,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_inter_mulSupport_eq' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.208648\nι : Type ?u.208651\nG : Type ?u.208654\nM : Type u_2\nN : Type ?u.208660\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\ns t : Set α\nh : ∀ (x : α), x ∈ mulSupport f → (x ∈ s ↔ x ∈ t)\n⊢ (s ∩ mulSupport fun i => f i) = t ∩ mulSupport fun i => ... | [
567,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.denseEmbedding_coe_real | [] | [
48,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePushoutShape.hom_id | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sUnion_null_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7681\nR : Type ?u.7684\nR' : Type ?u.7687\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\nS : Set (Set α)\nhS : Set.Countable S\n⊢ ↑m (⋃₀ S) = 0 ↔ ∀ (s : Set α), s ∈ S → ↑m s = 0",
"tactic": "rw [sUnion_eq_biUnion, m.biUnion_null... | [
145,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_left_neg_le_zero | [
{
"state_after": "case inl\nxl xr : Type u_1\nxL : xl → PGame\nxR : xr → PGame\ni : xr\n⊢ ∃ j, moveRight (moveLeft (-mk xl xr xL xR + mk xl xr xL xR) (Sum.inl i)) j ≤ 0\n\ncase inr\nxl xr : Type u_1\nxL : xl → PGame\nxR : xr → PGame\ni : xl\n⊢ ∃ j, moveRight (moveLeft (-mk xl xr xL xR + mk xl xr xL xR) (Sum.inr... | [
1677,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1665,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.comap_jacobson_of_surjective | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : Ideal R\nf : R →+* S\nhf : Function.Surjective ↑f\nK : Ideal S\n⊢ comap f (sInf {J | K ≤ J ∧ IsMaximal J}) = sInf {J | comap f K ≤ J ∧ IsMaximal J}",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : I... | [
230,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.compl_Iio | [] | [
1071,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.lt_add_one_iff | [
{
"state_after": "n✝ m n : ℕ\nk : Fin (n + 1)\n⊢ ¬k < k + 1 ↔ ¬k < last n",
"state_before": "n✝ m n : ℕ\nk : Fin (n + 1)\n⊢ k < k + 1 ↔ k < last n",
"tactic": "rw [← not_iff_not]"
},
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\nk : Fin (n + 1)\n⊢ ¬k < k + 1 ↔ ¬k < last n",
"... | [
984,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_mul_bot_of_neg | [] | [
949,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.continuous_cos | [
{
"state_after": "⊢ Continuous fun z => (exp (z * I) + exp (-z * I)) / 2",
"state_before": "⊢ Continuous cos",
"tactic": "change Continuous fun z => (exp (z * I) + exp (-z * I)) / 2"
},
{
"state_after": "no goals",
"state_before": "⊢ Continuous fun z => (exp (z * I) + exp (-z * I)) / 2",
... | [
66,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/Homotopy/Equiv.lean | ContinuousMap.HomotopyEquiv.coe_invFun | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.iUnion | [
{
"state_after": "case h\nι : Type u_2\nα : Type u_1\ns : ι → Set α\nhs : IndexedPartition s\nx : α\n⊢ (x ∈ ⋃ (i : ι), s i) ↔ x ∈ univ",
"state_before": "ι : Type u_2\nα : Type u_1\ns : ι → Set α\nhs : IndexedPartition s\n⊢ (⋃ (i : ι), s i) = univ",
"tactic": "ext x"
},
{
"state_after": "no goal... | [
375,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.mabs_mabs | [] | [
529,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | bit0_ne_zero | [] | [
91,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_fintypeIio | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Fintype.card ↑(Set.Iio b) = b",
"tactic": "rw [Fintype.card_ofFinset, card_Iio]"
}
] | [
156,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_ciInf | [] | [
1038,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ULift.norm_down | [] | [
2116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2115,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_gt_inter_gt | [] | [
450,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coe_eq_of_eq_mk | [] | [
115,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.swap_mul | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.819516\nα✝ : Type ?u.819519\nβ : Type ?u.819522\nf✝ g : Perm α✝\nx✝ y : α✝\ninst✝² : DecidableEq α✝\ninst✝¹ : Fintype α✝\nα : Type u_1\ninst✝ : DecidableEq α\nf : Perm α\nhf : IsCycle f\nx : α\nhx : ↑f x ≠ x\nhffx : ↑f (↑f x) ≠ x\n⊢ ↑(swap x (↑f x) *... | [
529,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_is_closed | [] | [
408,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.not_inl_le_inr | [] | [
153,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closure | [
{
"state_after": "case h₁\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nt : Set (PrimeSpectrum R)\n⊢ zeroLocus ↑(vanishingIdeal t) ⊆ closure t\n\ncase h₂\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nt : Set (PrimeSpectrum R)\n⊢ closure t ⊆ zeroLocus ↑(vanishingIdeal t)",... | [
470,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.cg_iff_countable | [
{
"state_after": "L : Language\nM : Type u_3\ninst✝¹ : Structure L M\ninst✝ : Countable ((l : ℕ) × Functions L l)\ns : Substructure L M\n⊢ CG s → Countable { x // x ∈ s }",
"state_before": "L : Language\nM : Type u_3\ninst✝¹ : Structure L M\ninst✝ : Countable ((l : ℕ) × Functions L l)\ns : Substructure L M\... | [
183,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_trans | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nh₁ : a ∣ b\nh₂ : b ∣ c\nd : Nat\nh₃ : b = a * d\ne : Nat\nh₄ : c = b * e\n⊢ c = a * (d * e)",
"tactic": "simp[h₃,h₄, Nat.mul_assoc]"
}
] | [
662,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
659,
11
] |
Mathlib/Order/Heyting/Basic.lean | le_sup_sdiff_sup_sdiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.95313\nα : Type u_1\nβ : Type ?u.95319\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ≤ b ⊔ (a \\ c ⊔ c \\ b)",
"tactic": "simpa using @sdiff_sdiff_sdiff_le_sdiff"
}
] | [
617,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self | [
{
"state_after": "case zero\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY : C\nn q : ℕ\nφ : Y ⟶ X.obj [n + 1].op\nv✝ : HigherFacesVanish q φ\nv : HigherFacesVanish Nat.zero φ\n⊢ φ ≫ HomologicalComplex.Hom.f (P Nat.zero) (n + 1) = φ\n\ncase succ\nC : Type u_2\ninst✝¹ : Cate... | [
139,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | eq_neg_self_iff | [] | [
109,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Function.Injective.map_swap | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nhf : Injective f\nx y z : α\n⊢ f (↑(Equiv.swap x y) z) = if f z = f x then f y else if f z = f y then f x else f z",
"state_before": "α : Sort u_1\nβ : Sort u_2\ninst✝¹ : DecidableEq α\ninst✝ : DecidableE... | [
1733,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.self_subset_cthickening | [] | [
1166,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nc₁ c₂ p₁ p₂ : P\nhc₁ : dist p₁ c₁ = dist p₂ c₁\nhc₂ : dist p₁ c₂ = dist p₂ c₂\nh : inner (c₂ -ᵥ c₁ + (c₂ -ᵥ c₁)) (p₂ -ᵥ p₁) = 0\n⊢ inner (c₂ -ᵥ c₁) (p... | [
128,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_zero_union_interior | [
{
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Mathlib/Analysis/Normed/Field/Basic.lean | NormedField.denseRange_nnnorm | [] | [
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Mathlib/Order/Interval.lean | Interval.coe_sInf | [
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Mathlib/Data/List/Count.lean | List.Sublist.count_le | [] | [
214,
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.ge_stable | [
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Mathlib/Order/Filter/Prod.lean | Filter.tendsto_prodAssoc_symm | [] | [
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Mathlib/Order/Bounded.lean | Set.unbounded_le_inter_le | [
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.balRight_toList | [
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433,
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Mathlib/CategoryTheory/Idempotents/HomologicalComplex.lean | CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d | [] | [
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.linearIsometry_apply | [] | [
227,
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226,
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Mathlib/Data/Set/Function.lean | Set.apply_piecewise | [
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Mathlib/Algebra/Homology/ImageToKernel.lean | homology.ext | [] | [
213,
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211,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_two | [
{
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688,
83
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Mathlib/Data/Set/Lattice.lean | Set.univ_subtype | [
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Mathlib/Analysis/SpecificLimits/Basic.lean | lt_geom | [
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Mathlib/Data/List/Basic.lean | List.all₂_cons | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.neBot_iff | [] | [
495,
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Mathlib/RingTheory/ReesAlgebra.lean | mem_reesAlgebra_iff | [] | [
68,
10
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero | [
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_le_csInf' | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.clm_apply | [] | [
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73
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128,
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Mathlib/Data/Vector3.lean | Vector3.insert_fz | [
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193,
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192,
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_le_tsub_iff_left | [] | [
390,
88
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Mathlib/Topology/Bornology/Constructions.lean | boundedSpace_subtype_iff | [
{
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167,
59
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165,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mul_add_inv_left | [
{
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Mathlib/Order/Hom/Lattice.lean | InfTopHom.dual_id | [] | [
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1491,
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Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_orbit_self | [
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70,
36
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69,
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.mk_mul_of_mem | [
{
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550,
62
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549,
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Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_const_add | [
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.exists_rat_pow_btwn | [
{
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700,
99
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693,
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Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.subset_smul | [
{
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294,
24
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288,
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Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_empty | [
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49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.vecMul_one | [
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Mathlib/Data/W/Basic.lean | WType.infinite_of_nonempty_of_isEmpty | [
{
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{
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123,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
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Mathlib/Computability/Primrec.lean | Primrec.list_map | [
{
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Std/Data/Rat/Lemmas.lean | Rat.divInt_num_den | [
{
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150,
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_span | [
{
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175,
41
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174,
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.sub_apply | [] | [
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6
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Mathlib/InformationTheory/Hamming.lean | hammingDist_ne_zero | [] | [
116,
26
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115,
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Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.prodCongr_symm | [] | [
288,
6
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286,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.range_eq_univ | [
{
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Mathlib/Logic/Nontrivial.lean | false_of_nontrivial_of_subsingleton | [] | [
137,
23
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136,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toSubMulAction_injective | [] | [
158,
98
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157,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.map_one | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Differentiable.hasFPowerSeriesOnBall | [] | [
619,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.inv_smul_integral_comp_div_add | [
{
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"state_before": "ι : Type ?u.14895046\n𝕜 : Type ?u.14895049\nE : Type u_1\nF : Type ?u.14895055\nA : Type ?u.14895058\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d✝ : ℝ\nf : ℝ → E\nc d : ℝ\n⊢ (c⁻¹ • ∫ (x : ℝ) in a..b, f (x / c + d))... | [
785,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.dist_eq_sum | [] | [
216,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_monomial | [
{
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"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q r✝ : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\nn : ℕ\nr : R\n⊢ eval₂ f x (↑(monomial n) r) = ↑f r * x ^ n",
"tactic": "simp [eval₂_eq_sum]"
}
] | [
82,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.length_cons | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.top_mul_top | [
{
"state_after": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Zero α\ninst✝ : Mul α\n⊢ Option.map₂ (fun x x_1 => x * x_1) ⊤ ⊤ = ⊤",
"state_before": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Zero α\ninst✝ : Mul α\n⊢ ⊤ * ⊤ = ⊤",
"tactic": "simp [mul_def]"
},
{
"state_after": "no goals",
... | [
46,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | le_of_span_le_span | [
{
"state_after": "ι : Type u'\nι' : Type ?u.1166078\nR : Type u_1\nK : Type ?u.1166084\nM : Type u_2\nM' : Type ?u.1166090\nM'' : Type ?u.1166093\nV : Type u\nV' : Type ?u.1166098\nv : ι → M\ninst✝⁷ : Ring R\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : AddCommGroup M''\ninst✝³ : Module R M\ninst... | [
1098,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_nat_lt | [] | [
860,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | ascending_central_series_le_upper | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH✝ : Subgroup G\ninst✝ : Normal H✝\nH : ℕ → Subgroup G\nhH : IsAscendingCentralSeries H\nn : ℕ\nx : G\nhx : x ∈ H (n + 1)\n⊢ x ∈ upperCentralSeries G (n + 1)",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH✝ : Subgroup G\ninst✝ : Normal H✝\nH : ℕ → Subgr... | [
202,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.not_irreducible_of_aleph0_le | [
{
"state_after": "a b : Cardinal\nn m : ℕ\nha : ℵ₀ ≤ a\n⊢ ¬¬IsUnit a ∨ ¬∀ (a_1 b : Cardinal), a = a_1 * b → IsUnit a_1 ∨ IsUnit b",
"state_before": "a b : Cardinal\nn m : ℕ\nha : ℵ₀ ≤ a\n⊢ ¬Irreducible a",
"tactic": "rw [irreducible_iff, not_and_or]"
},
{
"state_after": "a b : Cardinal\nn m : ℕ\... | [
98,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Adjunction.strongEpi_map_of_strongEpi | [
{
"state_after": "C : Type u_3\nD : Type u_4\ninst✝³ : Category C\ninst✝² : Category D\nF : C ⥤ D\nF' : D ⥤ C\nA B : C\nadj : F ⊣ F'\nf : A ⟶ B\nh₁ : Functor.PreservesMonomorphisms F'\nh₂ : Functor.PreservesEpimorphisms F\ninst✝¹ : StrongEpi f\nX Y : D\nZ : X ⟶ Y\ninst✝ : Mono Z\n⊢ HasLiftingProperty (F.map f) ... | [
319,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_append_comm | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂✝ l₂ : List α\n⊢ [] ++ l₂ ~ l₂ ++ []",
"tactic": "simp"
}
] | [
145,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Rel.lean | Rel.image_mono | [] | [
143,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
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