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/CompleteLatticeIntervals.lean | subset_sInf_of_within | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Set α\ninst✝¹ : InfSet α\ninst✝ : Inhabited ↑s\nt : Set ↑s\nh : sInf (Subtype.val '' t) ∈ s\n⊢ sInf (Subtype.val '' t) = ↑(sInf t)",
"tactic": "simp [dif_pos h]"
}
] | [
91,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_subset_cthickening_of_le | [] | [
1124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_mul_right_iff | [] | [
1568,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
] |
Mathlib/RingTheory/PowerBasis.lean | linearIndependent_pow | [
{
"state_after": "case pos\nR : Type ?u.641649\nS : Type u_2\nT : Type ?u.641655\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring S\ninst✝⁶ : Algebra R S\nA : Type ?u.641958\nB : Type ?u.641961\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : IsDomain B\ninst✝² : Algebra A B\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : Algeb... | [
444,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | List.pairwise_sameCycle_formPerm | [] | [
97,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toDual_pow | [] | [
144,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.infinite_iff | [] | [
1138,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Data/Set/Function.lean | Function.Semiconj.surjOn_range | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.111695\nι : Sort ?u.111698\nπ : α → Type ?u.111703\nfa : α → α\nfb : β → β\nf : α → β\ng : β → γ\ns t : Set α\nh : Semiconj f fa fb\nha : Surjective fa\n⊢ SurjOn fb (f '' univ) (f '' univ)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.11... | [
1636,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1633,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_toSubalgebra | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.isMaximal_of_isIntegral_of_isMaximal_comap | [] | [
264,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/Semicontinuous.lean | continuousAt_iff_lower_upperSemicontinuousAt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\nβ : Type ?u.225648\ninst✝³ : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nγ : Type u_2\ninst✝² : LinearOrder γ\ninst✝¹ : TopologicalSpace γ\ninst✝ : OrderTopology γ\nf : α → γ\n⊢ ContinuousAt f x ↔ LowerSemico... | [
1107,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofDual_div | [] | [
139,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Calculus/ParametricIntegral.lean | hasDerivAt_integral_of_dominated_loc_of_lip | [
{
"state_after": "α : Type u_2\ninst✝⁷ : MeasurableSpace α\nμ : MeasureTheory.Measure α\n𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type ?u.793874\ninst✝¹ : NormedAddCommGroup H\ninst✝ : Norme... | [
225,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_add_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp a (p + b) = toIcoDiv hp a b + 1",
"tactic": "rw [add_comm, toIcoDiv_add_right]"
}
] | [
320,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/List/Cycle.lean | List.prev_cons_cons_of_ne' | [
{
"state_after": "case nil\nα : Type u_1\ninst✝ : DecidableEq α\nx y z : α\nhy : x ≠ y\nhz : x = z\nh : x ∈ [y, z]\n⊢ prev [y, z] x h = y\n\ncase cons\nα : Type u_1\ninst✝ : DecidableEq α\nx y z : α\nhy : x ≠ y\nhz : x = z\nhead✝ : α\ntail✝ : List α\nh : x ∈ y :: z :: head✝ :: tail✝\n⊢ prev (y :: z :: head✝ :: ... | [
233,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.coe_copy | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_segment | [
{
"state_after": "R : Type u_2\nE : Type u_3\nF : Type ?u.49319\nι : Type u_1\nι' : Type ?u.49325\nα : Type ?u.49328\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\ninst✝ : Orde... | [
105,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.Comonad.right_counit | [] | [
175,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Std/Data/List/Lemmas.lean | List.mem_erase_of_ne | [] | [
1085,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1084,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.CommSq.cone_fst | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\na : Cauchy abs\n⊢ (Real.neg { cauchy := a }).cauchy = -{ cauchy := a }.cauchy",
"tactic": "rw [neg_def]"
}
] | [
157,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | card_support_eq_three_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : Finset.card (support σ) = 3\n⊢ IsThreeCycle σ",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\n⊢ Finset.card (support σ) = 3 ↔ IsThreeCycle σ",
"tactic": "refine' ⟨fun h => _... | [
590,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vadd_mem_iff_mem_of_mem_direction | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\nv : V\nhv : v ∈ direction s\np : P\nh : v +ᵥ p ∈ s\n⊢ p ∈ s",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k... | [
290,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.integrable_normed | [] | [
519,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
11
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_and_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17871\nδ : Type ?u.17874\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\np : α → Prop\nu : List β\n⊢ Forall₂ (fun a b => p a ∧ R a b) [] u ↔ (∀ (a : α), a ∈ [] → p a) ∧ Forall₂ R [] u",
"tactic": "simp only [... | [
120,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | nhds_one_symm' | [] | [
640,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/FieldTheory/Normal.lean | IntermediateField.restrictScalars_normal | [] | [
280,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Finsupp/AList.lean | AList.lookupFinsupp_eq_zero_iff | [
{
"state_after": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x => M\na : α\n⊢ Option.getD (lookup a l) 0 = 0 ↔ lookup a l = none ∨ 0 ∈ lookup a l",
"state_before": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x => M\na : α\n⊢ ↑(l... | [
104,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Module/Basic.lean | map_rat_cast_smul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.208296\nR✝ : Type ?u.208299\nk : Type ?u.208302\nS✝ : Type ?u.208305\nM : Type u_1\nM₂ : Type u_2\nM₃ : Type ?u.208314\nι : Type ?u.208317\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M₂\nF : Type u_3\ninst✝⁴ : AddMonoidHomClass F M M₂\nf : F\nR :... | [
497,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.neg_one_mem_of_prod_eq_neg_one | [
{
"state_after": "case intro.intro\nι : Type ?u.8005\nα : Type ?u.8008\nM : Type ?u.8011\nN : Type ?u.8014\nP : Type ?u.8017\nM₀ : Type ?u.8020\nG : Type ?u.8023\nR : Type ?u.8026\nl : List ℤ\nh : prod l = -1\nx : ℤ\nh₁ : x ∈ l\nh₂ : x ≠ 1\n⊢ -1 ∈ l",
"state_before": "ι : Type ?u.8005\nα : Type ?u.8008\nM :... | [
73,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.25492\ninst✝² : OrderedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nK : SimplicialComplex 𝕜 E\ns t : Finset E\nx : E\nhs : s ∈ K.faces\nht : t ∈ K.faces\nh :\n ¬Disjoint (↑(convexHull 𝕜).toOrderHom ↑s) (↑(convexHull 𝕜).toOrderHom ↑t) ∧\n ... | [
118,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | exists_eq_mul_left_of_dvd | [] | [
153,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_inter_distrib_left | [] | [
1765,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1764,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_map_eq | [
{
"state_after": "case none\nι : Type ?u.345717\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f (a :: l)) = map g (a :: l)\n\ncase some\nι : Type ?u.345717\nα : Type u\nβ : ... | [
3336,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3330,
1
] |
Mathlib/Algebra/Associated.lean | Associated.of_pow_associated_of_prime | [
{
"state_after": "α : Type u_1\nβ : Type ?u.233071\nγ : Type ?u.233074\nδ : Type ?u.233077\ninst✝ : CancelCommMonoidWithZero α\np₁ p₂ : α\nk₁ k₂ : ℕ\nhp₁ : Prime p₁\nhp₂ : Prime p₂\nhk₁ : 0 < k₁\nh : p₁ ^ k₁ ~ᵤ p₂ ^ k₂\nthis : p₁ ∣ p₂ ^ k₂\n⊢ p₁ ~ᵤ p₂",
"state_before": "α : Type u_1\nβ : Type ?u.233071\nγ :... | [
676,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.support_scaleRoots_le | [
{
"state_after": "A : Type ?u.27089\nK : Type ?u.27092\nR : Type u_1\nS : Type ?u.27098\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\ns : R\na✝ : ℕ\n⊢ a✝ ∈ support (scaleRoots p s) → a✝ ∈ support p",
"state_before": "A : Type... | [
63,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.pow_nat_rpow_nat_inv | [
{
"state_after": "x✝ y z x : ℝ\nhx : 0 ≤ x\nn : ℕ\nhn : n ≠ 0\nhn0 : ↑n ≠ 0\n⊢ (x ^ n) ^ (↑n)⁻¹ = x",
"state_before": "x✝ y z x : ℝ\nhx : 0 ≤ x\nn : ℕ\nhn : n ≠ 0\n⊢ (x ^ n) ^ (↑n)⁻¹ = x",
"tactic": "have hn0 : (n : ℝ) ≠ 0 := Nat.cast_ne_zero.2 hn"
},
{
"state_after": "no goals",
"state_befo... | [
628,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Ioc | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.182740\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.182746\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.182841\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.182931\ninst✝¹ : NormedAddCommGroup ... | [
444,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_congr | [
{
"state_after": "case intro\nι : Type ?u.344295\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf✝ f g : α → Option α\na : α\nl : List α\nH : ∀ (a_1 : α), a_1 ∈ a :: l → f a_1 = g a_1\nH₁ : f a = g a\nH₂ : ∀ (x : α), x ∈ l → f x = g x\n⊢ lookmap f (a :: l) = lookmap g (a :: l)",
"state_bef... | [
3323,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3316,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | Multiplicative.toAdd_symm_eq | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Set/Prod.lean | Set.singleton_prod | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.8218\nδ : Type ?u.8221\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx : α\ny : β\n⊢ (x, y) ∈ {a} ×ˢ t ↔ (x, y) ∈ Prod.mk a '' t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.8218\nδ : Type ?u.8221\ns s₁ s₂ : Set α\nt t₁ t₂... | [
137,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEmbedding.comap_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1014989\nδ : Type ?u.1014992\nι : Type ?u.1014995\nR : Type ?u.1014998\nR' : Type ?u.1015001\nm0 : MeasurableSpace α\nm1 : MeasurableSpace β\nf : α → β\nhf : MeasurableEmbedding f\nμ : MeasureTheory.Measure β\ns : Set α\n⊢... | [
4205,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4199,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.characteristic_iff_map_eq | [
{
"state_after": "G : Type u_1\nG' : Type ?u.351493\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.351502\ninst✝ : AddGroup A\nH K : Subgroup G\n⊢ Characteristic H ↔ ∀ (ϕ : G ≃* G), comap (MulEquiv.toMonoidHom (MulEquiv.symm ϕ)) H = H",
"state_before": "G : Type u_1\nG' : Type ?u.351493\ninst✝² : Group G... | [
2024,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2022,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_append_dom | [] | [
807,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.open_target' | [] | [
567,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_le_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.72707\nγ : Type ?u.72710\nδ : Type ?u.72713\na b : α\ninst✝ : LE α\n⊢ ↑a ≤ ↑b ↔ a ≤ b",
"tactic": "simp only [← toDual_le_toDual_iff, toDual_apply_coe, WithBot.coe_le_coe, toDual_le_toDual]"
}
] | [
828,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | ULift.nnnorm_up | [] | [
2134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2133,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.symm_dual_id | [] | [
589,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_of_Ioo | [
{
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"state_before": "α✝ : ... | [
66,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_nonneg' | [] | [
180,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
9
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | MulOpposite.op_pow | [] | [
1256,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/Order/CompleteLattice.lean | biInf_const | [] | [
1229,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.ne_one_iff_exists_prime_dvd | [
{
"state_after": "no goals",
"state_before": "⊢ 0 ≠ 1 ↔ ∃ p, Prime p ∧ p ∣ 0",
"tactic": "simpa using Exists.intro 2 Nat.prime_two"
},
{
"state_after": "no goals",
"state_before": "⊢ 1 ≠ 1 ↔ ∃ p, Prime p ∧ p ∣ 1",
"tactic": "simp [Nat.not_prime_one]"
},
{
"state_after": "n : ℕ\na... | [
723,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.apply_symm_apply | [] | [
892,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.isClosed_iff | [
{
"state_after": "X : Compactum\nS : Set X.A\n⊢ IsOpen (Sᶜ) ↔ ∀ (F : Ultrafilter X.A), S ∈ F → str X F ∈ S",
"state_before": "X : Compactum\nS : Set X.A\n⊢ IsClosed S ↔ ∀ (F : Ultrafilter X.A), S ∈ F → str X F ∈ S",
"tactic": "rw [← isOpen_compl_iff]"
},
{
"state_after": "case mp\nX : Compactum\... | [
188,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Init/Data/Nat/Basic.lean | Nat.zero_lt_bit0 | [] | [
23,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
18,
11
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_eqOn_closure_of_isPreconnected_of_isMaxOn | [] | [
262,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Lattice.lean | sup_left_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ⊔ (a ⊔ b) = a ⊔ b",
"tactic": "simp"
}
] | [
266,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Ico_self | [
{
"state_after": "ι : Type ?u.23589\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Set.Ioo a b ⊆ Set.Ico a b",
"state_before": "ι : Type ?u.23589\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Ioo a b ⊆ Ico a b",
... | [
227,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\nf g : β → α\nu₁ u₂ : α\ns : Multiset β\n⊢ fold op (op u₁ u₂) (map (fun x => op (f x) (g x)) 0) = op (fold op u₁ (map f 0)) (fold op u₂ (map g 0))",
"tactic": "simp"... | [
103,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.formPerm_subsingleton | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\ns✝¹ s' s✝ : Cycle α\nh✝ : Subsingleton s✝\ns : List α\nh : Subsingleton (Quot.mk Setoid.r s)\n⊢ formPerm (Quot.mk Setoid.r s) (_ : Nodup (Quot.mk Setoid.r s)) = 1",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ s' s : Cycle α\nh : Sub... | [
160,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/Order.lean | le_nhdsAdjoint_iff | [
{
"state_after": "α✝ : Type u\nβ : Type v\nα : Type u_1\na : α\nf : Filter α\nt : TopologicalSpace α\n⊢ t ≤ nhdsAdjoint a f ↔ 𝓝 a ≤ pure a ⊔ f ∧ ∀ (b : α), b ≠ a → IsOpen {b}",
"state_before": "α✝ : Type u\nβ : Type v\nα : Type u_1\na : α\nf : Filter α\nt : TopologicalSpace α\n⊢ t ≤ nhdsAdjoint a f ↔ 𝓝 a ... | [
656,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_div_div_le_of_le | [] | [
1449,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Order/Concept.lean | intentClosure_iUnion₂ | [] | [
125,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasCountableBasis.isCountablyGenerated | [] | [
1013,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.continuousAt_proj | [] | [
517,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_inv_nat_nhds_zero | [] | [
560,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
11
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.gcd_cons | [] | [
143,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/RingTheory/Algebraic.lean | AlgEquiv.isAlgebraic | [
{
"state_after": "case h.e'_6\nR : Type u\nS : Type ?u.153899\nA : Type v\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : Ring A\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra R S\ninst✝³ : Algebra S A\ninst✝² : IsScalarTower R S A\nB : Type u_1\ninst✝¹ : Ring B\ninst✝ : Algebra R B\ne : A ≃ₐ[R] B\nh : Algebra.IsA... | [
158,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/ContinuousOn.lean | Set.Subsingleton.continuousOn | [] | [
678,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.bounds_bddBelow | [] | [
328,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_dvd | [] | [
1157,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.Isometry.map_app | [] | [
78,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_singleton | [
{
"state_after": "n : ℕ\nα : Type u_1\nv : Vector α 1\n⊢ toList (head v ::ᵥ tail v) = [head (head v ::ᵥ tail v)]",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α 1\n⊢ toList v = [head v]",
"tactic": "rw [← v.cons_head_tail]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Typ... | [
210,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.add_antiperiod_eq | [] | [
528,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.constr_basisSpanSingleton | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nR : Type u_3\nS : Type u_2\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommRing S\ninst✝⁴ : IsDomain S\ninst✝³ : Algebra R S\nN : Type u_1\ninst✝² : Semiring N\ninst✝¹ : Module N S\ninst✝ : SMulCommClass R N S\nb : Basis ι R S\nx : S\nhx : x ≠ 0\ni : ι\n⊢ ↑... | [
1958,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Filter.Tendsto.ennrpow_const | [] | [
539,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ciInf_empty | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nα : Sort u_1\ninst✝ : IsEmpty α\nf : α → ℝ\n⊢ (⨅ (i : α), f i) = 0",
"tactic": "rw [iInf_of_empty', sInf_empty]"
}
] | [
834,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.mem_ordConnectedComponent_ordConnectedProj | [] | [
119,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/LocallyFinite.lean | Iio_ofDual | [] | [
948,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.strictMono_iff_lt_succ | [] | [
1885,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | List.nnnorm_prod_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.115517\nγ : Type ?u.115520\nι : Type ?u.115523\ninst✝¹ : SeminormedRing α\ninst✝ : NormOneClass α\nl : List α\n⊢ prod (map norm l) = (fun a => ↑a) (prod (map nnnorm l))",
"tactic": "simp [NNReal.coe_list_prod, List.map_map]"
}
] | [
333,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/GroupTheory/EckmannHilton.lean | EckmannHilton.one | [
{
"state_after": "no goals",
"state_before": "X : Type u\nm₁ m₂ : X → X → X\ne₁ e₂ : X\nh₁ : IsUnital m₁ e₁\nh₂ : IsUnital m₂ e₂\ndistrib : ∀ (a b c d : X), m₁ (m₂ a b) (m₂ c d) = m₂ (m₁ a c) (m₁ b d)\n⊢ e₁ = e₂",
"tactic": "simpa only [h₁.left_id, h₁.right_id, h₂.left_id, h₂.right_id] using distrib e₂ ... | [
61,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_iSup_comap_of_sujective | [] | [
916,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u\na : α\nn k : ℕ\n⊢ length (rotate (replicate n a) k) = n",
"tactic": "rw [length_rotate, length_replicate]"
}
] | [
139,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.nonneg_normed | [] | [
493,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_eq_multiplicity_iff | [] | [
254,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Std/Logic.lean | Decidable.not_not | [] | [
500,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
500,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_eq_left_iff_subset | [] | [
968,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.snd | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.30683\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nx : E × F\n⊢ ‖↑(Linear... | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_dite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.108111\nβ₂ : Type ?u.108114\nγ : Type ?u.108117\nι : Sort u_2\nι' : Sort ?u.108123\nκ : ι → Sort ?u.108128\nκ' : ι' → Sort ?u.108133\ninst✝¹ : CompleteLattice α\nf✝ g✝ s t : ι → α\na b : α\np : ι → Prop\ninst✝ : DecidablePred p\nf : (i : ι) → p i → α\ng : (i : ι) → ¬p... | [
1363,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_conjTranspose | [
{
"state_after": "l : Type ?u.71609\nm : Type ?u.71612\nn : Type u_1\no : Type ?u.71618\nm' : o → Type ?u.71623\nn' : o → Type ?u.71628\nR : Type ?u.71631\nS : Type ?u.71634\nα : Type v\nβ : Type w\nγ : Type ?u.71641\ninst✝² : DecidableEq n\ninst✝¹ : AddMonoid α\ninst✝ : StarAddMonoid α\nv : n → α\n⊢ (diagonal ... | [
520,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.HasAntitoneBasis.comp_mono | [] | [
1780,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1774,
1
] |
Mathlib/Order/Bounds/Basic.lean | bddAbove_Ioo | [] | [
680,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.Iio_eq_biUnion | [] | [
802,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coeFn_add | [] | [
236,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | TensorProduct.LieModule.mapIncl_def | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrable.integrableOn_nhds_isCompact | [
{
"state_after": "case refine'_1\nX : Type u_1\nY : Type ?u.125788\nE : Type u_2\nR : Type ?u.125794\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : MeasurableSpace Y\ninst✝¹ : TopologicalSpace Y\ninst✝ : NormedAddCommGroup E\nf : X → E\nμ : Measure X\ns : Set X\nhf : LocallyIntegrable f\nk :... | [
190,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.diff_ae_eq_right | [] | [
130,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousWithinAt_const | [] | [
180,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
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