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/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.differentiableWithinAt | [] | [
546,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryFinFinset_apply | [] | [
1543,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | IsSelfAdjoint.adjoint_conj | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.1357503\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : InnerProductSpace 𝕜 G\ninst✝¹ : CompleteS... | [
305,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_ofFn | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.2004\nβ : Type u_1\ninst✝ : CommMonoid β\nn : ℕ\nf : Fin n → β\n⊢ List.prod (List.ofFn f) = ∏ i : Fin n, f i",
"tactic": "rw [List.ofFn_eq_map, prod_univ_def]"
}
] | [
57,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Std/Data/List/Lemmas.lean | List.filter_eq_self | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\np : α✝ → Bool\nl : List α✝\n⊢ filter p l = l ↔ ∀ (a : α✝), a ∈ l → p a = true",
"tactic": "induction l with simp\n| cons a l ih =>\n cases h : p a <;> simp [*]\n intro h; exact Nat.lt_irrefl _ (h ▸ length_filter_le p l)"
},
{
"state_... | [
1246,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1242,
1
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Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousOn_tsum | [] | [
653,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curryFinFinset_apply_const | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
1897,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1892,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioc_union_Ioc | [] | [
1591,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1590,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_dropUntil_subset | [] | [
1164,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | le_add_tsub | [] | [
100,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.inv_apply_eq_inv' | [] | [
345,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Control/Fold.lean | Traversable.foldlm_toList | [
{
"state_after": "no goals",
"state_before": "α β γ : Type u\nt : Type u → Type u\ninst✝³ : Traversable t\ninst✝² : IsLawfulTraversable t\nm : Type u → Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → β → m α\nx : α\nxs : t β\n⊢ foldlm f x xs = unop (↑(foldlM.ofFreeMonoid f) (↑FreeMonoid.ofList (toL... | [
413,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
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Mathlib/Data/Set/Lattice.lean | Set.bijOn_iUnion_of_directed | [] | [
1637,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
1
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Mathlib/Topology/Order/Basic.lean | dense_of_exists_between | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : Nontrivial α\ns : Set α\nh : ∀ ⦃a b : α⦄, a < b → ∃ c, c ∈ s ∧ a < c ∧ c < b\nU : Set α\nU_open : IsOpen U\nU_nonempty : Set.Nonempty U\n⊢ Set.Nonempty (U ∩ s)",
"stat... | [
1297,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
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Mathlib/Data/Rat/Floor.lean | Rat.le_floor | [
{
"state_after": "α : Type ?u.897\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nz n : ℤ\nd : ℕ\nh : d ≠ 0\nc : Nat.coprime (natAbs n) d\n⊢ z ≤ n / ↑d ↔ ↑z ≤ mk' n d",
"state_before": "α : Type ?u.897\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nz n : ℤ\nd : ℕ\nh : d ≠ 0\nc : Nat.coprime (natA... | [
50,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
11
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Mathlib/Topology/Algebra/Star.lean | ContinuousOn.star | [] | [
70,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.monotone_spanningSets | [] | [
3468,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3467,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_prod_mk' | [
{
"state_after": "no goals",
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238,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | TFAE_exists_lt_isLittleO_pow | [
{
"state_after": "α : Type ?u.73187\nβ : Type ?u.73190\nι : Type ?u.73193\nf : ℕ → ℝ\nR : ℝ\nA : Set.Ico 0 R ⊆ Set.Ioo (-R) R\n⊢ TFAE\n [∃ a, a ∈ Set.Ioo (-R) R ∧ f =o[atTop] fun x => a ^ x, ∃ a, a ∈ Set.Ioo 0 R ∧ f =o[atTop] fun x => a ^ x,\n ∃ a, a ∈ Set.Ioo (-R) R ∧ f =O[atTop] fun x => a ^ x, ∃ a, a... | [
187,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.isUnit_iff | [
{
"state_after": "a b : Cardinal\nn m : ℕ\nh : IsUnit a\n⊢ a = 1",
"state_before": "a b : Cardinal\nn m : ℕ\n⊢ IsUnit a ↔ a = 1",
"tactic": "refine'\n ⟨fun h => _, by\n rintro rfl\n exact isUnit_one⟩"
},
{
"state_after": "case inl\nb : Cardinal\nn m : ℕ\nh : IsUnit 0\n⊢ 0 = 1\n\ncase inr\... | [
61,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.mul_le_edist | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4707\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nhf : AntilipschitzWith K f\nx y : α\n⊢ edist x y / ↑K ≤ edist (f x) (f y)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u... | [
115,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_zpow | [] | [
783,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.smul_mem | [] | [
121,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.mulIsPoly₂ | [
{
"state_after": "p : ℕ\nR S : Type u\nσ : Type ?u.696391\nidx : Type ?u.696394\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : Fact (Nat.Prime p)\nR✝ : Type u_1\ninst✝ : CommRing R✝\nx✝ y✝ : 𝕎 R✝\n⊢ (x✝ * y✝).coeff = fun n => peval (wittMul p n) ![x✝.coeff, y✝.coeff]",
"state_before": "p : ℕ\nR S : Ty... | [
550,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.center_le_centralizer | [] | [
1407,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_principal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.289553\nE : Type u_2\nF : Type u_3\nG : Type ?u.289562\nE' : Type ?u.289565\nF' : Type ?u.289568\nG' : Type ?u.289571\nE'' : Type ?u.289574\nF'' : Type ?u.289577\nG'' : Type ?u.289580\nR : Type ?u.289583\nR' : Type ?u.289586\n𝕜 : Type ?u.289589\n𝕜' : Type ?u.289592\... | [
1296,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.fderivWithin_apply | [] | [
1028,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Logic/Basic.lean | BEx.imp_left | [] | [
1059,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_mul | [] | [
1089,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | div_ne_zero_iff | [] | [
294,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.hasFiniteColimits_of_hasInitial_and_pushouts | [] | [
474,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na b : α\n⊢ destutter R [] = [] ↔ Chain' R []",
"tactic": "simp"
}
] | [
166,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.modEq_of_xn_modEq | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nipos : 0 < i\nhin : i ≤ n\nh : xn a1 j ≡ xn a1 i [MOD xn a1 n]\nj' : ℕ := j % (4 * n)\n⊢ 0 < 4",
"tactic": "decide"
},
{
"state_after": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nipos : 0 < i\nhin : i ≤ n\nh : xn a1 j ≡ xn a1 i [MOD... | [
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33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.464932\n𝕝 : Type ?u.464935\n𝕝₂ : Type ?u.464938\nE : Type u_1\nF : Type ?u.464944\nG : Type ?u.464947\nι : Type u_3\nι' : Type ?u.464953\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\np : SeminormFamily �... | [
542,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.congr_arg | [] | [
159,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.res_const' | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_zero | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\n⊢ n /. ↑d + 0 = n /. ↑d",
"tactic": "rw [← zero_divInt d, add_def'', zero_mul, add_zero, divInt_mul_right] <;> simp [h]"
}
] | [
203,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
] |
Mathlib/Control/Fold.lean | Traversable.foldl.unop_ofFreeMonoid | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.lift.range_le | [
{
"state_after": "case intro.mk\nα : Type u\nL✝ L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\ninst✝ : Group β\nf : α → β\nx y : FreeGroup α\ns : Subgroup β\nH : Set.range f ⊆ ↑s\nw✝ : FreeGroup α\nL : List (α × Bool)\n⊢ ↑(↑lift f) (Quot.mk Red.Step L) ∈ s",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α ... | [
769,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.sInter_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nf g : Filter α\ns✝ t : Set α\ns : Set (Set α)\nhfin : Set.Finite s\n⊢ ⋂₀ s ∈ f ↔ ∀ (U : Set α), U ∈ s → U ∈ f",
"tactic": "rw [sInter_eq_biInter, biInter_mem hfin]"
}
] | [
203,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.codRestrict_apply | [] | [
932,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/Topology/Order/Lattice.lean | Filter.Tendsto.inf_right_nhds' | [] | [
124,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_insert_left | [
{
"state_after": "α : Type u_1\nα' : Type ?u.36962\nβ : Type u_3\nβ' : Type ?u.36968\nγ : Type u_2\nγ' : Type ?u.36974\nδ : Type ?u.36977\nδ' : Type ?u.36980\nε : Type ?u.36983\nε' : Type ?u.36986\nζ : Type ?u.36989\nζ' : Type ?u.36992\nν : Type ?u.36995\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
187,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/List/Basic.lean | List.dropWhile_eq_nil_iff | [
{
"state_after": "case nil\nι : Type ?u.387507\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\n⊢ dropWhile p [] = [] ↔ ∀ (x : α), x ∈ [] → p x = true\n\ncase cons\nι : Type ?u.387507\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : Lis... | [
3632,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3629,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.preimage_embedding | [] | [
896,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt.eq_zero_of_not_dvd | [
{
"state_after": "p : ℕ\nz : ℤ\nh : ¬↑p ∣ z\n⊢ (if h : p ≠ 1 ∧ 0 < Int.natAbs z then\n Part.get (multiplicity p (Int.natAbs z)) (_ : multiplicity.Finite p (Int.natAbs z))\n else 0) =\n 0",
"state_before": "p : ℕ\nz : ℤ\nh : ¬↑p ∣ z\n⊢ padicValInt p z = 0",
"tactic": "rw [padicValInt, padicVal... | [
143,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.coe_decompose_mul_of_left_mem | [
{
"state_after": "case intro\nι : Type u_1\nR : Type ?u.376414\nA : Type u_2\nσ : Type u_3\ninst✝⁹ : Semiring A\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : CanonicallyOrderedAddMonoid ι\ninst✝⁶ : SetLike σ A\ninst✝⁵ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝⁴ : GradedRing 𝒜\nb : A\nn✝ i : ι\ninst✝³ : Sub ι\ninst✝² : Ord... | [
330,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
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Mathlib/FieldTheory/Normal.lean | AlgHom.normal_bijective | [
{
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... | [
131,
19
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115,
1
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Mathlib/Data/Nat/Interval.lean | Nat.Ico_succ_right | [
{
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{
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167,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/Data/Set/Ncard.lean | Set.nonempty_of_ncard_ne_zero | [
{
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{
"state_after":... | [
129,
53
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128,
1
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Mathlib/Data/Nat/PartENat.lean | PartENat.lt_find_iff | [
{
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{
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809,
28
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801,
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Mathlib/RingTheory/WittVector/StructurePolynomial.lean | bind₁_rename_expand_wittPolynomial | [
{
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229,
22
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212,
1
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Mathlib/LinearAlgebra/Dual.lean | Module.eval_ker | [
{
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{
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545,
53
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544,
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Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_of_mem_sphere | [] | [
63,
36
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62,
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Mathlib/Algebra/BigOperators/Associated.lean | Prime.dvd_finset_prod_iff | [] | [
183,
89
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181,
1
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Mathlib/Topology/Constructions.lean | tendsto_pi_nhds | [
{
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1223,
34
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1221,
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Mathlib/LinearAlgebra/AffineSpace/MidpointZero.lean | pi_midpoint_apply | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_last' | [
{
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] | [
750,
81
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749,
1
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Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.copy_eq | [] | [
111,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Relations.realize_irreflexive | [] | [
1005,
48
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1004,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.div_mem | [] | [
590,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
11
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.algebraMap_mk' | [
{
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1341,
78
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1333,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lcongr_apply_apply | [] | [
907,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
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Mathlib/Data/ENat/Basic.lean | ENat.toNat_top | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.mono | [] | [
466,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_filterMap | [] | [
2144,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2142,
1
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Mathlib/Topology/Order/Basic.lean | Ico_mem_nhdsWithin_Ioi' | [] | [
422,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
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Mathlib/Analysis/Convex/Function.lean | convexOn_iff_pairwise_pos | [
{
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348,
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337,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.divByMonic_eq_of_not_monic | [] | [
207,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Order/SymmDiff.lean | toDual_bihimp | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.apriori_dist_iterate_fixedPoint_le | [] | [
337,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_id | [] | [
777,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.image_smul | [] | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.eq_bot_of_ge | [] | [
99,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.VectorsProdEqOne.zero_eq | [] | [
384,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
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Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.subsumes_left | [] | [
91,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.mem_closure_iff_symm_ball | [
{
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"tactic": "simp [mem_closure_iff_nhds_basis (has... | [
770,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.continuous_pow | [
{
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"tactic": "rw [coe_pow]"
},
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nhf : Continuous... | [
953,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
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Mathlib/Topology/Bases.lean | Set.Countable.isSeparable | [] | [
413,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.inf_neBot_iff | [] | [
114,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | RingEquiv.restrictRootsOfUnity_coe_apply | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_pos | [] | [
71,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.ediam_preimage_le | [] | [
120,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Std/Logic.lean | and_and_and_comm | [
{
"state_after": "no goals",
"state_before": "a b c d : Prop\n⊢ (a ∧ b) ∧ c ∧ d ↔ (a ∧ c) ∧ b ∧ d",
"tactic": "rw [← and_assoc, @and_right_comm a, and_assoc]"
}
] | [
190,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
189,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.IsPredLimit.isMax_of_noMin | [] | [
320,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
11
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.degree_le_zero_iff_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhp : Monic p\n⊢ degree p ≤ 0 ↔ p = 1",
"tactic": "rw [← hp.natDegree_eq_zero_iff_eq_one, natDegree_eq_zero_iff_degree_le_zero]"
}
] | [
169,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.mem_span | [
{
"state_after": "ι : Type u_3\nι' : Type ?u.461943\nR : Type u_2\nR₂ : Type ?u.461949\nK : Type ?u.461952\nM : Type u_1\nM' : Type ?u.461958\nM'' : Type ?u.461961\nV : Type u\nV' : Type ?u.461966\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'... | [
571,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
11
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Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasTerminalChangeDiagram | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX : C\nF₁ : Discrete PEmpty ⥤ C\nF₂ : Discrete PEmpty ⥤ C\nh : HasLimit F₁\n⊢ (X : Discrete PEmpty) → ((Functor.const (Discrete PEmpty)).obj (limit F₁)).obj X ⟶ F₂.obj X",
"tactic": "aesop_cat"
},
{
"state_after": "no... | [
252,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | exists_pos_lt_mul | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.112188\nα : Type u_1\nβ : Type ?u.112194\ninst✝ : LinearOrderedSemifield α\na✝ b✝ c✝ d e : α\nm n : ℤ\na : α\nh : 0 < a\nb c : α\nhc₀ : 0 < c\nhc : b * c < a\n⊢ b < c⁻¹ * a",
"tactic": "rwa [← div_eq_inv_mul, lt_div_iff hc₀]"
}
] | [
576,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.cofork_ι_app_one | [] | [
956,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) ⁻¹' Ico b c = Ico (b + a) (c + a)",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
202,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.nat_le_card | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.236438\nβ : Type ?u.236441\nγ : Type ?u.236444\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nn : ℕ\n⊢ ↑n ≤ card o ↔ ↑n ≤ o",
"tactic": "rw [← Cardinal.ord_le, Cardinal.ord_nat]"
}
] | [
1561,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.is_mul_left_invariant_outerMeasure | [
{
"state_after": "no goals",
"state_before": "G : Type w\ninst✝³ : TopologicalSpace G\nμ : Content G\ninst✝² : T2Space G\ninst✝¹ : Group G\ninst✝ : TopologicalGroup G\nh :\n ∀ (g : G) {K : Compacts G},\n (fun s => ↑(toFun μ s)) (Compacts.map (fun b => g * b) (_ : Continuous fun b => g * b) K) =\n (... | [
325,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Set/Image.lean | Set.rangeFactorization_eq | [] | [
1049,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.vecMul_sub | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.913128\nm : Type u_1\nn : Type u_2\no : Type ?u.913137\nm' : o → Type ?u.913142\nn' : o → Type ?u.913147\nR : Type ?u.913150\nS : Type ?u.913153\nα : Type v\nβ : Type w\nγ : Type ?u.913160\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype m\nA B : M... | [
1921,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.29976\ninst✝¹ : Monoid R\ninst✝ : StarSemigroup R\nx : R\nhx : IsSelfAdjoint x\nn : ℕ\n⊢ IsSelfAdjoint (x ^ n)",
"tactic": "simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]"
}
] | [
186,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.id_comp | [] | [
191,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.le_def | [] | [
340,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_singleton_mul_right_inj | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.240143\ninst✝¹ : CommSemiring R\nI J K L : Ideal R\ninst✝ : IsDomain R\nx : R\nhx : x ≠ 0\n⊢ span {x} * I = span {x} * J ↔ I = J",
"tactic": "simp only [le_antisymm_iff, span_singleton_mul_right_mono hx]"
}
] | [
581,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Analysis/Filter.lean | CFilter.coe_mk | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
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