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/Topology/Basic.lean | interior_eq_empty_iff_dense_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ interior s = ∅ ↔ Dense (sᶜ)",
"tactic": "rw [dense_iff_closure_eq, closure_compl, compl_univ_iff]"
}
] | [
612,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_closure_singleton | [
{
"state_after": "M : Type u_1\nA : Type ?u.55052\nB : Type ?u.55055\ninst✝ : Monoid M\nx y : M\n⊢ (∃ x_1, ↑(↑(powersHom M) x) x_1 = y) ↔ ∃ n, x ^ n = y",
"state_before": "M : Type u_1\nA : Type ?u.55052\nB : Type ?u.55055\ninst✝ : Monoid M\nx y : M\n⊢ y ∈ closure {x} ↔ ∃ n, x ^ n = y",
"tactic": "rw [c... | [
337,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_singleton | [
{
"state_after": "Ω : Type u_1\ninst✝² : MeasurableSpace Ω\ninst✝¹ : MeasurableSingletonClass Ω\nω : Ω\nt : Set Ω\ninst✝ : Decidable (ω ∈ t)\n⊢ ↑↑Measure.count ({ω} ∩ t) = if ω ∈ t then 1 else 0",
"state_before": "Ω : Type u_1\ninst✝² : MeasurableSpace Ω\ninst✝¹ : MeasurableSingletonClass Ω\nω : Ω\nt : Set ... | [
97,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.nat_lt_continuum | [] | [
91,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_int | [] | [
1592,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1591,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.abs_le_sqrt | [
{
"state_after": "x y : ℝ\nh : x ^ 2 ≤ y\n⊢ sqrt (x ^ 2) ≤ sqrt y",
"state_before": "x y : ℝ\nh : x ^ 2 ≤ y\n⊢ abs x ≤ sqrt y",
"tactic": "rw [← sqrt_sq_eq_abs]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : x ^ 2 ≤ y\n⊢ sqrt (x ^ 2) ≤ sqrt y",
"tactic": "exact sqrt_le_sq... | [
313,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_subset_right | [] | [
1365,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1364,
1
] |
Mathlib/Data/List/AList.lean | AList.insert_insert_of_ne | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na a' : α\nb : β a\nb' : β a'\ns : AList β\nh : a ≠ a'\n⊢ { fst := a', snd := b' } :: kerase a' ({ fst := a, snd := b } :: kerase a s.entries) ~\n { fst := a, snd := b } :: kerase a ({ fst := a', snd := b' } :: kerase a' s.entries)",
"st... | [
328,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.c_sub_pf | [] | [
41,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_mul_nat | [
{
"state_after": "case zero\nF : Type ?u.175899\nα : Type u_1\nβ : Type ?u.175905\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ ∃ z, fract a * ↑Nat.zero - fract (a * ↑Nat.zero) = ↑z\n\ncase succ\nF : Type ?u.175899\nα : Type u_1\nβ : Type ?u.175905\ninst✝¹ : LinearOrderedRing α\ninst✝ :... | [
987,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re | [
{
"state_after": "no goals",
"state_before": "l : Filter ℂ\nhl : IsExpCmpFilter l\nn : ℕ\n⊢ (fun z => Abs.abs z.im ^ ↑n) ≤ᶠ[l] fun z => Real.exp z.re",
"tactic": "simpa using (hl.isLittleO_im_pow_exp_re n).bound zero_lt_one"
}
] | [
131,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries.map | [
{
"state_after": "case zero\nG : Type u_2\ninst✝² : Group G\nH✝ : Subgroup G\ninst✝¹ : Normal H✝\nH : Type u_1\ninst✝ : Group H\nf : G →* H\n⊢ Subgroup.map f (lowerCentralSeries G Nat.zero) ≤ lowerCentralSeries H Nat.zero\n\ncase succ\nG : Type u_2\ninst✝² : Group G\nH✝ : Subgroup G\ninst✝¹ : Normal H✝\nH : Typ... | [
506,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.pow_map_zero_of_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.143571\nR₂ : Type ?u.143574\nR₃ : Type ?u.143577\nR₄ : Type ?u.143580\nS : Type ?u.143583\nK : Type ?u.143586\nK₂ : Type ?u.143589\nM : Type u_2\nM' : Type ?u.143595\nM₁ : Type ?u.143598\nM₂ : Type ?u.143601\nM₃ : Type ?u.143604\nM₄ : ... | [
336,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTrivAt_baseSet | [
{
"state_after": "ι : Type u_3\nB : Type u_1\nF : Type u_2\nX : Type ?u.48839\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nZ : FiberBundleCore ι B F\ni : ι\nb✝ : B\na : F\nb : B\n⊢ b ∈ baseSet Z (indexAt Z b)",
"state_before": "ι : Type u_3\nB : Type u_1\nF : Type u... | [
740,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.WeaklyRegular.restrict_of_measurableSet | [
{
"state_after": "α : Type u_1\nβ : Type ?u.77698\ninst✝³ : MeasurableSpace α\ninst✝² : TopologicalSpace α\nμ : Measure α\ninst✝¹ : BorelSpace α\ninst✝ : WeaklyRegular μ\nA : Set α\nhA : MeasurableSet A\nh'A : ↑↑μ A ≠ ⊤\nthis : Fact (↑↑μ A < ⊤)\n⊢ WeaklyRegular (restrict μ A)",
"state_before": "α : Type u_1... | [
626,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_lt_inv | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.51782\nα : Type u_1\nβ : Type ?u.51788\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh₁ : 0 < a\nh₂ : a < 1\n⊢ 1 < a⁻¹",
"tactic": "rwa [lt_inv (@zero_lt_one α _ _ _ _ _) h₁, inv_one]"
}
] | [
304,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.infsep_pos_iff_nontrivial | [] | [
560,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_norm_le_of_liminf_right_slope_norm_lt_deriv_boundary | [] | [
259,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.generate_iUnion | [] | [
549,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_neg | [
{
"state_after": "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⊢ -b - -(toIocDiv hp (-a) b • p + 1 • p) = p - (b - toIocDiv hp (-a) b • p)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α... | [
550,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.eq_gt | [] | [
104,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.subNat_addNat | [] | [
1603,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1601,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coeSubtype | [] | [
436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Data/Set/Enumerate.lean | Set.enumerate_eq_none | [
{
"state_after": "case none\nα : Type u_1\nsel : Set α → Option α\ns : Set α\nn m : ℕ\nh : enumerate sel s (n + 1) = none\nhm : n + 1 ≤ m\nhs : sel s = none\n⊢ enumerate sel s m = none\n\ncase some\nα : Type u_1\nsel : Set α → Option α\ns : Set α\nn m : ℕ\nh : enumerate sel s (n + 1) = none\nhm : n + 1 ≤ m\nval... | [
60,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.balanced_closedBall_zero | [
{
"state_after": "case intro.intro\nR : Type ?u.1062708\nR' : Type ?u.1062711\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1062717\n𝕜₃ : Type ?u.1062720\n𝕝 : Type ?u.1062723\nE : Type u_2\nE₂ : Type ?u.1062729\nE₃ : Type ?u.1062732\nF : Type ?u.1062735\nG : Type ?u.1062738\nι : Type ?u.1062741\ninst✝⁶ : SeminormedRing 𝕜\ni... | [
853,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_erase_of_ne_of_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.207977\nγ : Type ?u.207980\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\n⊢ a ≠ b → a ∈ s → a ≠ b ∧ a ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.207977\nγ : Type ?u.207980\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\n⊢ a ≠ b → a ∈ s → a ∈ erase... | [
1887,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1886,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dvd_prod_of_subset | [
{
"state_after": "no goals",
"state_before": "ι✝ : Type ?u.809418\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\nι : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\ns t : Finset ι\nf : ι → M\nh : s ⊆ t\n⊢ s.val ≤ t.val",
"tactic": "simpa"
}
] | [
1738,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.disjoint_product | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.77766\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\n⊢ _root_.Disjoint (s ×ˢ t) (s' ×ˢ t') ↔ _root_.Disjoint s s' ∨ _root_.Disjoint t t'",
"tactic": "simp_rw [← disjoint_coe, coe_product, Set.disjoint_prod]"
}
] | [
263,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.tendsto_nhdsWithin_Iio | [
{
"state_after": "case inl\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\ninst✝¹² : ConditionallyCompleteLinearOrder α✝\ninst✝¹¹ : TopologicalSpace α✝\ninst✝¹⁰ : OrderTopology α✝\ninst✝⁹ : ConditionallyCompleteLinearOrder β✝\ninst✝⁸ : TopologicalSpace β✝\ninst✝⁷ : OrderClosedTopology β✝\ninst✝⁶ : Nonempty γ\nα : Type u... | [
2866,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2856,
1
] |
Mathlib/NumberTheory/Fermat4.lean | Fermat42.comm | [
{
"state_after": "a b c : ℤ\n⊢ a ≠ 0 ∧ b ≠ 0 ∧ a ^ 4 + b ^ 4 = c ^ 2 ↔ b ≠ 0 ∧ a ≠ 0 ∧ b ^ 4 + a ^ 4 = c ^ 2",
"state_before": "a b c : ℤ\n⊢ Fermat42 a b c ↔ Fermat42 b a c",
"tactic": "delta Fermat42"
},
{
"state_after": "a b c : ℤ\n⊢ a ≠ 0 ∧ b ≠ 0 ∧ b ^ 4 + a ^ 4 = c ^ 2 ↔ b ≠ 0 ∧ a ≠ 0 ∧ b ^ ... | [
37,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.div_im | [
{
"state_after": "no goals",
"state_before": "z w : ℂ\n⊢ (z / w).im = z.im * w.re / ↑normSq w - z.re * w.im / ↑normSq w",
"tactic": "simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]"
}
] | [
787,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Sheaf.eq_of_locally_eq₂ | [
{
"state_after": "case iUV\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : ConcreteCategory C\ninst✝² : HasLimits C\ninst✝¹ : ReflectsIsomorphisms ConcreteCategory.forget\ninst✝ : PreservesLimits ConcreteCategory.forget\nX : TopCat\nF : Sheaf C X\nι : Type v\nU : ι → Opens ↑X\nU₁ U₂ V : Opens ↑X\ni₁ : U₁ ⟶ V\ni₂ : U... | [
322,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_mul | [] | [
1380,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1379,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castLE_mk | [] | [
1024,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Data/List/Infix.lean | List.tails_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.41504\nl l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\n⊢ tails ([] ++ []) = map (fun l => l ++ []) (tails []) ++ tail (tails [])",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.41504\... | [
391,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.card_powersetLen | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : ℕ\ns : Multiset α\n⊢ ∀ (a : List α), ↑card (powersetLen n (Quotient.mk (isSetoid α) a)) = Nat.choose (↑card (Quotient.mk (isSetoid α) a)) n",
"tactic": "simp [powersetLen_coe]"
}
] | [
268,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsSeparator.def | [] | [
467,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.coe_pos | [] | [
69,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.hσ'_eq | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.65766\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq n a m : ℕ\nha : n = a + q\nhnm : ComplexShape.Rel c m n\n⊢ X.obj [n + 1].op = HomologicalComplex.X K[X] m",
"tactic": "congr"
},
{
"state_after": "C : Type u_2\n... | [
124,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
src/lean/Init/Data/Array/Mem.lean | List.sizeOf_get_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : SizeOf α\nas : List α\ni : Fin (length as)\n⊢ sizeOf (get as i) < sizeOf as",
"tactic": "match as, i with\n| [], i => apply Fin.elim0 i\n| a::as, ⟨0, _⟩ => simp_arith [get]\n| a::as, ⟨i+1, h⟩ =>\n simp [get]\n have h : i < as.... | [
19,
53
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
11,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_single | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.143364\nι : Type ?u.143367\nM : Type u_3\nM' : Type ?u.143373\nN : Type ?u.143376\nP : Type ?u.143379\nG : Type ?u.143382\nH : Type ?u.143385\nR : Type ?u.143388\nS : Type ?u.143391\ninst✝ : Zero M\nf : α ≃ β\na : α\nb : M... | [
349,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_or | [] | [
1351,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
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Mathlib/Algebra/Ring/Commute.lean | Commute.neg_one_right | [] | [
121,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Topology/Separation.lean | minimal_nonempty_closed_subsingleton | [
{
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264,
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255,
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_of_nonpos_left | [
{
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] | [
352,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
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Mathlib/Data/Set/Constructions.lean | FiniteInter.finiteInter_mem | [
{
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65,
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_commute | [
{
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{
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103,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_mem | [] | [
182,
26
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180,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_iff_tendsto' | [] | [
1834,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1830,
1
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inr_isoPushout_inv | [
{
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430,
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427,
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Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.π_obj | [] | [
73,
15
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72,
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Mathlib/Data/Rel.lean | Rel.core_inter | [
{
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] | [
227,
52
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226,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_id | [] | [
386,
6
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385,
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Mathlib/Data/Set/Intervals/Monotone.lean | StrictMonoOn.Ici_le_id | [] | [
226,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Topology/TietzeExtension.lean | BoundedContinuousFunction.tietze_extension_step | [
{
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99,
41
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Mathlib/Order/FixedPoints.lean | OrderHom.prevFixed_le | [] | [
215,
23
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214,
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Mathlib/Data/List/TFAE.lean | List.tfae_of_forall | [] | [
56,
52
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55,
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Std/Data/Int/Lemmas.lean | Int.negSucc_add_negSucc | [] | [
54,
94
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54,
9
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Mathlib/Data/List/Basic.lean | List.foldl1_eq_foldr1 | [
{
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2702,
89
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2699,
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Mathlib/Algebra/BigOperators/Basic.lean | Nat.cast_list_prod | [] | [
2195,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2194,
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Mathlib/Topology/Constructions.lean | continuous_ofMul | [] | [
94,
80
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94,
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Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.smul_eq_mulAut_conj | [] | [
301,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
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Mathlib/Analysis/Calculus/Deriv/Inv.lean | HasStrictDerivAt.div | [
{
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201,
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196,
1
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.continuousOn_symm | [] | [
248,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
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Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.hasFDerivWithinAt | [] | [
74,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
11
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Mathlib/Order/JordanHolder.lean | CompositionSeries.Equivalent.length_eq | [
{
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}
] | [
680,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
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Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.of_correctness_atTop_of_terminates | [
{
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278,
55
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270,
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Mathlib/RingTheory/Ideal/Prod.lean | Ideal.idealProdEquiv_symm_apply | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Algebra/Module/Basic.lean | Nat.smul_one_eq_coe | [
{
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... | [
761,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.floor_coe | [
{
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171,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_natDegree_succ_eq_zero | [] | [
375,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Int/Basic.lean | Int.pred_succ | [] | [
152,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_mk | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.compl_sup | [] | [
655,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
11
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.eq_of_le | [] | [
341,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.ext | [] | [
126,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.Ioi_iff_Ioo | [] | [
348,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.map_pure | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteCoproducts.tensorHom | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | CircleIntegrable.add | [] | [
251,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
8
] |
Mathlib/Data/Finset/Basic.lean | Finset.eq_singleton_or_nontrivial | [
{
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"tactic": "rw [← coe_eq_single... | [
807,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.nonempty_of_measure_ne_zero | [] | [
192,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.sup | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.954430\nγ : Type ?u.954433\nδ : Type ?u.954436\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝³ : MeasurableSpace δ\ninst✝² : NormedAddCommGroup β✝\ninst✝¹ : NormedAddCommGroup γ\nβ : Type u_1\ninst✝ : NormedLatticeAddCommGroup β\nf g : α → β\nhf : Memℒp f 1\nhg : Mem... | [
705,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.185633\ninst✝... | [
217,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.not_mem_bot | [] | [
822,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.prod_top | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.50616\nσ : Type ?u.50619\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS s : Subsemigroup M\nx : M × N\n⊢ x ∈ prod s ⊤ ↔ x ∈ comap (MulHom.fst M N) s",
"tactic": "simp [mem_prod, MulHom.coe_fst]"
}
] | [
668,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.self_trans_symm | [] | [
642,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.le_zero | [] | [
255,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_spanSingleton_self | [] | [
1312,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1311,
1
] |
Mathlib/Data/Quot.lean | Quot.induction_on₂ | [] | [
177,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
11
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.spanningCoe_inj | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.5780\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\n⊢ Subgraph.spanningCoe G₁ = Subgraph.spanningCoe G₂ ↔ G₁.Adj = G₂.Adj",
"tactic": "simp [Subgraph.spanningCoe]"
}
] | [
178,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_neg_iff | [] | [
244,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.antitoneOn_of_deriv_nonpos | [
{
"state_after": "no goals",
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961,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.pre_desc | [
{
"state_after": "case w\nJ : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF : J ⥤ C\ninst✝¹ : HasColimit F\nE : K ⥤ J\ninst✝ : HasColimit (E ⋙ F)\nc : Cocone F\nj✝ : K\n⊢ ι (E ⋙ F) j✝ ≫ pre F E ≫ desc F c = ι (E ⋙ F) j✝ ≫ desc (E ⋙ F) (Cocone.whisker E c)",
... | [
982,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.two_le_nValue | [
{
"state_after": "α : Type ?u.738856\nβ : Type ?u.738859\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 3 ≤ N\n⊢ ↑1 ^ 2 < log ↑N",
"state_before": "α : Type ?u.738856\nβ : Type ?u.738859\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 3 ≤ N\n⊢ 2 ≤ nValue N",
"tactic": "refine' succ_le_of_lt (lt_ceil.2 <| lt_sqrt_of_sq_lt _)"
},... | [
392,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Init/Algebra/Order.lean | le_of_lt_or_eq | [] | [
161,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.card_le_card_of_submodule | [] | [
820,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_append_of_mem | [
{
"state_after": "case nil\nι : Type ?u.81722\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na : α\nh✝ : a ∈ l₁\nh : a ∈ []\n⊢ indexOf a ([] ++ l₂) = indexOf a []\n\ncase cons\nι : Type ?u.81722\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : Dec... | [
1219,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.left_mem_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3492\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ a ∈ Ioo a b ↔ False",
"tactic": "simp [lt_irrefl]"
}
] | [
185,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_mem_Icc | [] | [
254,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
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