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/LinearAlgebra/LinearIndependent.lean | LinearIndependent.repr_eq | [
{
"state_after": "ι : Type u'\nι' : Type ?u.448902\nR : Type u_1\nK : Type ?u.448908\nM : Type u_2\nM' : Type ?u.448914\nM'' : Type ?u.448917\nV : Type u\nV' : Type ?u.448922\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹ : ... | [
809,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_iff | [
{
"state_after": "m✝ n : ℤ\nx✝ : Odd n\nm : ℤ\nhm : n = 2 * m + 1\n⊢ (2 * m % 2 + 1 % 2) % 2 = 1",
"state_before": "m✝ n : ℤ\nx✝ : Odd n\nm : ℤ\nhm : n = 2 * m + 1\n⊢ n % 2 = 1",
"tactic": "rw [hm, add_emod]"
},
{
"state_after": "no goals",
"state_before": "m✝ n : ℤ\nx✝ : Odd n\nm : ℤ\nhm : ... | [
47,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Topology/LocalExtr.lean | IsMinOn.isLocalMin | [] | [
159,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.IsMaximal.isCoatom | [] | [
237,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.162324\nγ : Type ?u.162327\nι : Sort ?u.162330\nκ : ι → Sort ?u.162335\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\nx : α\nS : Set (Set α)\n⊢ upperClosure (⋃₀ S) = ⨅ (s : Set α) (_ : s ∈ S), upperClosure s",
"tactic": "sim... | [
1454,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Mathlib/Order/Lattice.lean | sup_inf_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Lattice α\na b c d : α\n⊢ a ⊔ a ⊓ b = a",
"tactic": "simp"
}
] | [
714,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eqOnSource_refl | [] | [
942,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Topology/Algebra/Order/Group.lean | tendsto_abs_nhdsWithin_zero | [] | [
101,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_sup | [] | [
1200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_nnnorm_eq_of_ae_nonneg | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.296013\nγ : Type ?u.296016\nδ : Type ?u.296019\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ\nh_nonneg : 0 ≤ᵐ[μ] f\n⊢ (fun a => ↑‖f a‖₊) =ᵐ[μ] fun a => ENNReal.ofReal (f a)",
"state_before": "α : Type u_1\nβ : Type ?u.296013\nγ : Type ?u.296016\nδ : T... | [
350,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.eq_symm_apply | [] | [
418,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_zero_eq_comp | [] | [
787,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_zero_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1028530\nG : Type ?u.1028533\n𝕜 : Type ?u.1028536\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ℝ F'\nins... | [
1057,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.IsRoot.of_map | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R✝\nm n : ℕ\ninst✝² : CommSemiring R✝\ninst✝¹ : CommSemiring S\nf✝ : R✝ →+* S\nR : Type u_1\ninst✝ : CommRing R\nf : R →+* S\nx : R\np : R[X]\nh : IsRoot (Polynomial.map f p) (↑f x)\nhf : Function.Injective ... | [
1205,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_univ | [] | [
921,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Order/BoundedOrder.lean | isMax_top | [] | [
115,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Std/Logic.lean | or_or_distrib_left | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ a ∨ b ∨ c ↔ (a ∨ b) ∨ a ∨ c",
"tactic": "rw [or_or_or_comm, or_self]"
}
] | [
283,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
283,
1
] |
Mathlib/Topology/Order/Priestley.lean | exists_clopen_upper_or_lower_of_ne | [
{
"state_after": "case inl\nα : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : PartialOrder α\ninst✝ : PriestleySpace α\nx y : α\nh✝ : x ≠ y\nh : ¬x ≤ y\n⊢ ∃ U, IsClopen U ∧ (IsUpperSet U ∨ IsLowerSet U) ∧ x ∈ U ∧ ¬y ∈ U\n\ncase inr\nα : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : PartialOrder α\ninst✝ : P... | [
75,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSets_of_indepSets_of_le_left | [] | [
184,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.cons_self_properDivisors | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : n ≠ 0\n⊢ cons n (properDivisors n) (_ : ¬n ∈ properDivisors n) = divisors n",
"tactic": "rw [cons_eq_insert, insert_self_properDivisors h]"
}
] | [
93,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.aeval_U | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝² : CommRing R\ninst✝¹ : CommRing A\ninst✝ : Algebra R A\nx : A\nn : ℕ\n⊢ ↑(aeval x) (U R n) = eval x (U A n)",
"tactic": "rw [aeval_def, eval₂_eq_eval_map, map_U]"
}
] | [
38,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_nhds_right | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhdf : ∀ᶠ (x : ℝ) in 𝓝[Ioi a] a, DifferentiableAt ℝ f x\nhg' : ∀ᶠ (x : ℝ) in 𝓝[Ioi a] a, deriv g x ≠ 0\nhfa : Tendsto f (𝓝[Ioi a] a) (𝓝 0)\nhga : Tendsto g (𝓝[Ioi a] a) (𝓝 0)\nhdiv : Tendsto (fun x => deriv f x / deriv g x) (𝓝[Ioi a]... | [
395,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Topology/Connected.lean | Continuous.image_eq_of_connectedComponent_eq | [] | [
1490,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1486,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.infTo_commutes | [] | [
691,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Data/List/Sigma.lean | List.kerase_keys_subset | [] | [
423,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nontrivial_univ_iff | [] | [
2567,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2566,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.ringChar_of_prime_eq_zero | [] | [
609,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_Iic | [] | [
141,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Set/Image.lean | Function.Surjective.image_preimage | [] | [
1302,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | indicator_ae_eq_restrict_compl | [] | [
4669,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4667,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.compContinuousLinearMap_apply | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_iff_lt_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ a * b⁻¹ < c ↔ a < c * b",
"tactic": "rw [← mul_lt_mul_iff_right b, inv_mul_cancel_right]"
}
] | [
309,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Topology/Separation.lean | isCompact_isCompact_separated | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type ?u.127862\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\ns t : Set α\nhs : IsCompact s\nht : IsCompact t\nhst : s ×ˢ t ⊆ diagonal αᶜ\n⊢ ∃ U V, IsOpen U ∧ IsOpen V ∧ s ⊆ U ∧ t ⊆ V ∧ U ×ˢ V ⊆ diagonal αᶜ... | [
1243,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.add | [] | [
120,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Data/List/Rotate.lean | List.rotate_one_eq_self_iff_eq_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Nonempty α\nl : List α\nh : rotate l 1 = l\nn✝ n : ℕ\nhn : rotate l n = l\n⊢ rotate l (succ n) = l",
"tactic": "rwa [Nat.succ_eq_add_one, ← l.rotate_rotate, hn]"
}
] | [
323,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_add | [
{
"state_after": "u v : PrimeMultiset\n⊢ Multiset.prod (↑coePNatMonoidHom (u + v)) = prod u * prod v",
"state_before": "u v : PrimeMultiset\n⊢ prod (u + v) = prod u * prod v",
"tactic": "change (coePNatMonoidHom (u + v)).prod = _"
},
{
"state_after": "u v : PrimeMultiset\n⊢ Multiset.prod (↑coePN... | [
226,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensorHom_inv_id' | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝³ : MonoidalCategory C✝\nC : Type u\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nU V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C\nf : V ⟶ W\ninst✝ : IsIso f\ng : X ⟶ Y\nh : Y ⟶ Z\n⊢ (g ⊗ f) ≫ (h ⊗ inv f) = (g ⊗ 𝟙 V) ≫ (h ⊗ 𝟙 V)",
"... | [
392,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_isLimit_left | [
{
"state_after": "case inl\nα : Type ?u.221106\nβ : Type ?u.221109\nγ : Type ?u.221112\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\nl : IsLimit a\nb0 : 0 < 0\n⊢ IsLimit (a * 0)\n\ncase inr.inl.intro\nα : Type ?u.221106\nβ : Type ?u.221109\nγ : Type ?u.221112\nr : α → α → Prop\ns : β → β →... | [
857,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/List/AList.lean | AList.keys_nodup | [] | [
87,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min_of_mem | [
{
"state_after": "case intro.intro\nF : Type ?u.324381\nα : Type u_1\nβ : Type ?u.324387\nγ : Type ?u.324390\nι : Type ?u.324393\nκ : Type ?u.324396\ninst✝ : LinearOrder α\ns : Finset α\na : α\nh✝ : a ∈ s\nb : α\nh : b ∈ inf s some\nright✝ : b ≤ a\n⊢ ∃ b, Finset.min s = ↑b",
"state_before": "F : Type ?u.324... | [
1264,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_mul_left_iff | [] | [
1503,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1501,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.49125\ninst✝ : LinearOrder α\na : α\ni : Fin 1\n⊢ ↑(orderEmbOfFin {a} (_ : card {a} = 1)) i = a",
"tactic": "rw [Subsingleton.elim i ⟨0, zero_lt_one⟩, orderEmbOfFin_zero _ zero_lt_one, min'_singleton]"
}
] | [
211,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Atoms.lean | OrderIso.isAtom_iff | [] | [
806,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.equivFunOnFinite_symm_coe | [] | [
259,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_type_lt | [
{
"state_after": "α✝ : Type ?u.108718\nβ✝ : Type ?u.108721\nγ : Type ?u.108724\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : IsWellOrder β s\nthis : IsWellOrder (ULift α) (↑Equiv.ulift ⁻¹'o r)\n⊢ lift (t... | [
760,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Data/List/Rdrop.lean | List.dropWhile_idempotent | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ ∀ (hl : 0 < length (dropWhile p l)), ¬p (nthLe (dropWhile p l) 0 hl) = true",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ dropWhile p (dropWhile p l) = dropWhile p l",
"tactic": "simp only [dropWhile_eq_self_iff]"
... | [
183,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.descFactorial_eq_factorial_mul_choose | [
{
"state_after": "case inl\nn k : ℕ\nh : n < k\n⊢ descFactorial n k = k ! * choose n k\n\ncase inr\nn k : ℕ\nh : n ≥ k\n⊢ descFactorial n k = k ! * choose n k",
"state_before": "n k : ℕ\n⊢ descFactorial n k = k ! * choose n k",
"tactic": "obtain h | h := Nat.lt_or_ge n k"
},
{
"state_after": "ca... | [
263,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod_rightUnitor_inv_naturality | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX Y : C\ninst✝¹ : HasTerminal C\ninst✝ : HasBinaryProducts C\nf : X ⟶ Y\n⊢ (prod.rightUnitor X).inv ≫ prod.map f (𝟙 (⊤_ C)) = f ≫ (prod.rightUnitor Y).inv",
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91
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.card_eq_card_functions_add_card_relations | [
{
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178,
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Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_lineMap_lineMap | [
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Mathlib/Algebra/Order/Group/Abs.lean | abs_neg | [
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Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.minimalPrimes_eq_comap | [
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Mathlib/Data/Set/Finite.lean | Set.Finite.sep | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_comp | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ico_union_Icc | [] | [
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Mathlib/Logic/Relation.lean | Relation.ReflTransGen.single | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_congr | [
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Mathlib/Init/Algebra/Order.lean | gt_irrefl | [] | [
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Mathlib/Topology/Constructions.lean | embedding_inr | [] | [
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.div | [] | [
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Mathlib/Topology/Order/Basic.lean | Antitone.map_iSup_of_continuousAt' | [] | [
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100
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2723,
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Mathlib/Order/MinMax.lean | max_lt_iff | [] | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lt_aleph0_iff_set_finite | [] | [
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44
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_fin_zero | [] | [
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24
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Mathlib/Order/Heyting/Hom.lean | BiheytingHom.coe_comp | [] | [
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Mathlib/Combinatorics/Composition.lean | CompositionAsSet.blocks_length | [] | [
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Mathlib/Topology/PathConnected.lean | Path.truncate_self | [
{
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690,
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685,
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Mathlib/Algebra/Quaternion.lean | Quaternion.equivTuple_apply | [] | [
757,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.piComm_symm | [] | [
673,
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.eq_or_edist_eq_top_of_fixedPoints | [
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Mathlib/Logic/Equiv/Defs.lean | Equiv.right_inv' | [] | [
172,
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.abelian_iff_derived_one_eq_bot | [
{
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138,
50
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136,
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Mathlib/Data/Set/Basic.lean | Set.union_distrib_left | [] | [
1058,
15
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1057,
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.Adj.coe | [] | [
149,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_mk | [] | [
220,
93
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220,
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace | [
{
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412,
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Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | AddMonoidAlgebra.toDirectSum_mul | [
{
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156,
42
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135,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongr_one_swap | [] | [
234,
25
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232,
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Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_one | [] | [
148,
20
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147,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_uzero | [] | [
234,
20
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233,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_dirac' | [
{
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1384,
35
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1378,
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Mathlib/Data/Real/Sqrt.lean | ContinuousAt.sqrt | [] | [
495,
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494,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.uniformEmbedding | [] | [
2140,
51
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2136,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_three | [
{
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},
{
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909,
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906,
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Mathlib/GroupTheory/Perm/Subgroup.lean | Equiv.Perm.sumCongrHom.card_range | [] | [
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83
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40,
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.naturality_2 | [
{
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] | [
178,
7
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177,
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.congr_fun | [] | [
511,
24
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510,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_iff_eq | [] | [
324,
40
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322,
1
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Mathlib/Data/Prod/Lex.lean | Prod.Lex.toLex_strictMono | [
{
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133,
22
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129,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lift_symm_apply | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.tanh_ofReal_re | [] | [
723,
6
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722,
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.nullHomotopicMap'_f_of_not_rel_right | [
{
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423,
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416,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.not_mem_support_iff | [
{
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}
] | [
717,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
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Std/Data/Rat/Basic.lean | Rat.normalize.reduced | [
{
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98
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.fst_eq_coprod | [
{
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250,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Finsupp.coe_basisSingleOne | [] | [
135,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Order/Filter/CountableInter.lean | Filter.le_countableGenerate_iff_of_countableInterFilter | [
{
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261,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
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Mathlib/Order/Filter/Pointwise.lean | Filter.mem_inv | [] | [
201,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_X_pow_sub_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Ring R\nn : ℕ\nhn : 0 < n\nr : R\n⊢ leadingCoeff (X ^ n - ↑C r) = 1",
"tactic": "rw [sub_eq_add_neg, ← map_neg C r, leadingCoeff_X_pow_add_C hn]"
}
] | [
1456,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | monotone_vecEmpty | [] | [
45,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
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