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/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' v' : V\np : Walk G u' v'\n⊢ support (Walk.copy p (_ : u' = u') (_ : v' = v')) = support p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V... | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | dot_cross_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nv w : Fin 3 → R\n⊢ w ⬝ᵥ ↑(↑crossProduct v) w = 0",
"tactic": "rw [← cross_anticomm, Matrix.dotProduct_neg, dot_self_cross, neg_zero]"
}
] | [
109,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/Algebra/BigOperators/Basic.lean | ofMul_multiset_prod | [
{
"state_after": "ι : Type ?u.997044\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoid α\ns : Multiset α\n⊢ Multiset.prod s = Multiset.sum s",
"state_before": "ι : Type ?u.997044\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst... | [
2323,
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2322,
1
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Mathlib/Order/UpperLower/Basic.lean | isUpperSet_iUnion₂ | [] | [
139,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.sum_single_index | [] | [
116,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Topology/Algebra/Monoid.lean | ContinuousAt.pow | [] | [
613,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π | [] | [
1628,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1628,
1
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Mathlib/Data/TypeVec.lean | TypeVec.prod_snd_mk | [
{
"state_after": "case fz\nn : ℕ\nα✝ β✝ : TypeVec n\ni : Fin2 n\na✝ : α✝ i\nb✝ : β✝ i\nn✝ : ℕ\nα β : TypeVec (succ n✝)\na : α Fin2.fz\nb : β Fin2.fz\n⊢ prod.snd Fin2.fz (prod.mk Fin2.fz a b) = b\n\ncase fs\nn : ℕ\nα✝ β✝ : TypeVec n\ni : Fin2 n\na✝¹ : α✝ i\nb✝ : β✝ i\nn✝ : ℕ\na✝ : Fin2 n✝\ni_ih : ∀ {α β : TypeVe... | [
556,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.final_of_initial_op | [] | [
115,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_congr | [
{
"state_after": "α : Type u_1\nβ : Type ?u.77478\nγ : Type ?u.77481\ns✝ t s : Set α\ninst✝¹ inst✝ : Fintype ↑s\n⊢ toFinset s = toFinset s",
"state_before": "α : Type u_1\nβ : Type ?u.77478\nγ : Type ?u.77481\ns✝ t✝ s t : Set α\ninst✝¹ : Fintype ↑s\ninst✝ : Fintype ↑t\nh : s = t\n⊢ toFinset s = toFinset t",... | [
613,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
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Mathlib/Data/Int/GCD.lean | Int.gcd_assoc | [] | [
268,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_compl_eq_mk_compl_infinite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Infinite α\ns t : Set α\nhs : (#↑s) < (#α)\nht : (#↑t) < (#α)\n⊢ (#↑(sᶜ)) = (#↑(tᶜ))",
"tactic": "rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]"
}
] | [
1163,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_mul | [] | [
199,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.image_eq_preimage | [] | [
1019,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.val_le | [] | [
62,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nat_tsum | [
{
"state_after": "α : Type ?u.259758\nβ : Type ?u.259761\nγ : Type ?u.259764\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α → ℝ≥0∞\nf : ℕ → ℝ≥0∞\n⊢ HasSum (fun i => f i) (∑' (n : ℕ), f n)",
"state_before": "α : Type ?u.259758\nβ : Type ?u.259761\nγ : Type ?u.259764\na b c d : ℝ≥0... | [
935,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
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Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coe_coord_of_subsingleton_eq_one | [
{
"state_after": "case h\nι : Type u_1\nι' : Type ?u.129150\nk : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁴ : AddCommGroup V\ninst✝³ : AffineSpace V P\ninst✝² : Ring k\ninst✝¹ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j : ι\ne : ι ≃ ι'\ninst✝ : Subsingleton ι\ni : ι\nq : P\n⊢ ↑(coord b i) q = OfNa... | [
254,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ClosedEmbedding.measurable | [] | [
829,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Order/Bounds/Basic.lean | Antitone.mem_lowerBounds_image | [] | [
1314,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1313,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | Antitone.tendsto_alternating_series_of_tendsto_zero | [] | [
645,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
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Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMax.hasFDerivAt_eq_zero | [] | [
204,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_symm_preimage_inter_range_eventuallyEq | [
{
"state_after": "𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.164976\nM' : Type ?u.164979\nH' : Type ?u.164982\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\nf f' : LocalHomeomorp... | [
957,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.coeff_zero_reverse | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\n⊢ coeff (reverse f) 0 = leadingCoeff f",
"tactic": "rw [coeff_reverse, revAt_le (zero_le f.natDegree), tsub_zero, leadingCoeff]"
}
] | [
259,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.eq_inv_mul_iff_mul_eq | [] | [
326,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
11
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_eq | [] | [
1129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_opens | [] | [
258,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | LowerTopology.isOpen_iff_generate_Ici_compl | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3811\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : LowerTopology α\ns : Set α\n⊢ IsOpen s ↔ GenerateOpen {t | ∃ a, Ici aᶜ = t} s",
"state_before": "α : Type u_1\nβ : Type ?u.3811\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : LowerTopology... | [
172,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/Separation.lean | Filter.HasBasis.exists_inter_eq_singleton_of_mem_discrete | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\nι : Type u_1\np : ι → Prop\nt : ι → Set α\ns : Set α\ninst✝ : DiscreteTopology ↑s\nx : α\nhb : HasBasis (𝓝 x) p t\nhx : x ∈ s\ni : ι\nhi : p i\nhix : t i ∩ s ⊆ {x}\n⊢ ∃ i, p i ∧ t i ∩ s = {x}",
"state_before": "α : Typ... | [
831,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_or_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.164816\nι : Sort x\nf : Filter α\ninst✝ : NeBot f\np : α → Prop\nq : Prop\n⊢ (∃ᶠ (x : α) in f, p x ∨ q) ↔ (∃ᶠ (x : α) in f, p x) ∨ q",
"tactic": "simp"
}
] | [
1350,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
src/lean/Init/Core.lean | recSubsingleton | [] | [
902,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
893,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isClosed_iff_zeroLocus | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nZ : Set (PrimeSpectrum R)\n⊢ IsClosed Z ↔ ∃ s, Z = zeroLocus s",
"tactic": "rw [← isOpen_compl_iff, isOpen_iff, compl_compl]"
}
] | [
422,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.modOf_apply_of_exists_add | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\ng g' : G\nh : ∃ d, g' = g + d\n⊢ ¬¬∃ g₂, g' = g + g₂",
"tactic": "rwa [Classical.not_not]"
}
] | [
144,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.prodExtendRight_apply_eq | [] | [
831,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_re | [] | [
144,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | FundamentalGroupoid.map_eq | [] | [
372,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.finset_prod_singleton | [] | [
174,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_self_abs | [] | [
969,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Order/RelClasses.lean | IsStrictOrder.swap | [] | [
104,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_mul_invOf_self_cancel | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.16996\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA : Matrix m n α\nB : Matrix n n α\ninst✝ : Invertible B\n⊢ A ⬝ B ⬝ ⅟B = A",
"tactic": "rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matr... | [
97,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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] |
Mathlib/Order/Interval.lean | NonemptyInterval.dual_map₂ | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherian_top_iff | [
{
"state_after": "case mp\nR : Type u_1\nM : Type u_2\nP : Type ?u.20594\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid P\ninst✝¹ : Module R M\ninst✝ : Module R P\nh : IsNoetherian R { x // x ∈ ⊤ }\n⊢ IsNoetherian R M\n\ncase mpr\nR : Type u_1\nM : Type u_2\nP : Type ?u.20594\ninst✝⁴ : S... | [
142,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.of_subtype_image | [] | [
552,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.lt_def | [] | [
636,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.mem_neLocus | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nN : α → Type u_2\ninst✝² : DecidableEq α\ninst✝¹ : (a : α) → DecidableEq (N a)\ninst✝ : (a : α) → Zero (N a)\nf✝ g✝ f g : Π₀ (a : α), N a\na : α\n⊢ a ∈ neLocus f g ↔ ↑f a ≠ ↑g a",
"tactic": "simpa only [neLocus, Finset.mem_filter, Finset.mem_un... | [
46,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.eq_one_of_isUnit | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhm : Monic p\nhpu : IsUnit p\n✝ : Nontrivial R\n⊢ p = 1",
"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]\nhm : Monic p\nhpu : IsUnit p\n⊢ p = 1",... | [
252,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.bot_lie | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
145,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\nx : RatFunc K\nh : num x = 0\n⊢ x = 0",
"tactic": "rw [← num_div_denom x, h, RingHom.map_zero, zero_div]"
}
] | [
1253,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_π | [
{
"state_after": "J : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF✝ F : J ⥤ C\ninst✝¹ : HasLimit F\nG : K ⥤ C\ninst✝ : HasLimit G\ne : J ≌ K\nw : e.functor ⋙ G ≅ F\nk : K\n⊢ IsLimit.lift (limit.isLimit G)\n ((Cones.equivalenceOfReindexing (Equivalence... | [
392,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/PFun.lean | PFun.mem_preimage | [] | [
435,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Order/Heyting/Basic.lean | sup_sdiff_cancel' | [
{
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577,
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src/lean/Init/Prelude.lean | Nat.lt_of_le_of_ne | [] | [
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51
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Mathlib/Order/Compare.lean | eq_iff_eq_of_cmp_eq_cmp | [
{
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267,
53
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.congr' | [] | [
156,
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Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_zero | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_toMeasurable_inter_of_cover | [
{
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_toFormula | [
{
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_one | [] | [
142,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | Associates.le_singleton_iff | [
{
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Mathlib/Topology/Algebra/ConstMulAction.lean | closure_smul₀ | [
{
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_zero | [
{
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_coe_ne_top_iff_summable_coe | [
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Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.coprod_eq_sup | [
{
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151,
36
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Mathlib/Order/MinMax.lean | lt_max_of_lt_left | [] | [
92,
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Mathlib/Topology/Order/Basic.lean | isOpen_Ioo | [] | [
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37
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.le_iff_mem_closure | [
{
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54
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.AEStronglyMeasurable.integral_prod_right' | [
{
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.mul_le_left | [] | [
136,
63
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135,
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Mathlib/Data/Finset/Basic.lean | Finset.mem_union_right | [] | [
1354,
26
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1353,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_toIcoMod | [
{
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},
{
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511,
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Mathlib/RingTheory/Noetherian.lean | isNoetherian_of_tower | [
{
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533,
72
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Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.dual | [] | [
250,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
11
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Mathlib/Algebra/Hom/Ring.lean | RingHom.codomain_trivial_iff_range_trivial | [
{
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"tactic": "rw [← mul_one x, map_mul, h, mul_zero]"
}
] | [
605,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/LinearAlgebra/Finsupp.lean | LinearMap.leftInverse_splittingOfFunOnFintypeSurjective | [] | [
1262,
71
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1260,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_lt | [] | [
919,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.inf_adj | [] | [
266,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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] |
Mathlib/Algebra/Group/Basic.lean | eq_mul_of_div_eq' | [
{
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}
] | [
920,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
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Mathlib/Algebra/Order/Group/Abs.lean | neg_abs_le_neg | [
{
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] | [
168,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.inv_eq_iff_eq | [] | [
115,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofTop_apply | [] | [
2103,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2102,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_congr_ae | [] | [
82,
48
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80,
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Monotone.map_limsSup_of_continuousAt | [] | [
386,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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] |
Mathlib/Data/Set/Finite.lean | Set.Finite.coeSort_toFinset | [
{
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}
] | [
179,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_gt_gt | [
{
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590,
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569,
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheaf_of_yoneda | [] | [
759,
49
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757,
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Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.size_eq | [] | [
34,
62
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cotrident.IsColimit.hom_ext | [] | [
309,
46
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307,
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Mathlib/Data/Int/Order/Basic.lean | Int.mul_lt_of_lt_ediv | [] | [
430,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
11
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.map_powers | [
{
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516,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.derivedSeries_le_lowerCentralSeries | [
{
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181,
45
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175,
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Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_inr | [] | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_submatrix_sum_swap_sum_swap | [
{
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179,
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineBasis.exists_affineBasis_of_finiteDimensional | [
{
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793,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.image_eq_preimage | [] | [
567,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
11
] |
Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_smul_comp_perm_le_sum_smul | [] | [
249,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.mk'_eq_mk | [] | [
68,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.trans_eventuallyEq | [] | [
132,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Topology/ContinuousOn.lean | continuous_if' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.376081\nδ : Type ?u.376084\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : TopologicalSpace δ\np : α → Prop\nf g : α → β\ninst✝ : (a : α) → Decidable (p a)\nhpf : ∀ (a : α), a ∈ frontier {x | p x} → Tendst... | [
1174,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_mul_C_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q r f : R[X]\na : R\n⊢ natDegree f + natDegree (↑C a) = natDegree f + 0",
"tactic": "rw [natDegree_C a]"
}
] | [
105,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.tendsto_iterate_efixedPoint' | [] | [
213,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.powers_eq_closure | [
{
"state_after": "case h\nM : Type u_1\nA : Type ?u.128599\nB : Type ?u.128602\ninst✝ : Monoid M\nn x✝ : M\n⊢ x✝ ∈ powers n ↔ x✝ ∈ closure {n}",
"state_before": "M : Type u_1\nA : Type ?u.128599\nB : Type ?u.128602\ninst✝ : Monoid M\nn : M\n⊢ powers n = closure {n}",
"tactic": "ext"
},
{
"state_... | [
446,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
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