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/AlgebraicTopology/DoldKan/Compatibility.lean | AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isOpen_iff_of_mem | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nh : ∞ ∈ s\n⊢ IsOpen s ↔ IsClosed ((some ⁻¹' s)ᶜ) ∧ IsCompact ((some ⁻¹' s)ᶜ)",
"tactic": "simp only [isOpen_iff_of_mem' h, isClosed_compl_iff, and_comm]"
}
] | [
221,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
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Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.is_coprod_iff_isPushout | [
{
"state_after": "case mp\nJ : Type v'\ninst✝¹ : Category J\nC : Type u\ninst✝ : Category C\nW X✝ Y✝ Z : C\nf✝ : W ⟶ X✝\ng : W ⟶ Y✝\nh : X✝ ⟶ Z\ni : Y✝ ⟶ Z\nX E Y YE : C\nc : BinaryCofan X E\nhc : IsColimit c\nf : X ⟶ Y\niY : Y ⟶ YE\nfE : c.pt ⟶ YE\nH : CommSq f (BinaryCofan.inl c) iY fE\n⊢ Nonempty (IsColimit ... | [
151,
89
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121,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.toFun_eq_coe | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
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Mathlib/Analysis/Calculus/TangentCone.lean | IsOpen.uniqueDiffOn | [] | [
331,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.eq_class_eq_leftCoset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Group α\ns✝ : Subgroup α\na b : α\ns : Subgroup α\ng z : α\n⊢ z ∈ {x | ↑x = ↑g} ↔ z ∈ g *l ↑s",
"tactic": "rw [mem_leftCoset_iff, Set.mem_setOf_eq, eq_comm, QuotientGroup.eq, SetLike.mem_coe]"
}
] | [
558,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
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Mathlib/Logic/Function/Basic.lean | Function.Surjective.injective_comp_right | [] | [
227,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.extract_gcd' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns t : Multiset α\nhs : ∃ x, x ∈ s ∧ x ≠ 0\nht : s = map ((fun x x_1 => x * x_1) (gcd s)) t\n⊢ gcd s * gcd t = gcd s",
"tactic": "conv_lhs => rw [← normalize_gcd, ← gcd_map_mul,... | [
234,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.card_boundaries_eq_succ_length | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nc : Composition n\n⊢ Finset.card (boundaries c) = length c + 1",
"tactic": "simp [boundaries]"
}
] | [
281,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/MeasureTheory/Integral/Layercake.lean | Measure.countable_meas_le_ne_meas_lt | [] | [
302,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Algebra/Lie/UniversalEnveloping.lean | UniversalEnvelopingAlgebra.hom_ext | [
{
"state_after": "case h\nR : Type u₁\nL : Type u₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nA : Type u₃\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nf : L →ₗ⁅R⁆ A\ng₁ g₂ : UniversalEnvelopingAlgebra R L →ₐ[R] A\nh : LieHom.comp (AlgHom.toLieHom g₁) (ι R) = LieHom.comp (AlgHom.toLieHom g₂) (ι... | [
172,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/List/Lattice.lean | List.forall_mem_inter_of_forall_left | [] | [
188,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_eq_self_of_subset_right | [] | [
981,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_empty | [] | [
1042,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Computability/Partrec.lean | Nat.Partrec.of_eq_tot | [] | [
177,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_monoidHom_injective | [] | [
207,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_aeval | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_2\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝⁴ : CommSemiring R\ninst✝³ : CommSemiring S₁\np✝ q : MvPolynomial σ R\ninst✝² : Algebra R S₁\ninst✝¹ : CommSemiring S₂\nf : σ → S₁\nB : Type u_1\ninst✝ : CommSemiring B\ng : σ → S₁... | [
1476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_mul_of_div_eq_left | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH1 : b ∣ a\nH2 : div a b = c\n⊢ a = c * b",
"tactic": "rw [Int.mul_comm, Int.eq_mul_of_div_eq_right H1 H2]"
}
] | [
773,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
771,
11
] |
Mathlib/Data/List/Count.lean | List.count_join | [] | [
237,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.IsInvertedBy.of_comp | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nD : Type ?u.46661\ninst✝³ : Category D\nC₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\ninst✝² : Category C₁\ninst✝¹ : Category C₂\ninst✝ : Category C₃\nW : MorphismProperty C₁\nF : C₁ ⥤ C₂\nhF : IsInvertedBy W F\nG : C₂ ⥤ C₃\nX Y : C₁\nf : X ⟶ Y\nhf : W f\nthis :... | [
307,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | parallelepiped_eq_convexHull | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.96374\nE : Type u_1\nF : Type ?u.96380\ninst✝⁵ : Fintype ι\ninst✝⁴ : Fintype ι'\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ninst✝¹ : AddCommGroup F\ninst✝ : Module ℝ F\nv : ι → E\nA : Set E →+ Set E :=\n { toZeroHom := { toFun := ↑(convexHull ℝ).toOrderHom, map_z... | [
150,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.mono | [] | [
1308,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
11
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.algebraMap_matrix_apply | [
{
"state_after": "l : Type ?u.519207\nm : Type ?u.519210\nn : Type u_1\no : Type ?u.519216\nm' : o → Type ?u.519221\nn' : o → Type ?u.519226\nR : Type u_2\nS : Type ?u.519232\nα : Type v\nβ : Type w\nγ : Type ?u.519239\ninst✝⁶ : Fintype n\ninst✝⁵ : DecidableEq n\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring α\nin... | [
1315,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.zero_bot | [] | [
498,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_singleton | [] | [
153,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/Order.lean | continuous_le_rng | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.37963\nf : α → β\nι : Sort ?u.37970\nt₁ : TopologicalSpace α\nt₂ t₃ : TopologicalSpace β\nh₁ : t₂ ≤ t₃\nh₂ : coinduced f t₁ ≤ t₂\n⊢ coinduced f t₁ ≤ t₃",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.37963\nf : α → β\nι : Sort ?u.37970\nt₁ : Topol... | [
733,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_copy | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsTensorProduct.inductionOn | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommRing R\nM₁ : Type u_2\nM₂ : Type u_3\nM : Type u_4\nM' : Type ?u.113149\ninst✝¹³ : AddCommMonoid M₁\ninst✝¹² : AddCommMonoid M₂\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M'\ninst✝⁹ : Module R M₁\ninst✝⁸ : Module R M₂\ninst✝⁷ : Module R M\ninst✝⁶ : Module R... | [
135,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Ioc_add_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ (⋃ (n : ℤ), Ioc (a + ↑n) (a + ↑n + 1)) = univ",
"tactic": "simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using\n iUnion_Ioc_add_zsmul zero_lt_one a"
}
] | [
1094,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.ediam_eq | [
{
"state_after": "case inl\nα : Type ?u.434159\nβ : Type ?u.434162\nγ : Type ?u.434165\ninst✝ : PseudoEMetricSpace α\nh : Metric.Bounded ∅\n⊢ EMetric.diam ∅ = ENNReal.ofReal (sSup ∅ - sInf ∅)\n\ncase inr\nα : Type ?u.434159\nβ : Type ?u.434162\nγ : Type ?u.434165\ninst✝ : PseudoEMetricSpace α\ns : Set ℝ\nh : Me... | [
1519,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | EReal.measurable_of_measurable_real | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3039973\nγ : Type ?u.3039976\nγ₂ : Type ?u.3039979\nδ : Type ?u.3039982\nι : Sort y\ns t u : Set α\ninst✝ : MeasurableSpace α\nf : EReal → α\nh : Measurable fun p => f ↑p\n⊢ Set.Finite {⊥, ⊤}",
"tactic": "simp"
}
] | [
1990,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.BoundedFormula.card_le | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.158067\nP : Type ?u.158070\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\n⊢ lift (#List BoundedFormula.encoding.Γ) ≤ lift (max ℵ₀ (lift (#α) + lift (card L)))",
"state_before": "L : Language\nM : Type ... | [
323,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.rowLens_length_ofRowLens | [
{
"state_after": "w : List ℕ\nhw : List.Sorted (fun x x_1 => x ≥ x_1) w\nhpos : ∀ (x : ℕ), x ∈ w → 0 < x\n⊢ True ∧ ∀ (n : ℕ), n < List.length w → ∃ h, 0 < List.get w { val := n, isLt := (_ : (n, 0).fst < List.length w) }",
"state_before": "w : List ℕ\nhw : List.Sorted (fun x x_1 => x ≥ x_1) w\nhpos : ∀ (x :... | [
505,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.474375\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\n⊢ ↑(restrict v Set.univ) i = ↑v i",
"tacti... | [
718,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_inj | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : -a = -b\n⊢ a = b",
"tactic": "rw [← Int.neg_neg a, ← Int.neg_neg b, h]"
}
] | [
88,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
87,
11
] |
Mathlib/Dynamics/Ergodic/Conservative.lean | MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero | [] | [
116,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_rat_div | [] | [
411,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.equicontinuous_of_continuity_modulus | [] | [
125,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atTop_div_const | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.221463\nι' : Type ?u.221466\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.221475\ninst✝ : LinearOrderedSemifield α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\nhr : 0 < r\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x => f x / r) l atTop",
"tactic": "simpa on... | [
1052,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_algebraMap | [] | [
416,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_mul' | [] | [
379,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_cardinal | [
{
"state_after": "no goals",
"state_before": "⊢ (#Cardinal) = univ",
"tactic": "simpa only [card_type, card_univ] using congr_arg card type_cardinal"
}
] | [
151,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.biUnion_Ico_Ioc_map_succ | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : SuccOrder α\ninst✝¹ : IsSuccArchimedean α\ninst✝ : LinearOrder β\nf : α → β\nhf : Monotone f\nm n : α\nhnm : n ≤ m\n⊢ (⋃ (i : α) (_ : i ∈ Ico m n), Ioc (f i) (f (succ i))) = Ioc (f m) (f n)\n\ncase inr\nα : Type u_1\nβ : Ty... | [
50,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.antidiagonal_zero | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/RingTheory/Localization/AtPrime.lean | IsLocalization.AtPrime.Nontrivial | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.10429\ninst✝¹ : CommSemiring P\nI : Ideal R\nhp : Ideal.IsPrime I\ninst✝ : IsLocalization.AtPrime S I\nhze : ↑(algebraMap R S) 0 = ↑(algebraMap R S) 1\n⊢ False",
... | [
80,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.sub_tmul | [] | [
1256,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_mul_self_pred | [] | [
219,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_map_subset | [
{
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Mathlib/Topology/Instances/Int.lean | Int.closedBall_eq_Icc | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | mem_uniformity_edist | [] | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_nonneg_of_nonpos | [] | [
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Mathlib/LinearAlgebra/Ray.lean | SameRay.exists_nonneg_left | [
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Mathlib/Analysis/Convex/Basic.lean | Submodule.starConvex | [] | [
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Mathlib/Analysis/Seminorm.lean | Seminorm.ball_finset_sup' | [
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_restrictScalars' | [] | [
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_indicator_const | [
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Mathlib/Data/Set/Lattice.lean | Set.image2_eq_iUnion | [
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Mathlib/Analysis/Normed/Group/Basic.lean | cauchySeq_prod_of_eventually_eq | [
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_multiset_sum | [] | [
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.comap_map_eq | [
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iInf_mul_left' | [
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Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.rightHom_comp_inr | [
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Mathlib/Data/List/Zip.lean | List.unzip_left | [
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Mathlib/Data/Setoid/Partition.lean | Setoid.isPartition_classes | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | tendsto_iff_of_dist | [] | [
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | finrank_euclideanSpace | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_one_iff | [
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Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Filter.Tendsto.cesaro | [] | [
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Mathlib/Order/Filter/Pointwise.lean | Filter.pure_mul | [] | [
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Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_of_countable_of_charZero | [] | [
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_refl_restr | [
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.le_ωSup_of_le | [] | [
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Mathlib/Topology/SubsetProperties.lean | Filter.coprod_cocompact | [
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Mathlib/Data/Stream/Init.lean | Stream'.iterate_id | [
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Mathlib/GroupTheory/Index.lean | Subgroup.inf_relindex_left | [
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142,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag | [
{
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_inv_le | [
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... | [
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51
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.transnumAuxSeq_def | [] | [
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Mathlib/Data/Finset/Lattice.lean | iInf_eq_iInf_finset | [] | [
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Mathlib/Logic/Equiv/Option.lean | Equiv.removeNone_aux_none | [
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Mathlib/Logic/Function/Basic.lean | Function.Surjective.forall₃ | [] | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_toReal | [
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Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero | [
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322,
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Mathlib/Data/Rat/Defs.lean | Rat.divInt_div_divInt_cancel_right | [
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498,
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.measurable_of_measurable_coe | [
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Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_neg | [
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373,
91
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.ne_zero_of_trailingDegree_lt | [
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.ε_app_obj | [
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227,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.isAddFundamentalDomain | [
{
"state_after": "case intro\nE : Type u_2\nι : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nb : Basis ι ℝ E\ninst✝² : Finite ι\ninst✝¹ : MeasurableSpace E\ninst✝ : OpensMeasurableSpace E\nμ : MeasureTheory.Measure E\nval✝ : Fintype ι\n⊢ IsAddFundamentalDomain { x // x ∈ toAddSubgroup (spa... | [
258,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
11
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_div_cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.62857\nG : Type ?u.62860\nα : Type u_1\nM : Type ?u.62866\nN : Type ?u.62869\ninst✝ : DivisionCommMonoid α\na b✝ c d : α\nh : IsUnit a\nb : α\n⊢ a * b / a = b",
"tactic": "rw [mul_comm, h.mul_div_cancel]"
}
] | [
472,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
11
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.node' | [] | [
113,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ioc_of_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : c < 0\n⊢ (fun x => x * c) ⁻¹' Ioc a b = Ico (b / c) (a / c)",
"tactic": "simp [← Ioi_inter_Iic, ← Ici_inter_Iio, h, inter_comm]"
}
] | [
586,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ring_inverse_eq_map_inverse | [
{
"state_after": "case h.h\nR : Type u_2\nM : Type u_1\nM₂ : Type ?u.2031615\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : TopologicalSpace M₂\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : TopologicalAddGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R M₂\nx✝¹ : M →L[R] M\nx✝ : M\n⊢ ↑(Ring... | [
2550,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2548,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.not_lt_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.81518\nβ : Type ?u.81521\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx : ℝ≥0∞\n⊢ ¬x < ⊤ ↔ x = ⊤",
"tactic": "rw [lt_top_iff_ne_top, Classical.not_not]"
}
] | [
543,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | Infinite.orderOf_eq_zero_of_forall_mem_zpowers | [
{
"state_after": "α : Type u\na : α\ninst✝¹ : Group α\ninst✝ : Infinite α\ng : α\nh : ∀ (x : α), x ∈ zpowers g\n⊢ ∀ (n : ℕ), 0 < n → g ^ n ≠ 1",
"state_before": "α : Type u\na : α\ninst✝¹ : Group α\ninst✝ : Infinite α\ng : α\nh : ∀ (x : α), x ∈ zpowers g\n⊢ orderOf g = 0",
"tactic": "rw [orderOf_eq_zero... | [
177,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.cos_eq_neg_one_iff_angle_eq_pi | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) = cos π ↔ angle x y = π",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) = -1 ↔ angle x y = π",
"tactic": "rw ... | [
361,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\n⊢ Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂",
"state_before": "V : Type u_1\nP : Type u_2... | [
458,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Analysis/Complex/Liouville.lean | Complex.deriv_eq_smul_circleIntegral | [
{
"state_after": "case intro\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℂ E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℂ F\ninst✝ : CompleteSpace F\nc : ℂ\nf : ℂ → F\nR : ℝ≥0\nhR : 0 < ↑R\nhf : DiffContOnCl ℂ f (ball c ↑R)\n⊢ deriv f c = (2 * ↑π * I)⁻¹ • ∮ (z : ℂ) in ... | [
56,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.zero | [] | [
71,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.norm_id_of_nontrivial_seminorm | [
{
"state_after": "V : Type u_1\nV₁ : Type ?u.320008\nV₂ : Type ?u.320011\nV₃ : Type ?u.320014\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g : NormedAddGroupHom V₁ V₂\nh : ∃ x, ‖x‖ ≠ 0\nx : V\nhx : ‖x‖ ≠ 0\n⊢ 1 ≤... | [
437,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
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