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/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le' | [] | [
957,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.isPartialInv_left | [] | [
314,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.remainder_pos | [
{
"state_after": "no goals",
"state_before": "m : ℝ\nhm : 1 < m\nk x✝ : ℕ\n⊢ 0 ≤ 1 / m ^ (x✝ + (k + 1))!",
"tactic": "positivity"
},
{
"state_after": "no goals",
"state_before": "m : ℝ\nhm : 1 < m\nk : ℕ\n⊢ 0 < 1 / m ^ (0 + (k + 1))!",
"tactic": "positivity"
}
] | [
93,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_sInf | [
{
"state_after": "case h\nι : Sort ?u.93021\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ns : Set (Subgraph G)\nv x✝ : V\n⊢ x✝ ∈ neighborSet (sInf s) v ↔ x✝ ∈ (⋂ (G' : Subgraph G) (_ : G' ∈ s), neighborSet G' v) ∩ SimpleGraph.neighborSet G v",
"state_before": "ι : Sort ?u.93021\nV... | [
525,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nc : ℂ\nR : ℝ\nh0 : 0 < R\nf : ℂ → E\ny : E\ns : Set ℂ\nhs : Set.Countable s\nhc : ContinuousOn f (closedBall c R \\ {c})\nhd : ∀ (z : ℂ), z ∈ (ball c R \\ {c}) \\ s → DifferentiableAt ℂ f z\nhy : Tend... | [
398,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
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Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_inf | [
{
"state_after": "u v : PrimeMultiset\nn : ℕ+ := prod u\n⊢ prod (u ⊓ v) = PNat.gcd (prod u) (prod v)",
"state_before": "u v : PrimeMultiset\n⊢ prod (u ⊓ v) = PNat.gcd (prod u) (prod v)",
"tactic": "let n := u.prod"
},
{
"state_after": "u v : PrimeMultiset\nn : ℕ+ := prod u\nm : ℕ+ := prod v\n⊢ p... | [
419,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_subset_Icc | [
{
"state_after": "case intro.intro.intro.intro.intro\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.229927\nG : Type ?u.229930\nι : Type ?u.229933\nπ : ι → Type ?u.229938\ninst✝³ : OrderedSemiring 𝕜\ninst✝² : OrderedAddCommMonoid E\ninst✝¹ : Module 𝕜 E\ninst✝ : OrderedSMul 𝕜 E\nx y : E\nh : x ≤ y\na b : 𝕜\nha : ... | [
437,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/List/Card.lean | List.card_remove_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.28067\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\na a' : α\nas : List α\nh : a ∈ a' :: as\n⊢ card (a' :: as) = card (remove a (a' :: as)) + 1",
"tactic": "cases Decidable.em (a = a') with\n| inl h' =>\n simp [remove, if_pos h']... | [
120,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | powersMulHom_symm_apply | [] | [
981,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | Dvd.intro | [] | [
52,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | piecewise_ae_eq_of_ae_eq_set | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4394524\nδ : Type ?u.4394527\nι : Type ?u.4394530\nR : Type ?u.4394533\nR' : Type ?u.4394536\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t : Set α\nf g : α → β\nhst : s =ᶠ[ae μ] t\nx : α\nhx : x ∈ s ↔ x ∈ t\... | [
4623,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4622,
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_nat | [
{
"state_after": "case zero\nα : Type ?u.227526\nβ : Type ?u.227529\nγ : Type ?u.227532\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\n⊢ ↑Nat.zero ≤ ord ↑Nat.zero\n\ncase succ\nα : Type ?u.227526\nβ : Type ?u.227529\nγ : Type ?u.227532\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nn : ℕ\nIH : ↑... | [
1432,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
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Mathlib/Data/Finset/Basic.lean | Finset.coe_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.23076\nγ : Type ?u.23079\ns✝ s : Finset α\n⊢ ↑s = ∅ ↔ s = ∅",
"tactic": "rw [← coe_empty, coe_inj]"
}
] | [
626,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_zero | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\na b : Γ\nr : R\nΓ' : Type u_2\ninst✝ : PartialOrder Γ'\nf : Γ ↪o Γ'\nx✝ : Γ'\n⊢ coeff (embDomain f 0) x✝ = coeff 0 x✝",
"state_before": "Γ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\... | [
318,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.image2_subset_map₂ | [
{
"state_after": "case intro.intro.intro.intro\nι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\np : Sub... | [
139,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_le_upperBounds | [] | [
1043,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Algebra/FreeNonUnitalNonAssocAlgebra.lean | FreeNonUnitalNonAssocAlgebra.lift_symm_apply | [] | [
77,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.algHom_ext | [
{
"state_after": "case H.mk\nR : Type ?u.82639\nS : Type ?u.82642\nA : Type u_1\ninst✝¹ : Semiring A\ninst✝ : Algebra ℝ A\nf g : ℂ →ₐ[ℝ] A\nh : ↑f I = ↑g I\nx y : ℝ\n⊢ ↑f { re := x, im := y } = ↑g { re := x, im := y }",
"state_before": "R : Type ?u.82639\nS : Type ?u.82642\nA : Type u_1\ninst✝¹ : Semiring A... | [
130,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/Order.lean | induced_mono | [] | [
424,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_zpow | [
{
"state_after": "no goals",
"state_before": "f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\nn : ℕ\n⊢ τ ↑(f ^ ↑n) = ↑↑n * τ ↑f",
"tactic": "simp [translationNumber_pow f n]"
},
{
"state_after": "f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\nn : ℕ\n⊢ -((↑n + 1) * τ ↑f) = (-1 + -↑n) * τ ↑f",
"state... | [
755,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_anti_left | [
{
"state_after": "b c n : ℕ\nhc : 1 < c\nhb : c ≤ b\n⊢ n ≤ b ^ clog c n",
"state_before": "b c n : ℕ\nhc : 1 < c\nhb : c ≤ b\n⊢ clog b n ≤ clog c n",
"tactic": "rw [← le_pow_iff_clog_le (lt_of_lt_of_le hc hb)]"
},
{
"state_after": "no goals",
"state_before": "b c n : ℕ\nhc : 1 < c\nhb : c ≤ ... | [
347,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isTheta_exp_comp_exp_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx y z : ℝ\nl : Filter α\nf g : α → ℝ\n⊢ ((fun x => exp (f x)) =Θ[l] fun x => exp (g x)) ↔ IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => abs (f x - g x)",
"tactic": "simp only [isBoundedUnder_le_abs, ← isBoundedUnder_le_neg, neg_sub, IsTheta,... | [
378,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.le_zero | [] | [
401,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Iio_mem_atBot | [] | [
77,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Lattice.lean | sup_eq_maxDefault | [
{
"state_after": "case h.h\nα : Type u\nβ : Type v\ninst✝² : SemilatticeSup α\ninst✝¹ : DecidableRel fun x x_1 => x ≤ x_1\ninst✝ : IsTotal α fun x x_1 => x ≤ x_1\nx y : α\n⊢ x ⊔ y = maxDefault x y",
"state_before": "α : Type u\nβ : Type v\ninst✝² : SemilatticeSup α\ninst✝¹ : DecidableRel fun x x_1 => x ≤ x_... | [
905,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_sq_eq_def | [] | [
466,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_eq_iUnion | [] | [
1340,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Data/List/Basic.lean | List.take_take | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.159083\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn : ℕ\nl : List α\n⊢ take n (take 0 l) = take (min n 0) l",
"tactic": "rw [min_zero, take_zero, take_nil]"
},
{
"state_after": "no goals",
"state_before": "ι : Ty... | [
1955,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1950,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.t'_iij | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ : Category C'\nD : GlueData C\ni j : D.J\neq₁ : t' D i i j ≫ pullback.snd = pullback.fst ≫ t D i i\n⊢ t' D i i j = (pullbackSymmetry (f D i i) (f D i j)).hom",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ : Cat... | [
88,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.trivializationAt_continuousLinearMapAt | [] | [
808,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.diff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\nl₃ : List α\nh : l₁ <+ l₂\n⊢ List.diff l₁ (a :: l₃) <+ List.diff l₂ (a :: l₃)",
"tactic": "simp only [diff_cons, (h.erase _).diff_right]"
}
] | [
1543,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1541,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁹ : CommSemiring R\nl : Type ?u.2717466\nm : Type ?u.2717469\nn : Type u_1\ninst✝⁸ : Fintype n\ninst✝⁷ : Fintype m\ninst✝⁶ : DecidableEq n\nM₁ : Type u_3\nM₂ : Type ?u.2717493\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Mod... | [
811,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.continuous_toPouFun | [
{
"state_after": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\n⊢ LocallyFinite fun i => mulSupport fun x => 1 - ↑(toFun s f i) x",
"state_before": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\n⊢ Continuous (toP... | [
430,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.of_terminatedAt_iff_intFractPair_seq1_terminatedAt | [] | [
209,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Std/Data/Int/Lemmas.lean | Int.mem_toNat' | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ toNat' -[m+1] = some n ↔ -[m+1] = ↑n",
"tactic": "constructor <;> intro."
}
] | [
1410,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1408,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_smul | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
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] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_iUnion_of_directed | [
{
"state_after": "case pos\nι : Type u'\nι' : Type ?u.215590\nR : Type u_3\nK : Type ?u.215596\nM : Type u_2\nM' : Type ?u.215602\nM'' : Type ?u.215605\nV : Type u\nV' : Type ?u.215610\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Modu... | [
444,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.mem_roots_iff | [
{
"state_after": "R : Type u_1\nS : Type ?u.683267\nF : Type ?u.683270\nK : Type ?u.683273\nP : Cubic R\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nφ : R →+* S\ninst✝ : IsDomain R\nh0 : toPoly P ≠ 0\nx : R\n⊢ eval x (↑C P.a * X ^ 3 + ↑C P.b * X ^ 2 + ↑C P.c * X + ↑C P.d) = 0 ↔ P.a * x ^ 3 + P.b * x ^ 2 + P.c * x... | [
492,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_eq_sInf | [] | [
54,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.add_apply | [] | [
979,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Submodule.eq_top_of_disjoint | [
{
"state_after": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\ns t : Submodule K V\nhdim : finrank K { x // x ∈ s } + finrank K { x // x ∈ t } = finrank K V\nhdisjoint : Disjoint s t\nh_finrank_inf : finrank K { x // x ∈ s ⊓ t } = ... | [
800,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.mk_bit0 | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Fintype/Option.lean | Fintype.card_option | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
39,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/GroupTheory/Subgroup/Simple.lean | Subgroup.Normal.eq_bot_or_eq_top | [] | [
56,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.range_cos_infinite | [
{
"state_after": "⊢ Set.Infinite (Icc (-1) 1)",
"state_before": "⊢ Set.Infinite (range cos)",
"tactic": "rw [Real.range_cos]"
},
{
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"state_before": "⊢ Set.Infinite (Icc (-1) 1)",
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},
{
"state_after": "no goals"... | [
661,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | subalgebra_top_finrank_eq_submodule_top_finrank | [
{
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"state_before": "K : Type u\nV : Type v\nF : Type u_1\nE : Type u_2\ninst✝² : CommRing F\ninst✝¹ : ... | [
549,
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546,
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Mathlib/CategoryTheory/Abelian/Images.lean | CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison' | [
{
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124,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Order/BoundedOrder.lean | Ne.lt_top | [] | [
188,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_singleton | [] | [
76,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.lintegral_eq_of_tendsto | [] | [
388,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
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Mathlib/Algebra/DirectLimit.lean | Module.DirectedSystem.map_map | [] | [
84,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Logic/Basic.lean | iff_not_comm | [] | [
439,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Data/Real/GoldenRatio.lean | geom_gold_isSol_fibRec | [
{
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"state_before": "α : Type ?u.57955\ninst✝ : CommSemiring α\n⊢ LinearRecurrence.IsSolution fibRec fun x => φ ^ x",
"tactic": "rw [fibRec.geom_sol_iff_root_charPoly, fibRec_charPoly_eq]"
},
{
"state_after":... | [
200,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Order/CompleteLattice.lean | sInf_le_of_le | [] | [
224,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
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Mathlib/Algebra/Parity.lean | isSquare_inv | [
{
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170,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.finite_range | [] | [
81,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.eq_bot_or_top | [
{
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"state_before": "α : Type u\nβ : Type v\nK : Type u\ninst✝ : DivisionSemiring K\nI : Ideal K\n⊢ I = ⊥ ∨ I = ⊤",
"tactic": "rw [or_iff_not_imp_right]"
},
{
"state_after": "α : Type u\... | [
701,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.summable_of_eq_zero_or_self | [] | [
1170,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_le_range_sum_of_edist_le | [] | [
161,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasFDerivAtFilter.hasDerivAtFilter | [] | [
168,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm | [
{
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1401,
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1399,
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Mathlib/CategoryTheory/Opposites.lean | Quiver.Hom.unop_inj | [] | [
50,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_map | [
{
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1298,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.zero_re' | [] | [
151,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.eq | [] | [
77,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
18
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_add_nat_mul_two_pi | [] | [
279,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
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Mathlib/LinearAlgebra/Dimension.lean | exists_mem_ne_zero_of_rank_pos | [
{
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297,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
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Mathlib/Order/Cover.lean | Prod.mk_covby_mk_iff_left | [
{
"state_after": "no goals",
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"tactic": "simp_rw [covby_iff_wcovby_and_lt, mk_wcovby_mk_iff_left, mk_lt_mk_iff_left]"
}
] | [
529,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
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Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | conformal_id | [] | [
127,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_iUnion_eq' | [
{
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1684,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
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Mathlib/Deprecated/Group.lean | IsAddMonoidHom.isAddMonoidHom_mul_right | [] | [
239,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/Data/List/Cycle.lean | Cycle.Chain.imp | [
{
"state_after": "case H0\nα : Type u_1\nr : α → α → Prop\ns : Cycle α\nr₁ r₂ : α → α → Prop\nH : ∀ (a b : α), r₁ a b → r₂ a b\np : Chain r₁ Cycle.nil\n⊢ Chain r₂ Cycle.nil\n\ncase HI\nα : Type u_1\nr : α → α → Prop\ns : Cycle α\nr₁ r₂ : α → α → Prop\nH : ∀ (a b : α), r₁ a b → r₂ a b\na✝¹ : α\nl✝ : List α\na✝ :... | [
979,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
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Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.IsReflexivePair.swap | [] | [
117,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | normalizedFactorsEquivOfQuotEquiv_multiplicity_eq_multiplicity | [
{
"state_after": "R : Type u_1\nA : Type u_2\nK : Type ?u.1163688\ninst✝¹³ : CommRing R\ninst✝¹² : CommRing A\ninst✝¹¹ : Field K\ninst✝¹⁰ : IsDomain A\ninst✝⁹ : IsDedekindDomain A\nI : Ideal R\nJ : Ideal A\nB : Type ?u.1164225\ninst✝⁸ : CommRing B\ninst✝⁷ : IsDomain B\ninst✝⁶ : IsDedekindDomain B\nL✝ : Ideal B\... | [
1185,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_nonempty | [] | [
346,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Finset.prod_attach_univ | [
{
"state_after": "no goals",
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163,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.inner_map_self_eq_zero | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nE' : Type ?u.196495\nF : Type ?u.196498\nG : Type ?u.196501\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : NormedAddCommGroup G\ninst✝² : InnerProductSpac... | [
198,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
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Mathlib/Algebra/Homology/QuasiIso.lean | HomotopyEquiv.toQuasiIso | [
{
"state_after": "ι : Type u_3\nV : Type u\ninst✝¹³ : Category V\ninst✝¹² : HasZeroMorphisms V\ninst✝¹¹ : HasZeroObject V\ninst✝¹⁰ : HasEqualizers V\ninst✝⁹ : HasImages V\ninst✝⁸ : HasImageMaps V\ninst✝⁷ : HasCokernels V\nc : ComplexShape ι\nC✝ D✝ E : HomologicalComplex V c\nW : Type u_2\ninst✝⁶ : Category W\ni... | [
82,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | Subring.topologicalClosure_minimal | [] | [
264,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_le_of_le_comap | [] | [
282,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/GroupTheory/Coset.lean | mem_rightCoset | [] | [
90,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Analysis/Complex/Conformal.lean | isConformalMap_conj | [] | [
44,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_zero | [] | [
2900,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2900,
9
] |
Mathlib/Topology/UniformSpace/Basic.lean | isOpen_iff_ball_subset | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.58600\ninst✝ : UniformSpace α\ns : Set α\n⊢ (∀ (a : α), a ∈ s → s ∈ comap (Prod.mk a) (𝓤 α)) ↔ ∀ (x : α), x ∈ s → ∃ V, V ∈ 𝓤 α ∧ ball x V ⊆ s",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u... | [
720,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.eq_zero' | [] | [
347,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_mono_left | [] | [
1184,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
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Mathlib/Algebra/Regular/SMul.lean | isSMulRegular_of_group | [
{
"state_after": "R : Type u_2\nS : Type ?u.31171\nM : Type ?u.31174\na b : R\ns : S\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : MulAction G R\ng : G\nx y : R\nh : (fun x => g • x) x = (fun x => g • x) y\n⊢ x = y",
"state_before": "R : Type u_2\nS : Type ?u.31171\nM : Type ?u.31174\na b : R\ns : S\nG : Type u_... | [
241,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Deprecated/Subfield.lean | Univ.isSubfield | [] | [
60,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_mem_orthogonal | [] | [
357,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.equiv_apply | [] | [
1410,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_toOrderIso | [] | [
426,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.smul | [] | [
1327,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
11
] |
Mathlib/Dynamics/Minimal.lean | IsOpen.iUnion_preimage_smul | [] | [
82,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.Subtype.encode_eq | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.28657\nP : α → Prop\nencA : Encodable α\ndecP : DecidablePred P\nval✝ : α\nproperty✝ : P val✝\n⊢ encode { val := val✝, property := property✝ } = encode ↑{ val := val✝, property := property✝ }",
"state_before": "α : Type u_1\nβ : Type ?u.28657\nP : α → Pro... | [
428,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.inner_le_Lp_mul_Lq_tsum_of_nonneg' | [] | [
628,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.map_jacobson_of_surjective | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : Ideal R\nf : R →+* S\nhf : Function.Surjective ↑f\nh : RingHom.ker f ≤ I\n⊢ map f (jacobson I) = jacobson (map f I)",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : Ideal R\nf : R →+* S\nhf : Functi... | [
198,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.coprime_iff_not_dvd | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\npp : Prime p\nco : coprime p n\nd : p ∣ n\n⊢ p ∣ n * 1",
"tactic": "simp [d]"
}
] | [
546,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_preimage_toDual_iff | [] | [
185,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_ccos | [] | [
341,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.eventually_div_right_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.494359\nG : Type u_1\nH : Type ?u.494365\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableSpace H\ninst✝² : Group G\ninst✝¹ : MeasurableMul G\nμ : Measure G\ninst✝ : IsMulRightInvariant μ\nt : G\np : G → Prop\n⊢ (∀ᵐ (x : G) ∂μ, p (x / t)) ↔ ∀ᵐ (x : G... | [
336,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
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