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/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_mul_spanSingleton | [
{
"state_after": "case a\nR : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1334398\ninst✝³ : CommRing R₁\nK : Type ?u.1334404\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx y : P\n⊢ (fun ... | [
1370,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_tsum | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF : Type ?u.1336054\n𝕜 : Type ?u.1336057\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : Nor... | [
1500,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1472,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.derivWithin_integral_right | [] | [
937,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | RingHom.charZero_iff | [
{
"state_after": "R : Type u_1\nS : Type u_2\ninst✝¹ : NonAssocSemiring R\ninst✝ : NonAssocSemiring S\nϕ : R →+* S\nhϕ : Function.Injective ↑ϕ\nhR : CharZero R\na b : ℕ\nh : ↑a = ↑b\n⊢ a = b",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : NonAssocSemiring R\ninst✝ : NonAssocSemiring S\nϕ : R →+* S\n... | [
198,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.inv_add | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ a₂ : ℕ\n⊢ ↑(a₁ + a₂) = ↑a₁ + ↑a₂",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ : ℕ\nb₁ : R\na₂ : ℕ\nb₂ : R\nx✝¹ : ↑a₁ =... | [
894,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_one | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ Real.one.cauchy = 1",
"tactic": "rw [one_def]"
}
] | [
149,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/Constructions.lean | continuous_sigma | [] | [
1533,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_mono | [] | [
1116,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.linearIndependent_extend | [] | [
1327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.inv_re | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ z⁻¹.re = z.re / ↑normSq z",
"tactic": "simp [inv_def, division_def, ofReal']"
}
] | [
739,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | IsClosed.isComplete | [] | [
450,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_iSup | [] | [
943,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Order/Disjoint.lean | isCompl_iff | [] | [
461,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_exp | [] | [
208,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/RingTheory/Noetherian.lean | monotone_stabilizes_iff_noetherian | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\nP : Type ?u.119271\nN : Type w\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\n⊢ (∀ (f : ℕ →o Submodule R M), ∃ n, ∀ (m ... | [
355,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_equiv | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfg : f ≈ g\nhf : f ≈ 0\nhg : g ≈ 0\n⊢ norm f = norm g",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfg : f ≈ g\nhf : f ≈ 0\n⊢ norm f = norm g",
"tactic": "have hg : g ≈ 0 := Setoid.trans (Setoid.symm hfg) hf"
... | [
369,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.lt_add_one | [
{
"state_after": "x : PartENat\nhx : x ≠ ⊤\n⊢ 0 < 1",
"state_before": "x : PartENat\nhx : x ≠ ⊤\n⊢ x < x + 1",
"tactic": "rw [PartENat.lt_add_iff_pos_right hx]"
},
{
"state_after": "no goals",
"state_before": "x : PartENat\nhx : x ≠ ⊤\n⊢ 0 < 1",
"tactic": "norm_cast"
}
] | [
487,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.differentiableOn_arccos | [] | [
184,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.zero_contLinear | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/LocallyConvex/AbsConvex.lean | nhds_basis_abs_convex | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.8459\nG : Type ?u.8462\nι : Type ?u.8465\ns✝ : Set E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : Module ℝ E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : LocallyConvexSpace ℝ E\ni... | [
66,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/Associated.lean | Prime.dvd_of_dvd_pow | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.3519\nγ : Type ?u.3522\nδ : Type ?u.3525\ninst✝ : CommMonoidWithZero α\np : α\nhp✝ hp : Prime p\na : α\nn : ℕ\nh✝ : p ∣ a ^ n\nh : p ∣ a ^ Nat.zero\n⊢ p ∣ a\n\ncase succ\nα : Type u_1\nβ : Type ?u.3519\nγ : Type ?u.3522\nδ : Type ?u.3525\ninst✝ : CommMonoid... | [
63,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_comap | [] | [
1916,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_of_one_lt_of_le | [
{
"state_after": "b n : ℕ\nh : 1 < b\nhn : b ≤ n\n⊢ (if h : b ≤ n ∧ 1 < b then\n let_fun this := (_ : n / b < n);\n log b (n / b) + 1\n else 0) =\n log b (n / b) + 1",
"state_before": "b n : ℕ\nh : 1 < b\nhn : b ≤ n\n⊢ log b n = log b (n / b) + 1",
"tactic": "rw [log]"
},
{
"stat... | [
67,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_mul_right_right | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd n (n * m) = n",
"tactic": "rw [gcd_comm, gcd_mul_right_left]"
}
] | [
159,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
158,
9
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | iter_deriv_zpow' | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\ns : Set 𝕜\nm✝ m : ℤ\n⊢ ((deriv^[Nat.zero]) fun x => x ^ m) = fun x => (∏ i in Finset.range Nat.zero, (↑m - ↑i)) * x ^ (m - ↑Nat.zero)\n\ncase succ\n𝕜 : Ty... | [
119,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/RelClasses.lean | subset_iff_ssubset_or_eq | [] | [
800,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.26255\nι : Type ?u.26258\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ ball x 0 = ∅",
"tactic": "rw [ball_eq_empty]"
}
] | [
443,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_sup' | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.697599\nG' : Type ?u.697602\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.697611\ninst✝² : AddGroup A\nN : Type ?u.697617\ninst✝¹ : Group N\nC : Type u_1\ninst✝ : CommGroup C\ns t : Subgroup C\nx : C\n⊢ (∃ y, y ∈ s ∧ ∃ z, z ∈ t ∧ y * z = x) ↔ ∃ y... | [
3513,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3512,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_lt | [] | [
711,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_congr | [] | [
212,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.ext | [] | [
218,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousComponent_C_mul | [
{
"state_after": "no goals",
"state_before": "σ : Type u_2\nτ : Type ?u.308829\nR : Type u_1\nS : Type ?u.308835\ninst✝ : CommSemiring R\nn✝ : ℕ\nφ ψ : MvPolynomial σ R\nn : ℕ\nr : R\n⊢ ↑(homogeneousComponent n) (↑C r * φ) = ↑C r * ↑(homogeneousComponent n) φ",
"tactic": "simp only [C_mul', LinearMap.ma... | [
288,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic.eval_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\nq : R\nn : ℕ\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\n⊢ eval (↑f q) (cyclotomic n S) = ↑f (eval q (cyclotomic n R))",
"tactic": "rw [← map_cyclotomic n f, eval_map, eval₂_at_apply]"
}
] | [
302,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Complex/ExponentialBounds.lean | Real.log_two_near_10 | [
{
"state_after": "⊢ Abs.abs (log 2 - 287209 / 414355) ≤ 1 / 17179869184 + (1 / 10 ^ 10 - 1 / 2 ^ 34)",
"state_before": "⊢ Abs.abs (log 2 - 287209 / 414355) ≤ 1 / 10 ^ 10",
"tactic": "suffices |log 2 - 287209 / 414355| ≤ 1 / 17179869184 + (1 / 10 ^ 10 - 1 / 2 ^ 34) by\n norm_num1 at *\n assumption"
}... | [
71,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.mkAlgHom_coe | [
{
"state_after": "R : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\ns : A → A → Prop\n⊢ ↑{\n toRingHom :=\n {\n toMonoidHom :=\n {\n ... | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_swap | [
{
"state_after": "α : Type u_1\nα' : Type ?u.4456049\nβ : Type u_2\nβ' : Type ?u.4456055\nγ : Type ?u.4456058\nE : Type ?u.4456061\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
514,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.tendsto_left_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.69837\nι : Sort u_2\nι' : Sort ?u.69843\nla : Filter α\npa : ι → Prop\nsa : ι → Set α\nlb : Filter β\npb : ι' → Prop\nsb : ι' → Set β\nf : α → β\nhla : HasBasis la pa sa\n⊢ (∀ (t : Set β), t ∈ lb → ∃ i, pa i ∧ sa i ⊆ f ⁻¹' t) ↔ ∀ (t : Set β), t ∈ lb → ∃ ... | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Data/Set/Basic.lean | Set.compl_empty | [] | [
1660,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1659,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.not_liftRel_inl_inr | [] | [
405,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Homology/Additive.lean | CochainComplex.single₀MapHomologicalComplex_inv_app_zero | [] | [
442,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.eval_map | [
{
"state_after": "S : Type uᵒᵖ ⥤ Type u\nα β : Type u\nf : β ⟶ α\ns : S.obj α.op\nx : β\n⊢ S.map ((↾fun x_1 => x) ≫ f).op s = S.map (↾fun x_1 => f x).op s",
"state_before": "S : Type uᵒᵖ ⥤ Type u\nα β : Type u\nf : β ⟶ α\ns : S.obj α.op\nx : β\n⊢ eval S β (S.map f.op s) x = eval S α s (f x)",
"tactic": ... | [
135,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommProd_cons' | [
{
"state_after": "case h\nF : Type ?u.11255\nι : Type ?u.11258\nα : Type u_1\nβ : Type ?u.11264\nγ : Type ?u.11267\nf : α → β → β\nop : α → α → α\ninst✝¹ : Monoid α\ninst✝ : Monoid β\ns✝ : Multiset α\na : α\ncomm✝ : Set.Pairwise {x | x ∈ a ::ₘ s✝} Commute\ns : List α\ncomm : Set.Pairwise {x | x ∈ a ::ₘ Quotient... | [
166,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_le_iff | [] | [
357,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/CategoryTheory/Abelian/InjectiveResolution.lean | CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX : C\nI J : InjectiveResolution X\n⊢ I.ι ≫ (homotopyEquiv I J).hom = J.ι",
"tactic": "simp [homotopyEquiv]"
}
] | [
183,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.zero_mul_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.587676\nα : Type u_1\nβ : Type ?u.587682\nγ : Type ?u.587685\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : MulZeroClass α\ns✝ t s : Finset α\n⊢ 0 * s ⊆ 0",
"tactic": "simp [subset_iff, mem_mul]"
}
] | [
1094,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.revAt_add | [
{
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ici_sup | [] | [
1135,
25
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1134,
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.compLinearMap_apply | [] | [
553,
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551,
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_iUnion | [] | [
732,
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Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.surjective_of_epi_of_preservesPushout | [] | [
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59
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179,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.connectedComponentEquiv_trans | [
{
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Mathlib/Computability/Primrec.lean | Primrec.of_equiv_symm_iff | [
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317,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_eq_map | [
{
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Mathlib/LinearAlgebra/Dual.lean | LinearMap.range_dualMap_eq_dualAnnihilator_ker | [] | [
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64
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Std/Data/Nat/Gcd.lean | Nat.lcm_zero_left | [
{
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185,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_isTrail_iff_of_injective | [
{
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Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsEulerian.card_odd_degree | [
{
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172,
7
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Mathlib/Analysis/InnerProductSpace/Basic.lean | orthonormal_iUnion_of_directed | [
{
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Mathlib/Topology/Maps.lean | Embedding.tendsto_nhds_iff | [] | [
241,
33
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.map_target | [] | [
216,
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Mathlib/Order/Ideal.lean | Order.Ideal.IsProper.not_mem_of_compl_mem | [
{
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{
"state_after": "P : ... | [
500,
31
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496,
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.mk_add | [] | [
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Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero | [
{
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192,
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182,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_opposite_image_mul_preimage' | [
{
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242,
38
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Mathlib/Data/Complex/Exponential.lean | Real.sum_le_exp_of_nonneg | [
{
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1471,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_update_zero | [
{
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] | [
1120,
43
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1119,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.gc | [] | [
767,
69
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Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_injective_left | [] | [
148,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.toLin_restrict_ker_eq_inf_orthogonal | [
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_def | [] | [
526,
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525,
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Mathlib/Order/SuccPred/Limit.lean | Order.IsPredLimit.isMin | [
{
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{
"state_after": "no... | [
292,
40
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Mathlib/Algebra/Order/Group/Abs.lean | lt_abs | [] | [
69,
13
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_top | [
{
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Mathlib/Dynamics/FixedPoints/Basic.lean | Function.IsFixedPt.preimage_iterate | [
{
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Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.zero_eq' | [
{
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Mathlib/Data/List/Lattice.lean | List.inter_eq_nil_iff_disjoint | [
{
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183,
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181,
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.lieSpan_eq_bot_iff | [
{
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Mathlib/Topology/Algebra/Star.lean | continuousWithinAt_star | [] | [
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37
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_mul_le_of_nonneg_left | [] | [
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45
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423,
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Mathlib/Data/Finmap.lean | Finmap.insert_singleton_eq | [
{
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] | [
543,
75
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542,
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Mathlib/Data/PEquiv.lean | PEquiv.symm_bot | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_anti | [] | [
878,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
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src/lean/Init/Data/Array/Basic.lean | Array.reverse.termination | [
{
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{
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634,
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Mathlib/Topology/Order/Basic.lean | Icc_mem_nhdsWithin_Iic | [] | [
586,
65
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585,
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Mathlib/Algebra/GroupPower/Lemmas.lean | zsmul_int_one | [
{
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] | [
621,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
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Mathlib/Logic/Basic.lean | forall_eq_apply_imp_iff | [
{
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810,
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Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.isLocalization_of_submonoid_le | [
{
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245,
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209,
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Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_sep | [
{
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978,
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] |
Mathlib/Algebra/GCDMonoid/Basic.lean | GCDMonoid.irreducible_iff_prime | [] | [
896,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | RingHom.FinitePresentation.id | [] | [
424,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.not_tendsto_pow_atTop_atBot | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.212695\nι' : Type ?u.212698\nα : Type u_1\nβ : Type ?u.212704\nγ : Type ?u.212707\ninst✝ : LinearOrderedRing α\n⊢ ¬Tendsto (fun x => x ^ 0) atTop atBot",
"tactic": "simp [not_tendsto_const_atBot]"
}
] | [
989,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
src/lean/Init/Data/Nat/Gcd.lean | Nat.gcd_one_left | [
{
"state_after": "n : Nat\n⊢ gcd 0 (succ 0) = 1",
"state_before": "n : Nat\n⊢ gcd 1 n = 1",
"tactic": "rw [gcd_succ, mod_one]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ gcd 0 (succ 0) = 1",
"tactic": "rfl"
}
] | [
28,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
26,
9
] |
Mathlib/Data/Nat/PSub.lean | Nat.ppred_eq_pred | [] | [
100,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.of_mul_monic_right | [
{
"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]\nhq : Monic q\nhpq : ¬Monic p\n⊢ ¬Monic (p * q)",
"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]\nhq : Monic q\nhpq : Monic (p * q)\n⊢ Monic p",
... | [
149,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing | [] | [
222,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.restrictNonposSeq_disjoint' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.36768\ninst✝³ : MeasurableSpace α\nM : Type ?u.36774\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns : SignedMeasure α\ni j : Set α\nn m : ℕ\nh : n < m\n⊢ ∀ (x : α),\n ¬x ∈ MeasureTheory.SignedMeasure.restrictNonposSeq s i ... | [
218,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
9
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_eq_self | [] | [
2849,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2847,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.comp_apply | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/List/Basic.lean | List.foldlM_cons | [] | [
2799,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2797,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_eq_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10593\nγ : Type ?u.10596\nδ : Type ?u.10599\nι : Type ?u.10602\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t s : Set α\n⊢ ↑↑μ s = ⨅ (t : Set α) (_ : s ⊆ t) (_ : MeasurableSet t), ↑↑μ t",
"tactic": "rw [measure_eq_trim,... | [
159,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
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