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/PrincipalIdealDomain.lean | gcd_dvd_iff_exists | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : GCDMonoid R\na b z : R\n⊢ gcd a b ∣ z ↔ ∃ x y, z = a * x + b * y",
"tactic": "simp_rw [mul_comm a, mul_comm b, @eq_comm _ z, ← Ideal.mem_span_pair, ← s... | [
379,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Init/Data/Int/Basic.lean | Int.natAbs_add_nonneg | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ 0 ≤ ofNat n → 0 ≤ ofNat m → natAbs (ofNat n + ofNat m) = natAbs (ofNat n) + natAbs (ofNat m)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "x✝ : ℤ\nn : ℕ\n⊢ 0 ≤ x✝ → 0 ≤ -[n+1] → natAbs (x✝ + -[n+1]) = natAbs x✝ + ... | [
139,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_zero | [
{
"state_after": "⊢ 0 ≤ alephIdx 0",
"state_before": "⊢ aleph' 0 = 0",
"tactic": "rw [← nonpos_iff_eq_zero, ← aleph'_alephIdx 0, aleph'_le]"
},
{
"state_after": "no goals",
"state_before": "⊢ 0 ≤ alephIdx 0",
"tactic": "apply Ordinal.zero_le"
}
] | [
199,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.sizeOf_lt_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\ninst✝ : SizeOf α\nas : List α\nh : a ∈ as\n⊢ sizeOf a < sizeOf as",
"tactic": "induction h with\n| head => simp_arith\n| tail _ _ ih => exact Nat.lt_trans ih (by simp_arith)"
},
{
"state_after": "no goals",
"state_before": "c... | [
122,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
119,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_attach | [] | [
1503,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Data/Part.lean | Part.some_inj | [] | [
222,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.IsTransitive.union | [
{
"state_after": "x y z : ZFSet\nhx : IsTransitive x\nhy : IsTransitive y\n⊢ IsTransitive (⋃₀ {x, y})",
"state_before": "x y z : ZFSet\nhx : IsTransitive x\nhy : IsTransitive y\n⊢ IsTransitive (x ∪ y)",
"tactic": "rw [← sUnion_pair]"
},
{
"state_after": "x y z : ZFSet\nhx : IsTransitive x\nhy : ... | [
87,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Topology/Order/Basic.lean | left_nhdsWithin_Ioo_neBot | [] | [
2438,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2437,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalCore_le | [
{
"state_after": "G : Type u_1\nG' : Type ?u.448898\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.448907\ninst✝ : AddGroup A\ns : Set G\nH : Subgroup G\na : G\nh : a ∈ normalCore H\n⊢ 1 * a * 1⁻¹ ∈ H",
"state_before": "G : Type u_1\nG' : Type ?u.448898\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.4... | [
2540,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2538,
1
] |
Mathlib/Data/List/Range.lean | List.mem_finRange | [
{
"state_after": "case mk\nα : Type u\nn val✝ : ℕ\nisLt✝ : val✝ < n\n⊢ { val := ↑{ val := val✝, isLt := isLt✝ }, isLt := (_ : ↑{ val := val✝, isLt := isLt✝ } < n) } =\n { val := val✝, isLt := isLt✝ }",
"state_before": "α : Type u\nn : ℕ\na : Fin n\n⊢ { val := ↑a, isLt := (_ : ↑a < n) } = a",
"tactic"... | [
143,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.analyticAt_bilinear | [] | [
118,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.id_comp | [] | [
407,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Nat/Parity.lean | Function.Involutive.iterate_bit1 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α\nn✝ : ℕ\nhf : Involutive f\nn : ℕ\n⊢ f^[bit1 n] = f",
"tactic": "rw [bit1, ←succ_eq_add_one, iterate_succ, hf.iterate_bit0, comp.left_id]"
}
] | [
306,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.AEStronglyMeasurable.prod_swap | [
{
"state_after": "α : Type u_2\nα' : Type ?u.2385081\nβ : Type u_3\nβ' : Type ?u.2385087\nγ✝ : Type ?u.2385090\nE : Type ?u.2385093\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MeasurableSpace α'\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : MeasurableSpace β'\ninst✝⁴ : MeasurableSpace γ✝\nμ μ' : Measure α\nν ν' : Measure β\n... | [
185,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
8
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.mul_inv_cancel | [] | [
2159,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2158,
11
] |
Mathlib/Data/Set/NAry.lean | Set.mem_image3 | [] | [
234,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.pow_iff | [] | [
219,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\nm n : ZNum\n⊢ ↑m = ↑n ↔ m = n",
"tactic": "rw [← cast_to_int m, ← cast_to_int n, Int.cast_inj (α := α), to_int_inj]"
}
] | [
1417,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_univ_iff | [] | [
716,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.coe_mulLeft | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.t2Space_of_one_sep | [
{
"state_after": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nH : ∀ (x : G), x ≠ 1 → ∃ U, U ∈ 𝓝 1 ∧ ¬x ∈ U\n⊢ ∀ (a : G), a ∈ {1}ᶜ → {1}ᶜ ∈ 𝓝 a",
"state_before": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nH ... | [
726,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Topology/Bases.lean | Set.Finite.isSeparable | [] | [
417,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_symm_monoidOf | [] | [
1730,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1728,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_single_of_mem | [
{
"state_after": "ι : Type ?u.371468\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\na : α\nh : a ∈ s\nh₀ : ∀ (b : α), b ∈ s → b ≠ a → f b = 1\nthis : DecidableEq α\n⊢ ∏ x in s, f x = f a",
"state_before": "ι : Type ?u.371468\nβ ... | [
796,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_rw₁ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.948452\nδ : Type ?u.948455\nm : MeasurableSpace α\nμ ν : Measure α\nf f' : α → β\nh✝ : f =ᵐ[μ] f'\ng : β → ℝ≥0∞\na : α\nh : f a = f' a\n⊢ g (f a) = g (f' a)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.948452\nδ : Type ?u.948455\nm : Me... | [
760,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_le_card | [] | [
621,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_equiv_eq_comap_symm | [] | [
711,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.Not_isLeft | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.6982\nδ : Type ?u.6985\nx y : α ⊕ β\n⊢ ¬isLeft x = true ↔ isRight x = true",
"tactic": "simp"
}
] | [
133,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_add_of_distinct_val | [] | [
807,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_self_ne_one | [] | [
118,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
115,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_div_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1226326\n𝕜 : Type ?u.1226329\nα : Type ?u.1226332\nι : Type ?u.1226335\nκ : Type ?u.1226338\nE : Type u_1\nF : Type ?u.1226344\nG : Type ?u.1226347\ninst✝¹ : NormedGroup E\ninst✝ : NormedGroup F\na b : E\n⊢ ‖a / b‖ = 0 ↔ a = b",
"tactic": "rw [... | [
1989,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1989,
1
] |
Std/Logic.lean | or_or_distrib_right | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ (a ∨ b) ∨ c ↔ (a ∨ c) ∨ b ∨ c",
"tactic": "rw [or_or_or_comm, or_self]"
}
] | [
285,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
285,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | CauchySeq.inv | [] | [
463,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.mem_prod_iff_right | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.15882\nδ : Type ?u.15885\nι : Sort ?u.15888\ns✝ : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\ns : Set (α × β)\nf : Filter α\ng : Filter β\n⊢ (∃ t, t ∈ g ∧ ∀ᶠ (y : α) in f, ∀ (x : β), x ∈ t → (x, y) ∈ (fun p => (p.snd, p.fst)) ⁻¹' s) ↔\n ∃ t, t ∈ g... | [
267,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | ContDiffWithinAt.sqrt | [] | [
170,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.trivializationAt_coordChange_eq | [] | [
833,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.cast_card_eq_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nR : Type ?u.404199\ninst✝¹ : Field K\ninst✝ : Fintype K\n⊢ ↑q = 0",
"tactic": "simp"
}
] | [
169,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.149272\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard s ≤ 1 ↔ ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a = b",
"tactic": "simp_rw [ncard_eq_toFinset_card _ hs, Finset.card_le_one, Finite.mem_toFinse... | [
663,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Order/Lattice.lean | Pi.inf_def | [] | [
1025,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_dvd_iff | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nφ : MvPowerSeries σ R\n⊢ (∀ (m : σ →₀ ℕ), ↑m s < 1 → ↑(coeff R m) φ = 0) ↔ ∀ (m : σ →₀ ℕ), ↑m s = 0 → ↑(coeff R m) φ = 0",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nφ : MvPowerSeries σ R\n⊢ X s ∣ φ ↔ ∀ (m ... | [
799,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_biUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.7851\ns✝ : Set α\ninst✝ : Bornology α\ns : Set ι\nf : ι → Set α\nhs : Set.Finite s\n⊢ IsBounded (⋃ (i : ι) (_ : i ∈ s), f i) ↔ ∀ (i : ι), i ∈ s → IsBounded (f i)",
"tactic": "simp only [← isCobounded_compl_iff, compl_i... | [
286,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.totalEquiv_apply_coe | [] | [
768,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Order/Circular.lean | Btw.btw.cyclic_left | [] | [
170,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.ringHom_ext' | [] | [
1834,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_one_right | [
{
"state_after": "i : ℤ\n⊢ Nat.lcm (natAbs i) (natAbs 1) = natAbs i",
"state_before": "i : ℤ\n⊢ lcm i 1 = natAbs i",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "no goals",
"state_before": "i : ℤ\n⊢ Nat.lcm (natAbs i) (natAbs 1) = natAbs i",
"tactic": "apply Nat.lcm_one_right"
}
] | [
474,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneReducible.trans | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable γ\np : α → Prop\nq : β → Prop\nr : γ → Prop\nf : α → β\nc₁ : Computable f\nh₁ : ∀ (a : α), p a ↔ q (f a)\ng : β → γ\nc₂ : Computable g\nh₂ : ∀ (a : β), q a ↔ r (g a)\na : α\nh : p a\n⊢... | [
65,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.union | [] | [
471,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le_mulIndicator | [] | [
816,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableAt_neg_iff | [
{
"state_after": "no goals",
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434,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_iso_comp | [
{
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201,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.contLinear_eq_zero_iff_exists_const | [
{
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122,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.id_left | [] | [
326,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add_nat | [
{
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}
] | [
334,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.congr_of_eventuallyEq_insert | [] | [
460,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
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Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_continuousOn_iff | [] | [
406,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_mul_left_right | [
{
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"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH : IsCoprime (x * y) z\n⊢ IsCoprime y z",
"tactic": "rw [mul_comm] at H"
},
{
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136,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Analysis/Convex/Between.lean | Wbtw.trans_left_ne | [
{
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508,
35
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505,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.mul_pos | [] | [
996,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
11
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Mathlib/Data/List/Destutter.lean | List.destutter'_cons_neg | [
{
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}
] | [
57,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Order/Filter/Basic.lean | Filter.map_id | [] | [
1857,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1856,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_le_of_left_le | [
{
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"state_before": "ι : Type ... | [
346,
52
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342,
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Mathlib/Data/Set/Sups.lean | Set.infs_nonempty | [] | [
271,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_mul_of_neg_right | [
{
"state_after": "no goals",
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"tactic": "simpa only [mul_neg, neg_lt_neg_iff] using mul_lt_mul_of_pos_right h (neg_pos_of_neg hc)"
}
] | [
695,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.map_id | [] | [
408,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
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Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.integrable_comp_mul_left_iff | [
{
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}
] | [
163,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.mul_lt_sin | [
{
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"tactic": "rw [← inv_div]"
},
{
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244,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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Std/Data/List/Lemmas.lean | List.length_eq_one | [
{
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}
] | [
54,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
53,
1
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Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comap_eq_id_of_eq_id | [
{
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90,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAlt_neg | [] | [
1005,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.map_add_right_Ico | [
{
"state_after": "α : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ map (fun x => c + x) (Ico a b) = Ico (c + a) (c + b)",
"state_before": "α : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFi... | [
316,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
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Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.convergents_stable_of_terminated | [
{
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"tactic": "simp only [convergents, denominators_stable_of_terminated n_le_m terminate... | [
91,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.map_nhdsWithin_eq | [] | [
387,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_c_eq_zero' | [] | [
439,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.surjective | [] | [
998,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
11
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_concat | [
{
"state_after": "no goals",
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"... | [
62,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/LinearAlgebra/Ray.lean | SameRay.sameRay_comm | [] | [
103,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Init/Algebra/Order.lean | le_of_not_ge | [] | [
304,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.toConjAct_ofConjAct | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/CategoryTheory/Linear/Yoneda.lean | CategoryTheory.whiskering_linearCoyoneda | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq' | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.871897\ninst✝ : CommMonoid P\nf : LocalizationMap S N\na₁ b₁ : M\na₂ b₂ : { x // x ∈ S }\n⊢ mk' f a₁ a₂ = mk' f b₁ b₂ ↔ ↑(Localization.r S) (a₁, a₂) (b₁, b₂)",... | [
794,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
11
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff_eq_sdiff_union | [] | [
1593,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1593,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.represents_iff' | [
{
"state_after": "case mp\nι : Type u_1\ninst✝⁴ : Fintype ι\nM : Type u_3\ninst✝³ : AddCommGroup M\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : DecidableEq ι\nA : Matrix ι ι R\nf : Module.End R M\n⊢ Represents b A f → ∀ (j : ι)... | [
116,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.smul_def | [] | [
899,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
11
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Mathlib/Data/Set/Function.lean | Set.mapsTo_singleton | [] | [
400,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.of_isBigO_im_re_pow | [
{
"state_after": "l : Filter ℂ\nhre : Tendsto re l atTop\nn : ℕ\nhr : im =O[l] fun z => z.re ^ n\n⊢ im =O[l] fun z => z.re ^ ↑n",
"state_before": "l : Filter ℂ\nhre : Tendsto re l atTop\nn : ℕ\nhr : im =O[l] fun z => z.re ^ ↑n\n⊢ im =O[l] fun z => z.re ^ ↑n",
"tactic": "norm_cast at hr"
},
{
"st... | [
77,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_inj | [] | [
265,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_snd_neBot_iff | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.268461\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : Filter β\nhα : IsEmpty α\n⊢ NeBot (comap Prod.snd f) ↔ Nonempty α ∧ NeBot f\n\ncase inr\nα : Type u\nβ : Type v\nγ : Type w\nδ... | [
2393,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2389,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_fin_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n : ℕ\na : Fin m → α\nb : Fin n → α\n⊢ ofFn (Fin.append a b) = ofFn a ++ ofFn b",
"tactic": "simp_rw [ofFn_add, Fin.append_left, Fin.append_right]"
}
] | [
163,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/Complex/Conformal.lean | isConformalMap_complex_linear_conj | [] | [
72,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_zero | [] | [
350,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.sub_mem | [] | [
275,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.foldr_induction' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.132443\nf : α → β → β\nH : LeftCommutative f\nx : β\nq : α → Prop\np : β → Prop\nhpqf : ∀ (a : α) (b : β), q a → p b → p (f a b)\npx : p x\n⊢ ∀ (s : Multiset α), (∀ (a : α), a ∈ s → q a) → p (foldr f H x s)",
"state_before": "α : Type u_1\nβ : Type u... | [
1438,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
1
] |
Mathlib/NumberTheory/Fermat4.lean | not_fermat_42 | [
{
"state_after": "a b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nh : a ^ 4 + b ^ 4 = c ^ 2\n⊢ False",
"state_before": "a b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a ^ 4 + b ^ 4 ≠ c ^ 2",
"tactic": "intro h"
},
{
"state_after": "case intro.intro.intro.intro.intro\na b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nh : a ^ 4 + b ^ ... | [
310,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_union | [] | [
1543,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1542,
1
] |
Mathlib/Order/Max.lean | not_isMin | [] | [
351,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.coe_top | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.coe_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9518\nf✝ : α ↪ β\ns✝ : Finset α\nf : α ↪ β\ns : Finset α\n⊢ ∀ (x : β), x ∈ ↑(map f s) ↔ x ∈ ↑f '' ↑s",
"tactic": "simp only [mem_coe, mem_map, Set.mem_image, implies_true]"
}
] | [
105,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictFDerivAt_exp | [] | [
184,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.insert_infty_range_coe | [] | [
127,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Sigma/Interval.lean | Sigma.card_Ico | [] | [
68,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
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