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 |
|---|---|---|---|---|---|---|
Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.balance2 | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nl : RBNode α\nv : α\nr : RBNode α\nlv : All (fun x => cmpLT cmp x v) l\nvr : All (fun x => cmpLT cmp v x) r\nhl : Ordered cmp l\nhr : Ordered cmp r\n⊢ Ordered cmp\n (match l, v, r with\n | a, x, node red (node red b y c) z d => node red (node black a... | [
73,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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11
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Mathlib/Data/Option/NAry.lean | Option.map_map₂ | [
{
"state_after": "no goals",
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"tactic": "cases a <;> cases b <;> rfl"
}
] | [
94,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Algebra/Order/Floor.lean | Int.fract_fract | [] | [
952,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_of_fg_map | [] | [
229,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | Filter.Eventually.exists_measurable_mem_of_smallSets | [] | [
1711,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1707,
1
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Mathlib/Control/Traversable/Instances.lean | Option.comp_traverse | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα : Type u_1\nβ γ : Type u\nf : β → F γ\ng : α → G β\nx : Option α\n⊢ Option.traverse (Comp.mk ∘ (fun x x_1 => x <$> x_1) f ∘ g) x =... | [
43,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
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Mathlib/Analysis/Convex/Star.lean | starConvex_iff_forall_ne_pos | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.22483\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y z : E\ns : Set E\nhx : x ∈ s\n⊢ (∀ ⦃y : E⦄, y ∈ s → x ≠ y → ∀ ⦃a b : 𝕜⦄, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ ... | [
192,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_mul_zeta | [
{
"state_after": "case h\nn : ℕ\n⊢ ↑(Λ * ↑ζ) n = ↑log n",
"state_before": "⊢ Λ * ↑ζ = log",
"tactic": "ext n"
},
{
"state_after": "case h\nn : ℕ\n⊢ Real.log ↑n = ↑log n",
"state_before": "case h\nn : ℕ\n⊢ ↑(Λ * ↑ζ) n = ↑log n",
"tactic": "rw [coe_mul_zeta_apply, vonMangoldt_sum]"
},
... | [
128,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.min | [] | [
811,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
8
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Mathlib/Data/Fintype/Card.lean | Fintype.exists_ne_of_one_lt_card | [] | [
580,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Order/Heyting/Basic.lean | fst_compl | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_withDensity_eq_set_lintegral_mul_non_measurable₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1813525\nγ : Type ?u.1813528\nδ : Type ?u.1813531\nm m0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ns : Set α\nhf : AEMeasurable f\ng : α → ℝ≥0∞\nhs : MeasurableSet s\nh'f : ∀ᵐ (x : α) ∂Measure.restrict μ s, f x < ⊤\n⊢ (∫⁻ (a : α)... | [
1891,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1887,
1
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.ae_inf_principal_eq_mk | [] | [
68,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.max | [] | [
536,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
8
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | deriv_circleMap | [] | [
199,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.eq_rpow_one_div_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0\nz : ℝ\nhz : z ≠ 0\n⊢ x = y ^ (1 / z) ↔ x ^ z = y",
"tactic": "rw [← rpow_eq_rpow_iff hz, rpow_self_rpow_inv hz]"
}
] | [
259,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_from_zero | [
{
"state_after": "no goals",
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"tactic": "ext"
}
] | [
387,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.coe_trans | [] | [
908,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.le_card_support_of_mem_cycleType | [] | [
309,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_eq_of_bijective | [] | [
61,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.not_isBoundedUnder_of_tendsto_atTop | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.10574\nι : Type ?u.10577\nr : α → α → Prop\nf✝ g : Filter α\ninst✝² : Preorder β\ninst✝¹ : NoMaxOrder β\nf : α → β\nl : Filter α\ninst✝ : NeBot l\nhf : Tendsto f l atTop\nb : β\nhb : ∀ᶠ (x : β) in map f l, (fun x x_1 => x ≤ x_1) x b\n⊢ False"... | [
134,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_zpow | [] | [
741,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le | [
{
"state_after": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nF : Type ?u.59306\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\n𝕜 : Type u_2\nG : Type u_3\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → G\nC... | [
474,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/LinearAlgebra/Dual.lean | Module.Dual.eval_apply | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Measurable.const_sup | [] | [
116,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.constr_self | [] | [
646,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Computability/Partrec.lean | Computable.nat_rec | [
{
"state_after": "α : Type u_2\nβ : Type ?u.175913\nγ : Type ?u.175916\nσ : Type u_1\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → ℕ\ng : α → σ\nh : α → ℕ × σ → σ\nhf : Computable f\nhg : Computable g\nhh : Computable₂ h\na : α\n⊢ Nat.rec (Part.some (g a... | [
670,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Std/Classes/Order.lean | Std.TransCmp.le_lt_trans | [] | [
65,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
64,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeft_injective | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : Ring A\ninst✝¹ : Algebra R A\ninst✝ : NoZeroDivisors A\nx : A\nhx : x ≠ 0\nthis : Nontrivial A := { exists_pair_ne := Exists.intro x (Exists.intro 0 hx) }\n⊢ Function.Injective ↑(mulLeft R x)",
"state_before": "R : Type u_2\nA :... | [
242,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | Commute.mul_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na b : α\nh : Commute a b\nn : ℕ\n⊢ (a * b) ^ ↑n = a ^ ↑n * b ^ ↑n",
"tactic": "simp [zpow_ofNat, h.mul_pow n]"
},
{
... | [
375,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
11
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.hcomp_apply | [
{
"state_after": "no goals",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ x₂ x₃ : X\np₀ q₀ : Path x₀ x₁\np₁ q₁ : Path x₁ x₂\nF : Homotopy p₀ q₀\nG : Homotopy p₁ q₁\nx : ↑I × ↑I\n⊢ (if ↑x.snd ≤ 1 / 2 then extend (eval F x.fst) (2 * ↑x.snd) else exten... | [
186,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.compStarAlgHom'_comp | [] | [
1039,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.arrows_ext | [
{
"state_after": "case mk.mk\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nS R : Sieve X\narrows✝ : Presieve X\ndownward_closed✝¹ : ∀ {Y Z : C} {f : Y ⟶ X}, arrows✝ f → ∀ (g : Z ⟶ Y), arrows✝ (g ≫ f)\ndownward_closed✝ :\n ∀ {Y Z : C} {f : Y ⟶ X},\n { ar... | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.forall_fin_two | [] | [
1768,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1767,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.cos_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ cos θ ≠ 0 ↔ ∀ (k : ℤ), θ ≠ (2 * ↑k + 1) * π / 2",
"tactic": "rw [← not_exists, not_iff_not, cos_eq_zero_iff]"
}
] | [
217,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isRegular_of_ne_zero | [] | [
373,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_mono | [] | [
62,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/FieldTheory/Laurent.lean | RatFunc.laurent_algebraMap | [] | [
96,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/CompleteLattice.lean | monotone_sSup_of_monotone | [] | [
1810,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1809,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_swap_iff | [] | [
716,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_rec₁ | [] | [
588,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_mem_diff_of_mem | [] | [
1803,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1803,
1
] |
Mathlib/Data/List/Count.lean | List.countp_true | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\np q : α → Bool\n⊢ countp (fun x => true) l = length l",
"tactic": "simp"
}
] | [
132,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | rotation_apply | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_singleton | [
{
"state_after": "case intro.intro.intro\nf : StieltjesFunction\na : ℝ\nu : ℕ → ℝ\nu_mono : StrictMono u\nu_lt_a : ∀ (n : ℕ), u n < a\nu_lim : Tendsto u atTop (𝓝 a)\n⊢ ↑↑(StieltjesFunction.measure f) {a} = ofReal (↑f a - leftLim (↑f) a)",
"state_before": "f : StieltjesFunction\na : ℝ\n⊢ ↑↑(StieltjesFunctio... | [
544,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.171901\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedS... | [
266,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_mod_iff | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\nh : k ∣ n\nthis : k ∣ ?m.40585 h ↔ k ∣ ?m.40585 h + n * (m / n)\n⊢ k ∣ m % n ↔ k ∣ m",
"tactic": "rwa [mod_add_div] at this"
}
] | [
694,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
692,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.fst_mul | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Sigma/Order.lean | Sigma.mk_lt_mk_iff | [] | [
78,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_le_self_iff | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\n⊢ sinh x ≤ x ↔ sinh x - x ≤ sinh 0 - 0",
"tactic": "simp"
}
] | [
771,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.tendsto_abs_cocompact_atTop | [] | [
244,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.symm | [] | [
62,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Data/Finset/Order.lean | Directed.finset_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nr : α → α → Prop\ninst✝ : IsTrans α r\nι : Type u_1\nhι : Nonempty ι\nf : ι → α\nD : Directed r f\ns : Finset ι\nz x✝ : ι\n⊢ x✝ ∈ 0 → r (f x✝) (f z)",
"tactic": "simp"
}
] | [
29,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_zero | [] | [
96,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.cancel_iso_inv_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : Y ≅ X\ng g' : Y ⟶ Z\n⊢ f.inv ≫ g = f.inv ≫ g' ↔ g = g'",
"tactic": "simp only [cancel_epi]"
}
] | [
544,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.MeasurePreserving.prod | [] | [
657,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
11
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.a_mul_xa | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.symm_apply_eq | [] | [
437,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.one_apply | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.coeff_toPowerSeries | [] | [
1154,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | Conformal.conformalAt | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_of_isUnit | [
{
"state_after": "case intro\nl : Type ?u.158331\nm : Type ?u.158334\nn : Type u_2\no : Type ?u.158340\nR : Type u_1\nm_fin : Fintype m\ninst✝⁴ : Fintype n\ninst✝³ : Fintype o\ninst✝² : CommRing R\ninst✝¹ : StrongRankCondition R\ninst✝ : DecidableEq n\nA : (Matrix n n R)ˣ\n⊢ rank ↑A = Fintype.card n",
"stat... | [
104,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_one | [] | [
112,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | ContinuousWithinAt.const_smul | [] | [
93,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
8
] |
Mathlib/Topology/ContinuousOn.lean | eventuallyEq_nhdsWithin_iff | [] | [
431,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/CategoryTheory/Preadditive/Yoneda/Projective.lean | CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nP : C\n⊢ Functor.PreservesEpimorphisms (coyoneda.obj P.op) ↔ Functor.PreservesEpimorphisms (preadditiveCoyoneda.obj P.op)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nP : C\n⊢ Projective P ↔ Functor.Prese... | [
43,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.eq_of_right | [] | [
139,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist_le | [] | [
220,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.polynomial_comp_attachBound_mem | [
{
"state_after": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf : { x // x ∈ A }\ng : ℝ[X]\n⊢ ↑(↑(Polynomial.aeval f) g) ∈ A",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf : { x // x ∈ A }\ng ... | [
89,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/Calculus/ExtendDeriv.lean | has_deriv_at_interval_right_endpoint_of_tendsto_deriv | [
{
"state_after": "case intro.intro\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.126473\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set ℝ\ne : E\na : ℝ\nf : ℝ → E\nf_diff : DifferentiableOn ℝ f s\nf_lim : ContinuousWithinAt f s a\nhs : s ∈ 𝓝[Iio a] a\nf_li... | [
178,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_div_iff_mul_le | [
{
"state_after": "case top\nα : Type ?u.280595\nβ : Type ?u.280598\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh0✝ : b ≠ 0 ∨ c ≠ 0\nht✝ : b ≠ ⊤ ∨ c ≠ ⊤\nh0 : ⊤ ≠ 0 ∨ c ≠ 0\nht : ⊤ ≠ ⊤ ∨ c ≠ ⊤\n⊢ a ≤ c / ⊤ ↔ a * ⊤ ≤ c\n\ncase coe\nα : Type ?u.280595\nβ : Type ?u.280598\na b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\nh0✝ : b✝ ≠ 0 ∨ c ≠ 0\nht✝ ... | [
1571,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
11
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_mul_toMatrix_flip | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type u_2\nκ : Type ?u.628277\nκ' : Type ?u.628280\nR : Type u_3\nM : Type u_4\ninst✝⁹ : CommSemiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\nR₂ : Type ?u.628473\nM₂ : Type ?u.628476\ninst✝⁶ : CommRing R₂\ninst✝⁵ : AddCommGroup M₂\nin... | [
257,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.symm_comp_eq | [] | [
446,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Expr.of_cancel_le | [
{
"state_after": "ctx : Context\na b c d : Expr\nh : Poly.cancel (toNormPoly a) (toNormPoly b) = (toPoly c, toPoly d)\nthis : Poly.denote_le ctx (Poly.cancel (toNormPoly a) (toNormPoly b)) = Poly.denote_le ctx (toNormPoly a, toNormPoly b)\n⊢ (denote ctx a ≤ denote ctx b) = (denote ctx c ≤ denote ctx d)",
"s... | [
551,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
547,
1
] |
Mathlib/Data/List/OfFn.lean | List.nthLe_ofFn' | [] | [
83,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.iInf_toSubfield | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_3\ninst✝¹ : Field E\ninst✝ : Algebra F E\nι : Sort u_1\nS : ι → IntermediateField F E\n⊢ ↑(toSubfield (iInf S)) = ↑(⨅ (i : ι), toSubfield (S i))",
"tactic": "simp [iInf]"
}
] | [
176,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Hom.map_fun | [] | [
536,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.cond | [
{
"state_after": "case false\nα : Type u_1\nβ : Type ?u.10031\nγ : Type ?u.10034\nδ : Type ?u.10037\nδ' : Type ?u.10040\nι : Sort ?u.10043\ns t u : Set α\nm : MeasurableSpace α\ns₁ s₂ : Set α\nh₁ : MeasurableSet s₁\nh₂ : MeasurableSet s₂\n⊢ MeasurableSet (bif false then s₁ else s₂)\n\ncase true\nα : Type u_1\nβ... | [
235,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
11
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_iUnion | [] | [
257,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.int_cyclotomic_rw | [
{
"state_after": "n : ℕ\nh : n ≠ 0\n⊢ map (Int.castRingHom ℤ)\n (Exists.choose\n (_ : ∃ P, map (Int.castRingHom ℂ) P = cyclotomic' n ℂ ∧ degree P = degree (cyclotomic' n ℂ) ∧ Monic P)) =\n Exists.choose (_ : ∃ P, map (Int.castRingHom ℂ) P = cyclotomic' n ℂ ∧ degree P = degree (cyclotomic' n ℂ) ∧ ... | [
265,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.zmodEquivZpowers_apply_coe_nat | [
{
"state_after": "M : Type ?u.2907804\nN : Type ?u.2907807\nG : Type ?u.2907810\nR : Type u_1\nS : Type ?u.2907816\nF : Type ?u.2907819\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ninst✝¹ : DivisionCommMonoid G\nk l : ℕ\ninst✝ : CommRing R\nζ : Rˣ\nh : IsPrimitiveRoot ζ k\ni : ℕ\nthis : ↑i = ↑↑i\n⊢ ↑(zmodEqui... | [
715,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.count_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.48922\nδ : Type ?u.48925\na✝ : α\ns t : Multiset α\nf✝ g : α → Multiset β\ninst✝ : DecidableEq α\nm : Multiset β\nf : β → Multiset α\na : α\n⊢ count a (sum (map f 0)) = sum (map (fun b => count a (f b)) 0)",
"tactic": ... | [
204,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.pow_eq_pow_iff | [] | [
945,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.valuation_p | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nh : 1 < ↑p\n⊢ valuation ↑p = 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ valuation ↑p = 1",
"tactic": "have h : (1 : ℝ) < p := by exact_mod_cast (Fact.out : p.Prime).one_lt"
},
{
"state_after": "case refine'_1\np : ℕ\nhp : Fact (Nat.Pr... | [
1071,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.ceil_map_map_zero_le | [] | [
480,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.sub_add_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.193543\nγ : Type ?u.193546\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na b : α\ns t : Multiset α\n⊢ s - t + t ∩ s = s",
"state_before": "α : Type u_1\nβ : Type ?u.193543\nγ : Type ?u.193546\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na b : α\ns t : Multiset α\... | [
1900,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1895,
1
] |
Mathlib/Topology/Connected.lean | connectedComponent_eq_singleton | [] | [
1320,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
9
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_two_zero | [
{
"state_after": "R : Type u_1\nS : Type ?u.114565\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nk : ℕ\na : R\n⊢ 3 - ↑2 = 1",
"state_before": "R : Type u_1\nS : Type ?u.114565\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nk : ℕ\na : R\n⊢ dickson 2 0 0 = X ^ 0",
"tactic": "simp only [dickson_zero, pow_zero]"
}... | [
115,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_sub' | [] | [
104,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Computability/Partrec.lean | Computable.pred | [] | [
326,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_mono | [
{
"state_after": "F : Type ?u.9302\nι : Type ?u.9305\nα : Type u_1\nβ : Type ?u.9311\ninst✝ : OrderedRing α\nm n : ℤ\nh : m ≤ n\n⊢ (fun x => ↑x) m ≤ (fun x => ↑x) n",
"state_before": "F : Type ?u.9302\nι : Type ?u.9305\nα : Type u_1\nβ : Type ?u.9311\ninst✝ : OrderedRing α\n⊢ Monotone fun x => ↑x",
"tac... | [
119,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ext | [] | [
112,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.dvd_map_of_isScalarTower' | [
{
"state_after": "A : Type ?u.57254\nB : Type ?u.57257\ninst✝¹³ : Field A\ninst✝¹² : Ring B\ninst✝¹¹ : Algebra A B\nx : B\nR : Type u_1\nS : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Field K\ninst✝⁷ : CommRing L\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra R K\ninst✝⁴ ... | [
99,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.log_stirlingSeq_bounded_aux | [
{
"state_after": "d : ℝ := ∑' (k : ℕ), 1 / ↑(succ k) ^ 2\n⊢ ∃ c, ∀ (n : ℕ), Real.log (stirlingSeq 1) - Real.log (stirlingSeq (succ n)) ≤ c",
"state_before": "⊢ ∃ c, ∀ (n : ℕ), Real.log (stirlingSeq 1) - Real.log (stirlingSeq (succ n)) ≤ c",
"tactic": "let d := ∑' k : ℕ, ↑1 / (k.succ:ℝ) ^ 2"
},
{
... | [
177,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.iff_is_const | [] | [
183,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_consecutive | [] | [
70,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.projIcc_val | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.8882\ninst✝ : LinearOrder α\na b : α\nh : a ≤ b\nx val✝ : α\nproperty✝ : val✝ ∈ Icc a b\n⊢ projIcc a b h ↑{ val := val✝, property := property✝ } = { val := val✝, property := property✝ }",
"state_before": "α : Type u_1\nβ : Type ?u.8882\ninst✝ : LinearOrde... | [
80,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_coe | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nR : Type ?u.88276\nM : Type u_1\nσ : Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddCommMonoid M\ninst✝² : SetLike σ M\ninst✝¹ : AddSubmonoidClass σ M\nℳ : ι → σ\ninst✝ : Decomposition ℳ\ni : ι\nx : { x // x ∈ ℳ i }\n⊢ ↑(decompose ℳ) ↑x = ↑(of (fun ... | [
113,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.norm_indicatorConstLp' | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.691352\nG : Type ?u.691355\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs : MeasurableSet s\nhμs : ↑↑μ s ≠ ⊤\nc : E\nhp_pos ... | [
767,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Balanced.le_size | [
{
"state_after": "α : Type u_1\nt : RBNode α\nc : RBColor\nn✝ n : Nat\nx✝ y✝ : RBNode α\nv✝ : α\nhl : Balanced x✝ black n\nhr : Balanced y✝ black n\n⊢ 2 ^ n + 2 ^ n ≤ size x✝ + 1 + (size y✝ + 1)",
"state_before": "α : Type u_1\nt : RBNode α\nc : RBColor\nn✝ n : Nat\nx✝ y✝ : RBNode α\nv✝ : α\nhl : Balanced x... | [
81,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
73,
1
] |
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