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/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.injective_of_mono_of_preservesPullback | [] | [
165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_coe_mem_lie | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
111,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.sqrt_normSq_eq_norm | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5321595\ninst✝ : IsROrC K\nz : K\n⊢ Real.sqrt (↑normSq z) = ‖z‖",
"tactic": "rw [normSq_eq_def', Real.sqrt_sq (norm_nonneg _)]"
}
] | [
536,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.Monic.normalize_eq_self | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizationMonoid R\np : R[X]\nhp : Monic p\n⊢ ↑normalize p = p",
"tactic": "simp only [Polynomial.coe_normUnit, normalize_apply, hp.leadingCo... | [
106,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_inv | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nf : Cauchy abs\n⊢ { cauchy := f⁻¹ } = Real.inv' { cauchy := f }",
"tactic": "rw [inv']"
}
] | [
141,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.one_ne_coe | [] | [
161,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
src/lean/Init/Prelude.lean | Nat.succ_pos | [] | [
1609,
17
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1608,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.coeff_neg | [] | [
78,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.tendsto_iff_rtendsto' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl₁ : Filter α\nl₂ : Filter β\nf : α → β\n⊢ Tendsto f l₁ l₂ ↔ RTendsto' (Function.graph f) l₁ l₂",
"tactic": "simp [tendsto_def, Function.graph, rtendsto'_def, Rel.preimage_def, Set.preimage]"
}
] | [
205,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.coe_top | [] | [
776,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.differentiableAt_rpow_of_ne | [] | [
307,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.even_card_of_char_two | [] | [
517,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measurableSet_Ioi | [
{
"state_after": "f : StieltjesFunction\nc : ℝ\nt : Set ℝ\n⊢ length f (t ∩ Ioi c) + length f (t \\ Ioi c) ≤ length f t",
"state_before": "f : StieltjesFunction\nc : ℝ\n⊢ MeasurableSet (Ioi c)",
"tactic": "refine OuterMeasure.ofFunction_caratheodory fun t => ?_"
},
{
"state_after": "f : Stieltjes... | [
467,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Order/WellFounded.lean | WellFounded.lt_sup | [] | [
97,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
11
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.norm | [] | [
693,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.truncateAugment_inv_f | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.279314\nE : Type u_1\nF : Type ?u.279320\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝³ : CompleteSpace E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : PartialOrder α... | [
664,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_toEquiv | [] | [
328,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
9
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.symm' | [] | [
86,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/List/Basic.lean | List.surjective_head' | [] | [
867,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.emetric_ball_top | [] | [
1225,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.hasStrictDerivAt_const_rpow_of_neg | [
{
"state_after": "no goals",
"state_before": "x✝ y z a x : ℝ\nha : a < 0\n⊢ HasStrictDerivAt (fun x => a ^ x) (a ^ x * log a - exp (log a * x) * sin (x * π) * π) x",
"tactic": "simpa using (hasStrictFDerivAt_rpow_of_neg (a, x) ha).comp_hasStrictDerivAt x\n ((hasStrictDerivAt_const _ _).prod (hasStrictD... | [
338,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Topology/Basic.lean | closure_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ closure (sᶜ) = interior sᶜ",
"tactic": "simp [closure_eq_compl_interior_compl]"
}
] | [
557,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_le_of_le_toReal | [] | [
2089,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2087,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor_cancel_right | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ lxor' (lxor' m n) n = m",
"tactic": "rw [lxor'_assoc, lxor'_self, lxor'_zero]"
}
] | [
244,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_mul | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ (a + b) * c = a * c + b * c",
"tactic": "simp [Int.mul_comm, Int.mul_add]"
}
] | [
459,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
458,
11
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.natCast_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6224464\ninst✝ : IsROrC K\nn : ℕ\n⊢ ↑re ↑n = ↑n",
"tactic": "rw [← ofReal_natCast, ofReal_re]"
}
] | [
636,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_neg | [] | [
243,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Order/Filter/Extr.lean | isMinOn_const | [] | [
193,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/Hom/Basic.lean | WithTop.toDualBotEquiv_symm_coe | [] | [
1291,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1289,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Equalizers.lean | CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nG : C ⥤ D\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\nw : f ≫ h = g ≫ h\ninst✝³ : HasCoequalizer f g\ninst✝² : HasCoequalizer (G.map f) (G.map g)\ninst✝¹ : PreservesColimit (parallelPair f g) G\nX' Y' :... | [
227,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.sup_mem_closed_subalgebra | [
{
"state_after": "case h.e'_5\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nh : IsClosed ↑A\nf g : { x // x ∈ A }\n⊢ A = Subalgebra.topologicalClosure A",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X,... | [
163,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Functor.leftAdjoint_of_isEquivalence | [] | [
671,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Algebra/Field/Basic.lean | one_div_neg_eq_neg_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.23152\nβ : Type ?u.23155\nK : Type u_1\ninst✝¹ : DivisionMonoid K\ninst✝ : HasDistribNeg K\na✝ b a : K\n⊢ 1 / -a = 1 / (-1 * a)",
"tactic": "rw [neg_eq_neg_one_mul]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.23152\n... | [
105,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Subsingleton.antivary | [] | [
120,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Data/Matrix/DMatrix.lean | DMatrix.sub_apply | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mul'_apply | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arctan_eq_arccos | [
{
"state_after": "x : ℝ\nh : 0 ≤ x\n⊢ arcsin (x / sqrt (↑1 + x ^ 2)) = arcsin (sqrt (1 - (sqrt (↑1 + x ^ 2))⁻¹ ^ 2))\n\nx : ℝ\nh : 0 ≤ x\n⊢ 0 ≤ (sqrt (↑1 + x ^ 2))⁻¹",
"state_before": "x : ℝ\nh : 0 ≤ x\n⊢ arctan x = arccos (sqrt (↑1 + x ^ 2))⁻¹",
"tactic": "rw [arctan_eq_arcsin, arccos_eq_arcsin]"
},
... | [
196,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Quot.lean | Quotient.sound' | [] | [
770,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.foldr_induction | [] | [
1444,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
1
] |
Mathlib/Data/List/Basic.lean | List.map_congr | [
{
"state_after": "ι : Type ?u.130134\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf g : α → β\na : α\nl : List α\nh : ∀ (x : α), x ∈ a :: l → f x = g x\nh₁ : f a = g a\nh₂ : ∀ (x : α), x ∈ l → f x = g x\n⊢ map f (a :: l) = map g (a :: l)",
"state_before": "ι : Type ?u.130134\nα : Type u\... | [
1778,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1774,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.one_succAbove_succ | [
{
"state_after": "n✝ m n : ℕ\nj : Fin n\nthis : ↑(succAbove (succ 0)) (succ j) = succ (↑(succAbove 0) j)\n⊢ ↑(succAbove 1) (succ j) = succ (succ j)",
"state_before": "n✝ m n : ℕ\nj : Fin n\n⊢ ↑(succAbove 1) (succ j) = succ (succ j)",
"tactic": "have := succ_succAbove_succ 0 j"
},
{
"state_after"... | [
2247,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2244,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.continuousAt_arcsin | [] | [
105,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_of_not_bddAbove | [] | [
1607,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Algebra/Star/Pi.lean | Pi.star_def | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_nonneg | [] | [
84,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.comp_eq_of_eq | [] | [
911,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_coev | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.41809\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Set α\nsc : IsCompact s\nu : Set (β × α)\nuo : IsOpen u\n⊢ IsOpen (coev α β ⁻¹' CompactOpen.gen s u)",
"state_before": "α :... | [
343,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Control/LawfulFix.lean | Pi.uncurry_curry_continuous | [] | [
283,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Topology/Order/Basic.lean | TFAE_mem_nhdsWithin_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na b : α\nh : a < b\ns : Set α\n⊢ TFAE\n [s ∈ 𝓝[Iic b] b, s ∈ 𝓝[Icc a b] b, s ∈ 𝓝[Ioc a b] b, ∃ l, l ∈ Ico a b ∧ Ioc l b ⊆ s, ∃ l, l ∈ Iio b ∧ ... | [
1809,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformGroup_sInf | [] | [
225,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Memℒp.induction_dense | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.3350178\nι : Type ?u.3350181\nE : Type u_2\nF : Type ?u.3350187\n𝕜 : Type ?u.3350190\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf✝ : α → E\nμ : Measure α\nP : (α → E) → Prop\nh1P : ∀ (f g : α → E), P f → P g → P (f + g)\nh2P : ∀ (f : α → E),... | [
1071,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_inter_of_pos | [] | [
1764,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Order/Heyting/Basic.lean | top_himp | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.29794\nα : Type u_1\nβ : Type ?u.29800\ninst✝ : GeneralizedHeytingAlgebra α\na b✝ c d b : α\n⊢ b ≤ ⊤ ⇨ a ↔ b ≤ a",
"tactic": "rw [le_himp_iff, inf_top_eq]"
}
] | [
378,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.upperSemicontinuousAt | [] | [
816,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.mem_disjSum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ns : Multiset α\nt : Multiset β\ns₁ s₂ : Multiset α\nt₁ t₂ : Multiset β\na : α\nb : β\nx : α ⊕ β\n⊢ x ∈ disjSum s t ↔ (∃ a, a ∈ s ∧ inl a = x) ∨ ∃ b, b ∈ t ∧ inr b = x",
"tactic": "simp_rw [disjSum, mem_add, mem_map]"
}
] | [
54,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Real/Basic.lean | Real.le_def' | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ x y : ℝ\n⊢ Real.le x y ↔ x < y ∨ x = y",
"tactic": "rw [le_def]"
}
] | [
356,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.iff_id_eq_zero | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type u'\ninst✝¹ : Category D\ninst✝ : HasZeroMorphisms C\nX : C\nh : 𝟙 X = 0\nY : C\nf : X ⟶ Y\n⊢ 0 = default",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u'\ninst✝¹ : Category D\ninst✝ : HasZeroMorphisms C\nX : C\nh : 𝟙 X = 0\nY : C\n... | [
194,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_zipWith | [] | [
592,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuousOn_aeval | [] | [
97,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
11
] |
Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsFractionRing.isFractionRing_of_isLocalization | [
{
"state_after": "R : Type u_3\ninst✝¹¹ : CommRing R\nM : Submonoid R\nS✝ : Type ?u.661559\ninst✝¹⁰ : CommRing S✝\ninst✝⁹ : Algebra R S✝\nP : Type ?u.661815\ninst✝⁸ : CommRing P\nS : Type u_1\nT : Type u_2\ninst✝⁷ : CommRing S\ninst✝⁶ : CommRing T\ninst✝⁵ : Algebra R S\ninst✝⁴ : Algebra R T\ninst✝³ : Algebra S ... | [
293,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.le_of_le_of_eq | [] | [
753,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp_toGerm | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.444612\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ng : β → γ\nhg : Continuous g\nf✝ : α →ₘ[μ] β\nf : α → β\nx✝ : AEStron... | [
392,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.sub_const | [] | [
333,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
8
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_eq_zero_of_trim_eq_zero | [] | [
4381,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4380,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | pow_sub_of_lt | [
{
"state_after": "case inl\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nm✝ n✝ m n : ℕ\nh : n < m\n⊢ 0 ^ (m - n) = 0 ^ m * (0 ^ n)⁻¹\n\ncase inr\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\na✝ : G₀\nm✝ n✝ : ℕ\na : G₀\nm n : ℕ\nh : n < m\nha : a ≠ 0\n⊢ a ^ (m - n) = a ^ m * (a ^ n)⁻¹",
"state_before": "G₀ :... | [
37,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.continuous | [] | [
477,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
11
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | posTangentConeAt_univ | [] | [
111,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_add_infiniteNeg | [] | [
569,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_Ico_of_ae_eq | [] | [
165,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.optionEquivSumPUnit_none | [] | [
425,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_isLUB | [] | [
204,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | Filter.HasBasis.uniformity_of_nhds_one | [
{
"state_after": "α : Type u_2\nβ : Type ?u.173356\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\nι : Sort u_1\np : ι → Prop\nU : ι → Set α\nh : HasBasis (𝓝 1) p U\n⊢ HasBasis (Filter.comap (fun x => x.snd / x.fst) (𝓝 1)) p fun i => {x | x.snd / x.fst ∈ U i}",
"state_before": "α : Typ... | [
343,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | SetLike.homogeneous_zero_submodule | [] | [
347,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_smul | [
{
"state_after": "case a.h\nl : Type ?u.54869\nm : Type ?u.54872\nn : Type u_2\no : Type ?u.54878\nm' : o → Type ?u.54883\nn' : o → Type ?u.54888\nR : Type u_1\nS : Type ?u.54894\nα : Type v\nβ : Type w\nγ : Type ?u.54901\ninst✝³ : DecidableEq n\ninst✝² : Monoid R\ninst✝¹ : AddMonoid α\ninst✝ : DistribMulAction... | [
485,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_map | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.toFun_eq_coe | [] | [
591,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.log_b_ne_zero | [
{
"state_after": "case b_ne_zero\nb x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\n⊢ b ≠ 0\n\nb x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\nb_ne_zero : b ≠ 0\n⊢ log b ≠ 0",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\n⊢ log b ≠ 0",
"tactic": "have b_ne_zero : b ≠ 0"
},
{
"state_after": ... | [
87,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
9
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nN : α → Type u_2\ninst✝² : DecidableEq α\ninst✝¹ : (a : α) → DecidableEq (N a)\ninst✝ : (a : α) → Zero (N a)\nf g : Π₀ (a : α), N a\n⊢ neLocus f g = neLocus g f",
"tactic": "simp_rw [neLocus, Finset.union_comm, ne_comm]"
}
] | [
71,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.map_polynomial_aeval_of_nonempty | [
{
"state_after": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : IsAlgClosed 𝕜\na : A\np : 𝕜[X]\nhnon : Set.Nonempty (σ a)\n✝ : Nontrivial A\n⊢ σ (↑(aeval a) p) = (fun k => eval k p) '' σ a",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² :... | [
132,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | exists_dist_le_lt | [
{
"state_after": "𝕜 : Type ?u.210210\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y✝ z : E\nδ ε : ℝ\nhδ : 0 ≤ δ\nhε : 0 < ε\nh : dist x z < ε + δ\ny : E\nhy : dist x y = δ / (ε + δ) * dist x z ∧ dist y z = ε / (ε + δ) * dist x ... | [
187,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.norm_comp_le | [
{
"state_after": "𝕜 : Type u_1\nR : Type ?u.276372\nV : Type u_3\nW : Type u_4\nW₂ : Type u_2\nP : Type ?u.276384\nQ : Type ?u.276387\nQ₂ : Type ?u.276390\ninst✝¹⁶ : NormedAddCommGroup V\ninst✝¹⁵ : MetricSpace P\ninst✝¹⁴ : NormedAddTorsor V P\ninst✝¹³ : NormedAddCommGroup W\ninst✝¹² : MetricSpace Q\ninst✝¹¹ : ... | [
250,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.add_one_le_ceil_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.209172\nα : Type u_1\nβ : Type ?u.209178\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ z + 1 ≤ ⌈a⌉ ↔ ↑z < a",
"tactic": "rw [← lt_ceil, add_one_le_iff]"
}
] | [
1112,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mk_eq | [] | [
684,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_lt_left_iff_lt | [] | [
96,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.sub_const | [] | [
544,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
8
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.5703\nα : Type u_1\nβ : Type ?u.5709\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\n⊢ 0 ≤ a⁻¹ ↔ 0 ≤ a",
"tactic": "simp only [le_iff_eq_or_lt, inv_pos, zero_eq_inv]"
}
] | [
61,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.one | [] | [
120,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ | [
{
"state_after": "n : ℕ\nh₁ : 0 < 4 * (↑n + 1) ^ 2\n⊢ Real.log (stirlingSeq (succ n)) - Real.log (stirlingSeq (succ (succ n))) ≤ 1 / (4 * ↑(succ n) ^ 2)",
"state_before": "n : ℕ\n⊢ Real.log (stirlingSeq (succ n)) - Real.log (stirlingSeq (succ (succ n))) ≤ 1 / (4 * ↑(succ n) ^ 2)",
"tactic": "have h₁ : ↑... | [
153,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eq_of_eq_on_source_univ | [] | [
1005,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.pow_eq_on_of_mem_support | [
{
"state_after": "case zero\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : ∀ (x : α), x ∈ support f ∩ support g → ↑f x = ↑g x\n⊢ ∀ (x : α), x ∈ support f ∩ support g → ↑(f ^ Nat.zero) x = ↑(g ^ Nat.zero) x\n\ncase succ\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : ... | [
391,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Associates.prod_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37103\nγ : Type ?u.37106\nδ : Type ?u.37109\ninst✝ : CommMonoid α\np : Multiset (Associates α)\n⊢ Multiset.prod 0 = 1 ↔ ∀ (a : Associates α), a ∈ 0 → a = 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before... | [
133,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.comap_injective_of_surjective | [] | [
628,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.comap_fst | [
{
"state_after": "case h.mk\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.298370\nM₆ : Type ?u.298373\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R ... | [
563,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.EventuallyEq.prod_map | [] | [
175,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_filter_not | [] | [
118,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | List.prod_toFinset | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.887074\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\nM : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CommMonoid M\nf : α → M\nx✝ : Nodup []\n⊢ Finset.prod (toFinset []) f = prod (map f [])",
"tactic": "simp"
},
{... | [
2046,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2041,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.exists_mem_basis | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.44090\nE : Type u_3\nF : Type ?u.44096\nG : Type ?u.44099\nE' : Type ?u.44102\nF' : Type u_4\nG' : Type ?u.44108\nE'' : Type ?u.44111\nF'' : Type ?u.44114\nG'' : Type ?u.44117\nR : Type ?u.44120\nR' : Type ?u.44123\n𝕜 : Type ?u.44126\n... | [
238,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_mono | [] | [
209,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.prod | [] | [
1520,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
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