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/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_OrderAddMonoidHom_id | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Multiset/Pi.lean | Multiset.Pi.cons_same | [] | [
44,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_zero | [
{
"state_after": "no goals",
"state_before": "⊢ sign 0 = 0",
"tactic": "rw [sign, if_neg (lt_irrefl _), if_neg (lt_irrefl _)]"
}
] | [
46,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.derivFamily_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.166484\nr : α → α → Prop\nι : Type u\nf : ι → Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nhι : (#ι) < c\nhc' : c ≠ ℵ₀\nhf : ∀ (i : ι) (b : Ordinal), b < ord c → f i b < ord c\na : Ordinal\n⊢ lift (#ι) < c",
"tactic": "rwa [lift_id]"
}
] | [
1185,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Data/List/Basic.lean | List.replicate_left_injective | [] | [
485,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Order/Chain.lean | subset_succChain | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9526\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\nh : ¬(IsChain r s ∧ ∃ x, SuperChain r s x)\n⊢ s ⊆ SuccChain r s",
"state_before": "α : Type u_1\nβ : Type ?u.9526\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\nh : ¬∃ t, IsChain r s ∧ SuperChai... | [
190,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Function.lean | Set.eqOn_refl | [] | [
205,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.nnabs_of_nonneg | [
{
"state_after": "case a\nx : ℝ\nh : 0 ≤ x\n⊢ ↑(↑nnabs x) = ↑(toNNReal x)",
"state_before": "x : ℝ\nh : 0 ≤ x\n⊢ ↑nnabs x = toNNReal x",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nx : ℝ\nh : 0 ≤ x\n⊢ ↑(↑nnabs x) = ↑(toNNReal x)",
"tactic": "rw [coe_toNNReal ... | [
1068,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | List.norm_prod_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.110463\nγ : Type ?u.110466\nι : Type ?u.110469\ninst✝ : SeminormedRing α\na : α\nx✝ : [a] ≠ []\n⊢ ‖prod [a]‖ ≤ prod (map norm [a])",
"tactic": "simp"
},
{
"state_after": "α : Type u_1\nβ : Type ?u.110463\nγ : Type ?u.110466\... | [
320,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_one | [
{
"state_after": "case inl\nι : Type ?u.798449\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\nf : α → Prop\ninst✝ : DecidablePred f\nhf : Set.PairwiseDisjoint (↑s) f\na : β\nh : ∃ i, i ∈ s ∧ f i\n⊢ (∏ i in s, if f i then a else 1) = a\n\ncase inr\nι : Type ... | [
1691,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_closedBall_mul | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1994959\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
452,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | Complex.isPrimitiveRoot_exp_of_coprime | [
{
"state_after": "i n : ℕ\nh0 : n ≠ 0\nhi : Nat.coprime i n\n⊢ exp (2 * ↑π * I * (↑i / ↑n)) ^ n = 1 ∧ ∀ (l : ℕ), exp (2 * ↑π * I * (↑i / ↑n)) ^ l = 1 → n ∣ l",
"state_before": "i n : ℕ\nh0 : n ≠ 0\nhi : Nat.coprime i n\n⊢ IsPrimitiveRoot (exp (2 * ↑π * I * (↑i / ↑n))) n",
"tactic": "rw [IsPrimitiveRoot.... | [
52,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.edist_le_of_fixedPoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\nhf : ContractingWith K f\nx y : α\nh : edist x y ≠ ⊤\nhy : IsFixedPt f y\n⊢ edist x y ≤ edist x (f x) / (1 - ↑K)",
"tactic": "simpa only [hy.eq, edist_self, add_zero] using hf.ed... | [
82,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_def' | [] | [
147,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.isPrenex_toPrenexImp | [
{
"state_after": "case of_isQF\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.138402\nP : Type ?u.138405\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.138433\nn l : ℕ\nφ✝¹ ψ✝¹ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv : ... | [
850,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Std/Logic.lean | decide_eq_false_iff_not | [] | [
525,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
524,
9
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfDom_comp | [] | [
1534,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.someExistsOneDivLT_measurableSet | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.7479\ninst✝³ : MeasurableSpace α\nM : Type ?u.7485\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns : SignedMeasure α\ni j : Set α\nhi : ¬restrict s i ≤ restrict 0 i\n⊢ MeasurableSet (MeasureTheory.SignedMeasure.someE... | [
153,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
9
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_one | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\n⊢ Tendsto (fun n => (↑1^[n]) 0 / ↑n) atTop (𝓝 0)",
"tactic": "simp [tendsto_const_nhds]"
}
] | [
713,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.perm_factors_mul | [
{
"state_after": "case refine'_1\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ prod (factors a ++ factors b) = a * b\n\ncase refine'_2\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ ∀ (p : ℕ), p ∈ factors a ++ factors b → Prime p",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ factors (a * b) ~ factors a ++ factors b",
... | [
207,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_iff_tendsto | [] | [
318,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.prod_smul | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : ι → Type u_2\ninst✝³ : (i : ι) → Monoid (M i)\nN : Type ?u.466820\ninst✝² : Monoid N\ninst✝¹ : (i : ι) → DecidableEq (M i)\ninst✝ : DecidableEq ι\nm : FreeProduct M\n⊢ ∀ (w : Word M), prod (m • w) = m * prod w",
"tactic": "induction m using... | [
458,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.monotone_restrict | [] | [
506,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Order/Iterate.lean | Function.Commute.iterate_pos_le_iff_map_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nf g : α → α\nh : Commute f g\nhf : Monotone f\nhg : StrictMono g\nx : α\nn : ℕ\nhn : 0 < n\n⊢ (f^[n]) x ≤ (g^[n]) x ↔ f x ≤ g x",
"tactic": "simpa only [not_lt] using not_congr (h.symm.iterate_pos_lt_iff_map_lt' hg hf hn)... | [
211,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.inner_le_Lp_mul_Lq | [
{
"state_after": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhpq : IsConjugateExponent p q\nthis :\n ↑(∑ i in s,\n (fun i => { val := abs (f i), property := (_ : 0 ≤ abs (f i)) }) i *\n (fun i => { val := abs (g i), property := (_ : 0 ≤ abs (g i)) }) i) ≤\n ↑((∑ i in s, (fun i => { val ... | [
564,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Init/Logic.lean | heq_of_eq_rec_right | [] | [
76,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.oreDiv_add_oreDiv | [] | [
607,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.univ_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2002\nγ : Type ?u.2005\ninst✝ : Fintype α\ns t : Finset α\n⊢ univ = ∅ ↔ IsEmpty α",
"tactic": "rw [← not_nonempty_iff, ← univ_nonempty_iff, not_nonempty_iff_eq_empty]"
}
] | [
113,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sigmaFinite_iff | [] | [
3442,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3441,
1
] |
Mathlib/Deprecated/Group.lean | Inv.isGroupHom | [] | [
402,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | Units.embedding_embedProduct | [] | [
111,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.ext | [] | [
73,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_le_of_surjective | [] | [
486,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_le_div_iff_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a⁻¹ ≤ b / c ↔ c ≤ a * b",
"tactic": "rw [inv_le_div_iff_le_mul, mul_comm]"
}
] | [
834,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset.ext | [] | [
3289,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3288,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasSum_lt | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.336123\nγ : Type ?u.336126\nf g : α → ℝ≥0∞\nsf sg : ℝ≥0∞\ni : α\nh : ∀ (a : α), f a ≤ g a\nhi : f i < g i\nhsf : sf ≠ ⊤\nhf : HasSum f sf\nhg : HasSum g sg\nhsg : sg = ⊤\n⊢ sf < sg\n\ncase neg\nα : Type u_1\nβ : Type ?u.336123\nγ : Type ?u.336126\nf g : α → ... | [
1276,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_sigma | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.312096\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nσ : α → Type u_1\ns : Finset α\nt : (a : α) → Finset (σ a)\nf : Sigma σ → β\n⊢ ∏ x in Finset.sigma s t, f x = ∏ a in s, ∏ s in t a, f { fst :=... | [
529,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.bicomp_mono | [] | [
380,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.antideriv_cos_comp_const_mul | [
{
"state_after": "z : ℂ\nn : ℕ\nhz : z ≠ 0\nx : ℝ\na : HasDerivAt (fun y => y * (2 * z)) (2 * z) ↑x\n⊢ HasDerivAt (fun y => Complex.sin (2 * z * ↑y) / (2 * z)) (Complex.cos (2 * z * ↑x)) x",
"state_before": "z : ℂ\nn : ℕ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y => Complex.sin (2 * z * ↑y) / (2 * z)) (Complex... | [
52,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_pow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\nx : α\nn : ℕ\n⊢ Multiset.Rel Associated (factors (x ^ 0)) (0 • factors x)",
"tactic": "rw [zero_smul, pow_zero, factors_one, Multiset.rel_zero_rig... | [
530,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_add | [
{
"state_after": "case pos\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → AddZeroClass (β i)\ni : ι\nb₁ b₂ : β i\ni' : ι\nh : i = i'\n⊢ ↑(single i (b₁ + b₂)) i' = ↑(single i b₁ + single i b₂) i'\n\ncase neg\nι : Type u\nγ : Type w\nβ : ι → Typ... | [
884,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.compl_setOf_mem | [] | [
114,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonneg_mul_lem | [
{
"state_after": "d x y : ℕ\na : ℤ√↑d\nha : Nonneg a\nthis : { re := ↑x, im := ↑y } * a = ↑x * a + sqrtd * (↑y * a)\n⊢ Nonneg ({ re := ↑x, im := ↑y } * a)",
"state_before": "d x y : ℕ\na : ℤ√↑d\nha : Nonneg a\n⊢ Nonneg ({ re := ↑x, im := ↑y } * a)",
"tactic": "have : (⟨x, y⟩ * a : ℤ√d) = (x : ℤ√d) * a +... | [
825,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist_inv_nat | [] | [
255,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.tendsto_lintegral_of_dominated_convergence' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1001538\nγ : Type ?u.1001541\nδ : Type ?u.1001544\nm : MeasurableSpace α\nμ ν : Measure α\nF : ℕ → α → ℝ≥0∞\nf bound : α → ℝ≥0∞\nhF_meas : ∀ (n : ℕ), AEMeasurable (F n)\nh_bound : ∀ (n : ℕ), F n ≤ᵐ[μ] bound\nh_fin : (∫⁻ (a : α), bound a ∂μ) ≠ ⊤\nh_lim : ∀ᵐ (a : α) ∂μ,... | [
1077,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
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Mathlib/Data/Nat/Order/Basic.lean | Nat.mul_self_inj | [] | [
322,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
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Mathlib/GroupTheory/Exponent.lean | Monoid.lcm_orderOf_dvd_exponent | [
{
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187,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | IsCountablySpanning.prod | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.mul_def | [] | [
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_unit | [
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.coeSubgraph_injective | [] | [
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Mathlib/Data/List/AList.lean | AList.lookup_insert_ne | [] | [
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Mathlib/Data/Fintype/Units.lean | Fintype.card_units | [
{
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70
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Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalExtr.hasFDerivAt_eq_zero | [] | [
215,
71
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Mathlib/Algebra/Order/Ring/Lemmas.lean | zero_lt_mul_left | [
{
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.tsum_apply | [] | [
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439,
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Mathlib/Topology/Algebra/Constructions.lean | MulOpposite.map_op_nhds | [] | [
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Mathlib/Data/Int/Cast/Field.lean | Int.cast_div | [
{
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{... | [
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.ofList_append | [
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_mul_left | [
{
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Mathlib/Topology/Constructions.lean | exists_finset_piecewise_mem_of_mem_nhds | [
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.singularPart_zero | [
{
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268,
34
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266,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAt.congr_of_eventuallyEq | [] | [
600,
71
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598,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_eq_of_le_of_coeff_ne_zero | [] | [
194,
43
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_compl_mul_self_apply | [
{
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419,
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Mathlib/Order/Monotone/Monovary.lean | MonotoneOn.monovaryOn | [] | [
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83
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336,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.of_mem_support_derivative | [
{
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}
] | [
202,
96
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199,
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toAddEquiv_eq_coe | [] | [
193,
6
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192,
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.matrix_trace_commutator_zero | [] | [
94,
24
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.mk_comp_algebraMap | [] | [
219,
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217,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAtFilter.mono | [] | [
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31
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360,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_center_iff | [] | [
732,
10
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Mathlib/Topology/Sequences.lean | SeqContinuous.continuous | [] | [
225,
81
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223,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Ici' | [
{
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1342,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.norm | [] | [
2038,
26
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2037,
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src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.runCatch_bind_lift | [] | [
69,
177
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
69,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.deriv_integral_left | [] | [
809,
47
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806,
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Mathlib/LinearAlgebra/Determinant.lean | Basis.isUnit_det | [] | [
571,
61
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570,
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Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.lift_spec | [
{
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186,
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Mathlib/SetTheory/Game/PGame.lean | PGame.zero_lf_one | [] | [
1890,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1889,
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Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_zero | [
{
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Mathlib/Data/MvPolynomial/Funext.lean | MvPolynomial.funext_iff | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Exponential.lean | Complex.cos_two_mul | [
{
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}
] | [
1034,
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1032,
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_iUnion_finite | [
{
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713,
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vadd_cancel_right | [
{
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108,
70
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107,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq_of_equiv_aux | [
{
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.id_tensor_associator_naturality | [
{
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344,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
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Mathlib/Topology/ContinuousFunction/Compact.lean | BoundedContinuousFunction.dist_toContinuousMap | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lid_symm_apply | [] | [
638,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_id | [] | [
1106,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_iff_mk'_eq | [] | [
372,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.inf_toSubalgebra | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_eq_zero_iff_not_mem | [
{
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"tactic": "classical simp [indicator_apply, imp_false]"
},
{
... | [
734,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_apply_le_dist | [
{
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"state_before": "α : Type u_2\nβ : Type u_1\nE : Type ?u.70790\ninst✝³ : TopologicalSpace α\ninst✝² : CompactSpace α\ninst✝¹ : MetricSpace β\ninst✝ : NormedAddCommGroup E\nf g : C(α, β)\nC : ℝ\nx : α\n⊢ dist (↑f x) (↑g x) ≤ dist f g",
"tactic": "simp only [← dist_mkOfCompact... | [
134,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translation_number₀' | [
{
"state_after": "f g : CircleDeg1Lift\nn : ℕ\n⊢ dist (↑(f ^ (n + 1)) 0 / (↑n + 1)) (τ f) ≤ ((fun n => 1 / ↑n) ∘ fun a => a + 1) n",
"state_before": "f g : CircleDeg1Lift\n⊢ Tendsto (fun n => ↑(f ^ (n + 1)) 0 / (↑n + 1)) atTop (𝓝 (τ f))",
"tactic": "refine'\n tendsto_iff_dist_tendsto_zero.2 <|\n sq... | [
785,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_sup | [] | [
654,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.sum | [
{
"state_after": "case empty\nα : Type u_2\nβ : Type ?u.590520\nE : Type ?u.590523\nF : Type u_4\nG : Type ?u.590529\nE' : Type u_3\nF' : Type ?u.590535\nG' : Type ?u.590538\nE'' : Type ?u.590541\nF'' : Type ?u.590544\nG'' : Type ?u.590547\nR : Type ?u.590550\nR' : Type ?u.590553\n𝕜 : Type ?u.590556\n𝕜' : Typ... | [
1794,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffAt.inner | [] | [
86,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
8
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.ucs_le_of_normalizer_eq_self | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk✝ : ℕ\nN N₁ N₂ : LieSubmodule R L M\nh : normalizer N₁ = N₁\nk : ℕ\n⊢ ucs k ⊥ ≤ ucs k N₁",
... | [
400,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | charmatrix_reindex | [
{
"state_after": "case a.h.a\nR : Type u\ninst✝⁴ : CommRing R\nn : Type w\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nm : Type v\ninst✝¹ : DecidableEq m\ninst✝ : Fintype m\ne : n ≃ m\nM : Matrix n n R\ni j : m\nx : ℕ\n⊢ coeff (charmatrix (↑(reindex e e) M) i j) x = coeff (↑(reindex e e) (charmatrix M) i j) x",... | [
89,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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