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/IndicatorFunction.lean | Set.mulIndicator_mul_compl_eq_piecewise | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.72118\nι : Type ?u.72121\nM : Type u_2\nN : Type ?u.72127\ninst✝¹ : MulOneClass M\ns t : Set α\nf✝ g✝ : α → M\na : α\ninst✝ : DecidablePred fun x => x ∈ s\nf g : α → M\nx : α\n⊢ (mulIndicator s f * mulIndicator (sᶜ) g) x = piecewise s f g x",
"state_before... | [
472,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_append_stream_left | [] | [
566,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.coe_id | [] | [
598,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Order/Lattice.lean | Prod.snd_sup | [] | [
1279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Ioi | [] | [
450,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_pow_coprime | [
{
"state_after": "case pos\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nh : coprime (orderOf y) m\nhg : orderOf y = 0\n⊢ orderOf (y ^ m) = orderOf y\n\ncase neg\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nh : coprime ... | [
373,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_pos | [] | [
543,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.eq_prod_roots_of_splits_id | [
{
"state_after": "no goals",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\np : K[X]\nhsplit : Splits (RingHom.id K) p\n⊢ p = ↑C (leadingCoeff p) * Multiset.prod (Multiset.map (fun a => X - ↑C a) (roots p))",
"tactic": "simpa using ... | [
360,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_neg_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.133553\nE : Type ?u.133556\nF : Type u_3\nG : Type ?u.133562\nE' : Type u_2\nF' : Type ?u.133568\nG' : Type ?u.133571\nE'' : Type ?u.133574\nF'' : Type ?u.133577\nG'' : Type ?u.133580\nR : Type ?u.133583\nR' : Type ?u.133586\n𝕜 : Type ... | [
893,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.pointwise_smul_def | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_eq_zero_of_ae_zero' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.2313924\nF : Type u_2\nG : Type ?u.2313930\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhq0_ne : q ≠ 0\nhμ : μ ≠ 0\nf : α → F\nh... | [
700,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_naturality | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\ni : Δ ⟶ Δ'\ninst✝ : Mono i\n⊢ (if h : Δ' = Δ then eqToHom (_ : HomologicalComplex.X K (len Δ') = HomologicalComplex.X K (len Δ))\n else if h : Isδ₀ i then Homologica... | [
142,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.symm_injective | [] | [
142,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.id_eq_nilFun | [
{
"state_after": "case a.h\nn : ℕ\nα : TypeVec 0\nx : Fin2 0\nx✝ : α x\n⊢ id x x✝ = nilFun x x✝",
"state_before": "n : ℕ\nα : TypeVec 0\n⊢ id = nilFun",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case a.h\nn : ℕ\nα : TypeVec 0\nx : Fin2 0\nx✝ : α x\n⊢ id x x✝ = nilFun... | [
451,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.le_ae_restrict | [] | [
2898,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2897,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_ne_pi_of_not_collinear | [] | [
465,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_of_forall_integral_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝² : MeasurableSpace Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμ : FiniteMeasure Ω\nh : ∀ (f : Ω →ᵇ ℝ), Tendsto (fun i => ∫ (x : Ω), ↑f x ∂↑(μs i)) F (𝓝 (∫ (x : Ω), ↑f x ∂↑μ))\n⊢ ∀ (f : Ω →ᵇ ℝ≥0), Te... | [
725,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.add_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.84885\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddCommSemigroup α\nh : Periodic f c\na x : α\n⊢ (fun x => f (x + a)) (x + c) = (fun x => f (x + a)) x",
"tactic": "simpa only [add_right_comm] using h (x + a)"
}
] | [
188,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Surjective.of_comp | [] | [
171,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_biUnion | [] | [
854,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.map_bracket_eq | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ : LieIdeal R L'\nI₁ I₂ : LieIdeal R L\nh : Function.Surjective ↑f\n⊢ ⁅map f I₁, map f I₂⁆ ≤ map f ⁅I₁, I₂⁆",... | [
290,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.mul_left_inj | [] | [
769,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_mul_div_succ | [
{
"state_after": "m✝ n✝ k m n : ℕ\nn0 : 0 < n\n⊢ m / n < m / n + 1",
"state_before": "m✝ n✝ k m n : ℕ\nn0 : 0 < n\n⊢ m < n * (m / n + 1)",
"tactic": "rw [mul_comm, ← Nat.div_lt_iff_lt_mul' n0]"
},
{
"state_after": "no goals",
"state_before": "m✝ n✝ k m n : ℕ\nn0 : 0 < n\n⊢ m / n < m / n + 1"... | [
798,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.not_isUniform_iff | [
{
"state_after": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\na b : α\n⊢ (¬∀ ⦃s' : Finset α⦄,\n s' ⊆ s →\n ∀ ⦃t' : Finset α⦄,\n t' ⊆ t →\n ↑(card s) * ε ≤ ↑(card s') →\n ... | [
112,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58836\nγ : Type ?u.58839\na : α\n⊢ ↑card {a} = 1",
"tactic": "simp only [← cons_zero, card_zero, eq_self_iff_true, zero_add, card_cons]"
}
] | [
749,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Pred.rec | [] | [
1423,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.eq_comp_symm | [] | [
415,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.distortion_of_const | [] | [
453,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.CG.range | [
{
"state_after": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : CG L M\nf : M →[L] N\n⊢ Substructure.CG (map f ⊤)",
"state_before": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : CG L M\nf : M →[L] N\n⊢ Substructur... | [
240,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_finite_toFinset_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.201940\nι : Type ?u.201943\nG : Type ?u.201946\nM : Type u_2\nN : Type ?u.201952\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\ns : Set α\nhs : Set.Finite s\n⊢ (s ∩ mulSupport fun i => f i) = ↑(Finite.toFinset hs) ∩ mulSupport... | [
516,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime.dvd_mul_right | [] | [
125,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/List/Nodup.lean | List.not_nodup_cons_of_mem | [] | [
76,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.comp_codRestrict | [] | [
215,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/List/Sort.lean | List.eq_of_perm_of_sorted | [
{
"state_after": "case nil\nα : Type uu\nr : α → α → Prop\na : α\nl : List α\ninst✝ : IsAntisymm α r\nl₁ l₂✝ : List α\np✝ : l₁ ~ l₂✝\ns₂✝ : Sorted r l₂✝\nl₂ : List α\np : [] ~ l₂\ns₂ : Sorted r l₂\n⊢ [] = l₂\n\ncase cons\nα : Type uu\nr : α → α → Prop\na✝ : α\nl : List α\ninst✝ : IsAntisymm α r\nl₁✝ l₂✝ : List ... | [
99,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.self_invAct_invAct_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Rack R\nx y : R\nh : (op x ◃ op x) ◃ op y = op x ◃ op y\n⊢ (x ◃⁻¹ x) ◃⁻¹ y = x ◃⁻¹ y",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ (x ◃⁻¹ x) ◃⁻¹ y = x ◃⁻¹ y",
"tactic": "have h := @self_act_act_eq _ _ (op x) (op y)"
},
{
"state_after": "no go... | [
293,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Topology/Order.lean | induced_generateFrom_eq | [] | [
567,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.pairwise_disjoint_powersetLen | [] | [
283,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ tan θ = 0 ↔ ∃ k, θ = ↑k * π / 2",
"tactic": "rw [← not_iff_not, not_exists, ← Ne, tan_ne_zero_iff]"
}
] | [
56,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.dart_card_eq_twice_card_edges | [
{
"state_after": "V : Type u\nG : SimpleGraph V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype (Sym2 V)\ninst✝ : DecidableEq V\n⊢ card univ = 2 * card (edgeFinset G)",
"state_before": "V : Type u\nG : SimpleGraph V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype (Sym2 ... | [
110,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Ico | [
{
"state_after": "case inl\nf : StieltjesFunction\na b : ℝ\nhab : b ≤ a\n⊢ ↑↑(StieltjesFunction.measure f) (Ico a b) = ofReal (leftLim (↑f) b - leftLim (↑f) a)\n\ncase inr\nf : StieltjesFunction\na b : ℝ\nhab : a < b\n⊢ ↑↑(StieltjesFunction.measure f) (Ico a b) = ofReal (leftLim (↑f) b - leftLim (↑f) a)",
"... | [
583,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.re_eq_complex_re | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | RingHom.map_dfinsupp_sumAddHom | [] | [
2345,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2342,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.tendsto_abs_tan_of_cos_eq_zero | [
{
"state_after": "x : ℝ\nhx✝ : cos x = 0\nhx : Complex.cos ↑x = 0\n⊢ Tendsto (fun x => abs (tan x)) (𝓝[{x}ᶜ] x) atTop",
"state_before": "x : ℝ\nhx : cos x = 0\n⊢ Tendsto (fun x => abs (tan x)) (𝓝[{x}ᶜ] x) atTop",
"tactic": "have hx : Complex.cos x = 0 := by exact_mod_cast hx"
},
{
"state_after... | [
45,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.lsingle_apply | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.18205\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\ninst✝ : IsWellOrder β s\nf g : r ≼i s\na : α\n⊢ ↑f a = ↑g a",
"tactic": "rw [Subsingleton.elim f g]"
}
] | [
148,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSets_singleton_iff | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\nι : Type ?u.1351878\ninst✝ : MeasurableSpace Ω\ns t : Set Ω\nμ : MeasureTheory.Measure Ω\nh : ↑↑μ (s ∩ t) = ↑↑μ s * ↑↑μ t\ns1 t1 : Set Ω\nhs1 : s1 ∈ {s}\nht1 : t1 ∈ {t}\n⊢ ↑↑μ (s1 ∩ t1) = ↑↑μ s1 * ↑↑μ t1",
"tactic": "rwa [Set.mem_singleton_iff.... | [
257,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.inv | [] | [
358,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mapLe_isPath | [] | [
1619,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1617,
1
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Mathlib/Algebra/Order/Floor.lean | round_add_one | [
{
"state_after": "no goals",
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}
] | [
1362,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
1
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean | MaximalSpectrum.toPrimeSpectrum_continuous | [] | [
87,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.app_hom | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.natDegree_toSubring | [
{
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] | [
383,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yz_succ | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Chain.map_comp | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Data/List/BigOperators/Basic.lean | List.alternatingProd_cons_cons' | [] | [
637,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_id | [] | [
349,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
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Mathlib/Order/LocallyFinite.lean | Finset.mem_Ioo | [] | [
343,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/Data/Set/Image.lean | Set.image_preimage_eq_of_subset | [
{
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"tactic": "rw [image_preimage_eq_inter_range, inter_eq_self_of_subset_left hs]"
}... | [
787,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
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Mathlib/Order/Hom/Basic.lean | OrderHom.dual_id | [] | [
578,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
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Mathlib/Topology/Algebra/Order/Group.lean | ContinuousAt.abs | [] | [
87,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
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Mathlib/Analysis/Calculus/Deriv/Linear.lean | LinearMap.hasDerivAt | [] | [
95,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
11
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | toMatrix_distrib_mul_action_toLinearMap | [
{
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830,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.append_left | [] | [
298,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
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Mathlib/Algebra/Group/Basic.lean | div_eq_mul_one_div | [
{
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"tactic": "rw [div_eq_mul_inv, one_div]"
}
] | [
330,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_smul | [] | [
983,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurableSet_inr_image | [
{
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1030,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
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Mathlib/Data/Stream/Init.lean | Stream'.mem_cons | [] | [
122,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Order/SuccPred/Limit.lean | Order.IsSuccLimit.succ_lt | [
{
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153,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/LinearAlgebra/Ray.lean | exists_pos_left_iff_sameRay | [
{
"state_after": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhx : x ≠ 0\nhy : y ≠ 0\nh : ∃ r, 0 < r ∧ r • x = y\n⊢ SameRay R x y",
"state_before": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ ... | [
715,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.pb_inv | [
{
"state_after": "n : Type ?u.145025\np : Type ?u.145028\nq : Type ?u.145031\nl : Type u_1\nR : Type u₂\ninst✝⁸ : DecidableEq n\ninst✝⁷ : DecidableEq p\ninst✝⁶ : DecidableEq q\ninst✝⁵ : DecidableEq l\ninst✝⁴ : CommRing R\ninst✝³ : Fintype p\ninst✝² : Fintype q\ninst✝¹ : Fintype l\ninst✝ : Invertible 2\n⊢ fromBl... | [
350,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_vadd_left_iff | [
{
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285,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
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Mathlib/Algebra/Free.lean | FreeSemigroup.lift_of | [] | [
542,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_right_comm | [] | [
946,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_iUnion_le_tsum_nat' | [
{
"state_after": "case pos\nα : Type u_1\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f i))... | [
1400,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
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Mathlib/Topology/UniformSpace/Basic.lean | symm_of_uniformity | [] | [
512,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_dvd_factorial | [
{
"state_after": "case zero\nm✝ n✝ m n : ℕ\nh✝ : m ≤ n\nh : m ≤ zero\n⊢ m ! ∣ zero !\n\ncase succ\nm✝ n✝¹ m n✝ : ℕ\nh✝ : m ≤ n✝\nn : ℕ\nIH : m ≤ n → m ! ∣ n !\nh : m ≤ succ n\n⊢ m ! ∣ (succ n)!",
"state_before": "m✝ n✝ m n : ℕ\nh : m ≤ n\n⊢ m ! ∣ n !",
"tactic": "induction' n with n IH"
},
{
"st... | [
83,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
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Mathlib/Algebra/Group/Prod.lean | MonoidHom.prod_unique | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.58502\nB : Type ?u.58505\nG : Type ?u.58508\nH : Type ?u.58511\nM : Type u_1\nN : Type u_3\nP : Type u_2\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nf : M →* N × P\nx : M\n⊢ ↑(MonoidHom.prod (comp (fst N P) f) (comp (snd N... | [
583,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.comp_tendsto | [] | [
330,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.units_smul_span_eq_top | [] | [
1237,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_prod | [] | [
474,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.mk_coord_apply_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.843940\nR : Type u_2\nR₂ : Type ?u.843946\nK : Type ?u.843949\nM : Type u_3\nM' : Type ?u.843955\nM'' : Type ?u.843958\nV : Type u\nV' : Type ?u.843963\nv : ι → M\ninst✝⁸ : Ring R\ninst✝⁷ : CommRing R₂\ninst✝⁶ : AddCommGroup M\ninst✝⁵ ... | [
1160,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1158,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_mono | [] | [
199,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.isComplete_map_iff | [] | [
254,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Order/Directed.lean | IsMax.isTop | [] | [
268,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
11
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | Embedding.to_uniformEmbedding | [] | [
424,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Std/Data/String/Lemmas.lean | String.all_eq | [
{
"state_after": "no goals",
"state_before": "s : String\np : Char → Bool\n⊢ all s p = List.all s.data p",
"tactic": "rw [all, any_eq, List.all_eq_not_any_not]"
}
] | [
723,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
722,
1
] |
Mathlib/Topology/Order/Basic.lean | TopologicalSpace.SecondCountableTopology.of_separableSpace_orderTopology | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : DenselyOrdered α\ninst✝ : SeparableSpace α\ns : Set α\nhc : Set.Countable s\nhd : Dense s\n⊢ SecondCountableTopology α",
"state_before": "α : Type u... | [
1366,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_dirac | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.1486181\n𝕜 : Type ?u.1486184\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : CompleteSpace E\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : SMulCommClass ℝ 𝕜 E\ninst✝⁶ : N... | [
1599,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_bot_left | [] | [
282,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_mem_upperBounds | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.146221\nβ : Type ?u.146224\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Set ℝ≥0\n⊢ ↑r ∈ upperBounds (some '' s) ↔ r ∈ upperBounds s",
"tactic": "simp (config := { contextual := true }) [upperBounds, ball_image_iff, -mem_image, *]"
}
] | [
953,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
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Mathlib/Data/List/BigOperators/Basic.lean | List.get?_zero_mul_tail_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.67807\nα : Type ?u.67810\nM : Type u_1\nN : Type ?u.67816\nP : Type ?u.67819\nM₀ : Type ?u.67822\nG : Type ?u.67825\nR : Type ?u.67828\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl✝ l₁ l₂ : List M\na : M\nl : List M\n⊢ Option.getD (get? ... | [
232,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.eq_of_openSegment_subset_frontier | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\n𝕝 : Type ?u.173927\nE : Type u_2\nF : Type ?u.173933\nβ : Type ?u.173936\ninst✝⁸ : OrderedRing 𝕜\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : TopologicalSpace F\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 E\ninst✝² : Module 𝕜 F\ns t : Set... | [
342,
76
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334,
1
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Mathlib/Order/Height.lean | Set.chainHeight_eq_iSup_Ici | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.32030\ns t : Set α\ninst✝ : Preorder α\n⊢ chainHeight s ≤ ⨆ (i : α) (_ : i ∈ s), chainHeight (s ∩ Ici i)\n\ncase a\nα : Type u_1\nβ : Type ?u.32030\ns t : Set α\ninst✝ : Preorder α\n⊢ (⨆ (i : α) (_ : i ∈ s), chainHeight (s ∩ Ici i)) ≤ chainHeight s",
"stat... | [
273,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_ofReal_of_neg | [] | [
250,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_induction | [
{
"state_after": "case intro\nR✝ : Type ?u.243597\nM✝ : Type ?u.243600\ninst✝⁷ : Semiring R✝\ninst✝⁶ : AddCommMonoid M✝\ninst✝⁵ : Module R✝ M✝\nP✝ : Type ?u.243636\ninst✝⁴ : AddCommMonoid P✝\ninst✝³ : Module R✝ P✝\nf : M✝ →ₗ[R✝] P✝\nR : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst... | [
347,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Topology/Order.lean | discreteTopology_iff_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt t₁ t₂ : TopologicalSpace α\ns : Set α\ninst✝ : TopologicalSpace α\n⊢ DiscreteTopology α ↔ ∀ (x : α), 𝓝 x = pure x",
"tactic": "simp only [discreteTopology_iff_singleton_mem_nhds, ← nhds_neBot.le_pure_iff, le_pure_iff]"
}
] | [
337,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | imageToKernel_epi_comp | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.17286\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ng : B ⟶ C\ninst✝² : HasKernels V\ninst✝¹ : HasImages V\nZ : V\nh : Z ⟶ A\ninst✝ : Epi h\nw : (h ≫ f) ≫ g = 0\n⊢ h ≫ f ≫ g = h ≫ 0",
"tactic": "simpa using ... | [
131,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_toNNReal | [] | [
230,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
9
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.coeff_add_eq_left_of_lt | [] | [
189,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.le_natDegree_of_mem_supp | [] | [
185,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
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