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/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Multiset.aestronglyMeasurable_prod' | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.316502\nγ : Type ?u.316505\nι : Type ?u.316508\ninst✝⁵ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\nf g : α → β\nM : Type u_2\ninst✝² : CommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : Contin... | [
1403,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.apply_eq_iff_symm_apply | [] | [
406,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\nh0 : p₁ ≠ p₂ ∨ p₃ = p₂\n⊢ 0 < ∠ p₂ p₃ p₁",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ ... | [
411,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.bind_assoc | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\nf : α → Seq1 β\ng : β → Seq1 γ\na : α\ns : Seq α\n⊢ bind (bind (a, s) f) g = bind (a, s) fun x => bind (f x) g",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq1 α\nf : α → Seq1 β\ng : β → Seq1 γ\n⊢ bind (bind s f) g = bind s fun x ... | [
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30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.ringHom_ext | [
{
"state_after": "case hl\nR : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_4\nM' : Type u_3\nM'' : Type u_2\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : ... | [
897,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.IsWeightedHomogeneous.prod | [
{
"state_after": "case refine_1\nR : Type u_3\nM : Type u_4\ninst✝¹ : CommSemiring R\nσ : Type u_2\ninst✝ : AddCommMonoid M\nφ✝ ψ : MvPolynomial σ R\nm n✝ : M\nι : Type u_1\ns : Finset ι\nφ : ι → MvPolynomial σ R\nn : ι → M\nw : σ → M\n⊢ (∀ (i : ι), i ∈ ∅ → IsWeightedHomogeneous w (φ i) (n i)) → IsWeightedHomog... | [
298,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.uncurry_bicompr | [] | [
835,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Data/List/Cycle.lean | List.pmap_next_eq_rotate_one | [
{
"state_after": "case hl\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : Nodup l\n⊢ length (pmap (next l) l (_ : ∀ (x : α), x ∈ l → x ∈ l)) = length (rotate l 1)\n\ncase h\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : Nodup l\n⊢ ∀ (n : ℕ) (h₁ : n < length (pmap (next l) l (_ : ∀ (x ... | [
363,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
src/lean/Init/SimpLemmas.lean | let_congr | [] | [
46,
34
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
44,
1
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Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_of_factorization_le_one | [
{
"state_after": "n : ℕ\nhn : n ≠ 0\nhn' : ∀ (p : ℕ), ↑(factorization n) p ≤ 1\n⊢ ∀ (a : ℕ), List.count a (factors n) ≤ 1",
"state_before": "n : ℕ\nhn : n ≠ 0\nhn' : ∀ (p : ℕ), ↑(factorization n) p ≤ 1\n⊢ Squarefree n",
"tactic": "rw [squarefree_iff_nodup_factors hn, List.nodup_iff_count_le_one]"
},
... | [
60,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Set/Basic.lean | Set.univ_eq_empty_iff | [] | [
671,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.natDegree_derivative_lt | [
{
"state_after": "case inl\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np : R[X]\nhp : natDegree p ≠ 0\nhp' : ↑derivative p = 0\n⊢ natDegree (↑derivative p) < natDegree p\n\ncase inr\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\n... | [
221,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Functor/LeftDerived.lean | CategoryTheory.NatTrans.leftDerived_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹⁴ : Category C\nD : Type u_2\ninst✝¹³ : Category D\ninst✝¹² : Preadditive C\ninst✝¹¹ : HasZeroObject C\ninst✝¹⁰ : HasEqualizers C\ninst✝⁹ : HasImages C\ninst✝⁸ : HasProjectiveResolutions C\ninst✝⁷ : Preadditive D\ninst✝⁶ : HasEqualizers D\ninst... | [
150,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/Algebra/Order/UpperLower.lean | IsOpen.upperClosure | [] | [
76,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
11
] |
Mathlib/Data/Nat/Pow.lean | Nat.one_le_pow' | [] | [
65,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measure_interior_of_null_frontier | [] | [
414,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioo_eq_zero_of_le | [] | [
98,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.OrderIso.apply_blimsup | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nι : Type ?u.142814\ninst✝¹ : CompleteLattice α\nf g : Filter β\np q : β → Prop\nu v : β → α\ninst✝ : CompleteLattice γ\ne : α ≃o γ\n⊢ sInf ((fun a => ↑e a) '' {a | ∀ᶠ (x : β) in f, p x → u x ≤ a}) = sInf {a | ∀ᶠ (x : β) in f, p x → ↑e (u x) ≤ a}",
... | [
954,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_mul_distrib | [
{
"state_after": "case empty\nF : Type ?u.219899\nι : Type ?u.219902\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.219911\nf✝ : α → β → β\nop : α → α → α\ninst✝¹ : Monoid β\ninst✝ : Monoid γ\ns : Finset α\nf g : α → β\ncomm_ff✝ : Set.Pairwise ↑s fun x y => Commute (f x) (f y)\ncomm_gg✝ : Set.Pairwise ↑s fun x y => C... | [
410,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_arrow_factors_left | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
429,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.bijective_bijInv | [] | [
1154,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.mono_of_mono_right | [] | [
472,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.NeBot.le_pure_iff | [] | [
417,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_image_eq_span_vsub_set_left_ne | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_1\np : ι → P\ns : Set ι\ni : ι\nhi : i ∈ s\n⊢ Submodule.span k (insert ((fun x x_1 => x -ᵥ x_1) (p i) (p i)) ((fun x x_1 => x -ᵥ x_1) (p i) '' (p '' (s \... | [
1087,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.inner_nonneg_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.43212\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nT : E →L[𝕜] E\nhT : IsPositive T\nx : E\n⊢ 0 ≤... | [
74,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ite_ae_eq_of_measure_zero | [
{
"state_after": "α : Type u_2\nβ : Type ?u.717923\nγ✝ : Type ?u.717926\nδ : Type ?u.717929\nι : Type ?u.717932\nR : Type ?u.717935\nR' : Type ?u.717938\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ✝\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\nγ : Type u_1\nf g : α → γ\... | [
3379,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3373,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.image_iso | [] | [
170,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.comap_span | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV₁ : Type u_4\nP₁ : Type u_2\nV₂ : Type u_5\nP₂ : Type u_3\nV₃ : Type ?u.642758\nP₃ : Type ?u.642761\ninst✝⁹ : Ring k\ninst✝⁸ : AddCommGroup V₁\ninst✝⁷ : Module k V₁\ninst✝⁶ : AffineSpace V₁ P₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module k V₂\ninst✝... | [
1698,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.beq_refl | [
{
"state_after": "no goals",
"state_before": "a : Nat\n⊢ beq a a = true",
"tactic": "induction a with simp [Nat.beq]\n| succ a ih => simp [ih]"
},
{
"state_after": "no goals",
"state_before": "case succ\na : Nat\nih : beq a a = true\n⊢ beq a a = true",
"tactic": "simp [ih]"
}
] | [
94,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
92,
9
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_pi | [
{
"state_after": "case H\nG : Type ?u.351081\ninst✝⁴ : Group G\nH : Subgroup G\ninst✝³ : Normal H\nη : Type u_1\nGs : η → Type u_2\ninst✝² : (i : η) → Group (Gs i)\ninst✝¹ : Fintype η\ninst✝ : ∀ (i : η), Group.IsNilpotent (Gs i)\n⊢ ∀ (c : ℕ), nilpotencyClass ((i : η) → Gs i) ≤ c ↔ (Finset.sup Finset.univ fun i ... | [
821,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | lipschitzWith_iff_norm_div_le | [
{
"state_after": "no goals",
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822,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Topology/Basic.lean | frontier_univ | [
{
"state_after": "no goals",
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"tactic": "simp [frontier]"
}
] | [
737,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_offDiag | [] | [
541,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_eq_iff | [
{
"state_after": "ψ θ : Angle\nthis : Int.natAbs 2 = 2\n⊢ 2 • ψ = 2 • θ ↔ ψ = θ ∨ ψ = θ + ↑π",
"state_before": "ψ θ : Angle\n⊢ 2 • ψ = 2 • θ ↔ ψ = θ ∨ ψ = θ + ↑π",
"tactic": "have : Int.natAbs 2 = 2 := rfl"
},
{
"state_after": "no goals",
"state_before": "ψ θ : Angle\nthis : Int.natAbs 2 = 2... | [
191,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_lt_of_translationNumber_lt_nat | [] | [
865,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Sentence.realize_cardGe | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.762328\nP : Type ?u.762331\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn✝ : ℕ\nT : Theory L\nn : ℕ\n⊢ (∃ xs,\n BoundedFormula.Realize\n (List.foldr (fun x x_1 => x ⊓ x_1) ⊤\n ... | [
1054,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_div' | [
{
"state_after": "no goals",
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"tactic": "apply prod_range_induction... | [
1405,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/Data/Set/Basic.lean | Set.disjoint_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ Disjoint s t ↔ ∀ ⦃a : α⦄, a ∈ t → ¬a ∈ s",
"tactic": "rw [disjoint_comm, disjoint_left]"
}
] | [
1533,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
] |
Mathlib/Topology/Constructions.lean | pi_eq_generateFrom | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.372393\nδ : Type ?u.372396\nε : Type ?u.372399\nζ : Type ?u.372402\nι : Type u_2\nπ : ι → Type u_1\nκ : Type ?u.372413\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf : α → (i : ι) → π i\n⊢ Pi.topolog... | [
1389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1382,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_intCast | [] | [
287,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atBot_iff_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.244706\nι' : Type ?u.244709\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.244718\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nh : Tendsto f l atTop\n⊢ Tendsto (fun x => r * f x) l atBot ↔ r < 0",
"tactic": "simp [te... | [
1180,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_irrefl | [] | [
86,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.eq | [] | [
2011,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2009,
11
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_prod | [] | [
1013,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_ofReal_im | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℂ\nx : ℝ\n⊢ (exp ↑x).im = 0",
"tactic": "rw [← ofReal_exp_ofReal_re, ofReal_im]"
}
] | [
585,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | EMetric.diam_closure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.430325\nγ : Type ?u.430328\ninst✝ : PseudoEMetricSpace α\ns : Set α\nx : α\nhx : x ∈ closure s\ny : α\nhy : y ∈ closure s\n⊢ edist x y ≤ diam s",
"state_before": "α : Type u_1\nβ : Type ?u.430325\nγ : Type ?u.430328\ninst✝ : PseudoEMetricSpace α\ns : Set α\n⊢ diam... | [
1483,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pf_zero_add | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
309,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Algebra/Category/Ring/Colimits.lean | CommRingCat.Colimits.quot_zero | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.refl_apply | [] | [
604,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryFan.mk_snd | [] | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
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Mathlib/Data/Matrix/Hadamard.lean | Matrix.one_hadamard | [
{
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"state_before": "α : Type u_... | [
129,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ioo_of_neg | [
{
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"tactic": "simp [← Ioi_inter_Iio, h, inter_comm]"
}
] | [
580,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
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Mathlib/Topology/Basic.lean | le_nhds_iff | [
{
"state_after": "no goals",
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"tactic": "simp [nhds_def]"
}
] | [
875,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.disjoint_ndinsert_right | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α\na : α\ns t : Multiset α\n⊢ ¬a ∈ s ∧ Disjoint t s ↔ ¬a ∈ s ∧ Disjoint s t",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α\na : α\ns t : Multiset α\n⊢ Disjoint s (ndinsert a t) ↔ ¬a ∈ s ∧ Disjoint s t",
"tactic... | [
132,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Order/JordanHolder.lean | CompositionSeries.snoc_last | [] | [
566,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
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] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Multiset.aestronglyMeasurable_prod | [
{
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1411,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.mem_orthogonal_singleton_iff_inner_left | [
{
"state_after": "no goals",
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89,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/LinearAlgebra/Dfinsupp.lean | Submodule.mem_iSup_finset_iff_exists_sum | [
{
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"st... | [
413,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.fstIdx_ne_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.373127\ninst✝ : Monoid N\nw : Word M\ni : ι\n⊢ ¬fstIdx w ≠ some i ↔ ¬∀ (l : (i : ι) × M i), l ∈ List.head? w.toList → i ≠ l.fst",
"tactic": "simp [fstIdx]"
}
] | [
293,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.union_right_iff | [] | [
106,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.subtype_coe | [] | [
204,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_of_sub_eq_succ | [
{
"state_after": "no goals",
"state_before": "m n l : Nat\nH : m - n = succ l\nH' : m ≤ n\n⊢ False",
"tactic": "simp [Nat.sub_eq_zero_of_le H'] at H"
}
] | [
166,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
165,
11
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.comap_equiv_eq_map_symm | [] | [
605,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_linear_le | [] | [
1142,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.pow_dvd_nthHom_sub | [
{
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"state_before": "p : ... | [
506,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.K'.elim_update_stack | [
{
"state_after": "case h\na b c d d' : List Γ'\nx : K'\n⊢ update (elim a b c d) stack d' x = elim a b c d' x",
"state_before": "a b c d d' : List Γ'\n⊢ update (elim a b c d) stack d' = elim a b c d'",
"tactic": "funext x"
},
{
"state_after": "no goals",
"state_before": "case h\na b c d d' : ... | [
1298,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.num_den_reduced | [] | [
66,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Icc | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Icc a b) = Icc ↑a ↑b",
"tactic": "simp [Icc_eq_finset_subtype, Finset.fin, Finset.map_map, Icc_filter_lt_of_lt_right]"
}
] | [
60,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_injective2 | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx✝ : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\ni✝ : Fin n\ny✝ : α (succ i✝)\nz x₀ y₀ : α 0\nx y : (i : Fin n) → α (succ i)\nh : cons x₀ x = cons y₀ y\ni : Fin n\n⊢ x i = y i",
"tactic": "simpa using co... | [
104,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/Compare.lean | Ordering.swap_eq_iff_eq_swap | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.6377\nβ : Type ?u.6380\no o' : Ordering\n⊢ swap o = o' ↔ o = swap o'",
"tactic": "rw [← swap_inj, swap_swap]"
}
] | [
82,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Set/Image.lean | Function.Injective.subsingleton_image_iff | [] | [
1298,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1296,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.universally_mono | [] | [
607,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.zsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz m : ℤ\nhm : b - a = m • p\n⊢ z • b - z • a = m • z • p",
"tactic": "rw [← smul_sub, hm, smul_comm]"
}
] | [
160,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
11
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_mono | [] | [
157,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_sup | [] | [
156,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.liftpPreservation_iff_uniform | [
{
"state_after": "no goals",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\n⊢ LiftpPreservation ↔ IsUniform",
"tactic": "rw [← suppPreservation_iff_liftpPreservation, suppPreservation_iff_uniform]"
}
] | [
728,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.continuous_circleTransform | [
{
"state_after": "case hg.hf\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR✝ : ℝ\nz✝ w✝ : ℂ\nR : ℝ\nhR : 0 < R\nf : ℂ → E\nz w : ℂ\nhf : ContinuousOn f (sphere z R)\nhw : w ∈ ball z R\n⊢ Continuous fun x => deriv (circleMap z R) x\n\ncase hg.hg.hf\nE : Type u_1\ninst✝¹ : NormedAddCommG... | [
88,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Order/Grade.lean | grade_covby_grade_iff | [] | [
198,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | ContinuousOn.circleIntegrable' | [] | [
293,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_arrows | [] | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.toIdeal_homogeneousHull_eq_iSup | [
{
"state_after": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.216424\nA : Type u_1\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nI : Ideal A\n⊢ toIdeal (homogeneousHull 𝒜 I) = span (⋃ (i : ι), ↑(GradedRin... | [
590,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.piecewise_apply | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.LaxBraidedFunctor.comp_toNatTrans | [] | [
279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_le_false | [] | [
685,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_nat_iff_fintype | [
{
"state_after": "α β : Type u\nn : ℕ\n⊢ (∃ t, ↑t = univ ∧ Finset.card t = n) ↔ ∃ h, Fintype.card α = n",
"state_before": "α β : Type u\nn : ℕ\n⊢ (#α) = ↑n ↔ ∃ h, Fintype.card α = n",
"tactic": "rw [mk_eq_nat_iff_finset]"
},
{
"state_after": "case mp\nα β : Type u\nn : ℕ\n⊢ (∃ t, ↑t = univ ∧ Fin... | [
2087,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2081,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLE_arrow | [] | [
325,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left' | [] | [
947,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_univ | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.3515\nE : Type u_2\nF : Type ?u.3521\nβ : Type ?u.3524\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalSpace F\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 F\ns : Set E\nx✝ y✝ : E\na✝⁶ b✝ : �... | [
72,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.38508\ninst✝¹ : CommSemigroup R\ninst✝ : StarSemigroup R\nx y : R\nhx : IsSelfAdjoint x\nhy : IsSelfAdjoint y\n⊢ IsSelfAdjoint (x * y)",
"tactic": "simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]"
}
] | [
213,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformEmbedding_of_spaced_out | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α✝\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nα : Type u_1\nf : α → β\ns : Set (β × β)\nhs : s ∈ 𝓤 β\nhf : Pairwise fun x y => ¬(f x, f y) ∈ s\nx✝ : UniformSpace α := ⊥\n⊢ UniformEmbedding f",
"state_before": "α✝ : Type u\n... | [
224,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.zero_mem | [] | [
115,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
11
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.zero_sigma | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.isOpen | [] | [
128,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_div_const | [
{
"state_after": "α : Type ?u.104399\nβ : Type ?u.104402\nγ : Type ?u.104405\na b c✝ d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nc : ℝ≥0∞\nc_ne_zero : c ≠ 0\n⊢ ∀ (x : ℝ≥0∞), ContinuousAt (fun x => x * c⁻¹) x",
"state_before": "α : Type ?u.104399\nβ : Type ?u.104402\nγ : Type ?u.104405\na b c✝... | [
423,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
11
] |
Mathlib/Data/Opposite.lean | Opposite.unop_injective | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nx✝¹ x✝ : αᵒᵖ\nunop✝¹ unop✝ : α\n⊢ { unop := unop✝¹ }.unop = { unop := unop✝ }.unop → { unop := unop✝¹ } = { unop := unop✝ }",
"tactic": "simp"
}
] | [
62,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.exists_maximal_subfieldWithHom | [] | [
279,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Logic/Basic.lean | rec_heq_iff_heq | [
{
"state_after": "α : Sort u_1\na : α\nβ : Sort u_2\nC : α → Sort u_2\nx : C a\ny : β\n⊢ HEq ((_ : a = a) ▸ x) y ↔ HEq x y",
"state_before": "α : Sort u_1\na : α\nβ : Sort u_2\nb : α\nC : α → Sort u_2\nx : C a\ny : β\ne : a = b\n⊢ HEq (e ▸ x) y ↔ HEq x y",
"tactic": "subst e"
},
{
"state_after":... | [
570,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_powerset | [] | [
471,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonnegg_pos_neg | [
{
"state_after": "d✝ : ℤ\nc d a b : ℕ\n⊢ Nonnegg d c (-↑b) ↑a ↔ SqLe b c a d",
"state_before": "d✝ : ℤ\nc d a b : ℕ\n⊢ Nonnegg c d (↑a) (-↑b) ↔ SqLe b c a d",
"tactic": "rw [nonnegg_comm]"
},
{
"state_after": "no goals",
"state_before": "d✝ : ℤ\nc d a b : ℕ\n⊢ Nonnegg d c (-↑b) ↑a ↔ SqLe b c... | [
503,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.coeff_eq_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz z₀ : 𝕜\ny : Fin n → 𝕜\n⊢ coeff p n = ... | [
286,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
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