English
Let IsEtale have the HasOfPostcompProperty with LocallyOfFiniteType ⊓ FormallyUnramified; then IsEtale is closed under post-composition.
Русский
Пусть для IsEtale выполняется свойство HasOfPostcomp с локально конечным типом ⊓ формально неразмытого; тогда Étale свойство замкнуто по пост-композиции.
LaTeX
$$$\\text{HasOfPostcompProperty IsEtale (LocallyOfFiniteType \\cap FormallyUnramified)}$$$
Lean4
instance : MorphismProperty.HasOfPostcompProperty @IsEtale (@LocallyOfFiniteType ⊓ @FormallyUnramified) :=
by
rw [MorphismProperty.hasOfPostcompProperty_iff_le_diagonal]
intro X Y f ⟨hft, hfu⟩
exact inferInstanceAs <| IsEtale (pullback.diagonal f)
