of_equiv — Mathlib

English

If R → A is formally étale, then it is formally unramified.

Русский

Если R → A формально étale, то оно формально нерасчленимо.

LaTeX

$$$[h : FormallyEtale\; R\; A] \Rightarrow [FormallyUnramified\; R\; A]$$$

Lean4

/-- Being étale is transported via algebra isomorphisms. -/
theorem of_equiv [Etale R A] (e : A ≃ₐ[R] B) : Etale R B
    where
  formallyEtale := FormallyEtale.of_equiv e
  finitePresentation := FinitePresentation.equiv e

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