equivMap — Mathlib

English

There is an algebra isomorphism between L and its image L.map f given by an injective algebra hom f.

Русский

Существует алгебраическое изоморфизм между L и L.map f, заданный инъективным алгебра-гомоморфом.

LaTeX

$$$L \\equiv_A^F L.map f$$$

Lean4

/-- An intermediate field is isomorphic to its image under an `AlgHom`
(which is automatically injective). -/
noncomputable def equivMap : L ≃ₐ[F] L.map f :=
  (AlgEquiv.ofInjective _ (f.comp L.val).injective).trans (equivOfEq (fieldRange_comp_val L f))

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