lift_reprField — Mathlib

English

The liftAlgHom composed with reprField equals the inclusion of the adjoin field into the ambient fraction field.

Русский

Подборная композиция liftAlgHom и reprField равна включению в поле частных дробей.

LaTeX

$$$$ (IsFractionRing.liftAlgHom (algebraicIndependent_iff_injective_aeval.2 hx)).comp hx.reprField = IntermediateField.val _. $$$$

Lean4

@[simp]
theorem lift_reprField (p) : IsFractionRing.lift (algebraicIndependent_iff_injective_aeval.2 hx) (hx.reprField p) = p :=
  Subtype.ext_iff.1 (AlgEquiv.apply_symm_apply hx.aevalEquivField p)

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