nontrivial — Mathlib

English

Base-ring equivalence preserves fraction field structure.

Русский

Базовый эквивариант сохраняет структуру поля дробей.

LaTeX

$$$IsFractionRing.isFractionRing_iff_of_base_ringEquiv(h) : IsFractionRing R S \iff IsFractionRing P S$$$

Lean4

protected theorem nontrivial (R S : Type*) [CommRing R] [Nontrivial R] [CommRing S] [Algebra R S] [IsFractionRing R S] :
    Nontrivial S := by
  apply nontrivial_of_ne
  · intro h
    apply @zero_ne_one R
    exact
      IsLocalization.injective S (le_of_eq rfl)
        (((algebraMap R S).map_zero.trans h).trans (algebraMap R S).map_one.symm)

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