instNonemptyNormalizationMonoidOfNormalizedGCDMonoid

English

If α has a NormalizedGCDMonoid structure, then α has a NormalizationMonoid structure.

Русский

Если на α есть структура NormalizedGCDMonoid, то существует структура NormalizationMonoid(α).

LaTeX

$$$$ (\\exists \\mathcal{NG} : \\text{NormalizedGCDMonoid}(\\alpha)) \\Rightarrow (\\exists \\mathcal{N} : \\text{NormalizationMonoid}(\\alpha)). $$$$

Lean4

instance [h : Nonempty (NormalizedGCDMonoid α)] : Nonempty (NormalizationMonoid α) :=
  h.elim fun _ ↦ inferInstance

Похожие утверждения