toMultiplicative_toAdditive — Mathlib

English

There is an equivalence between Multiplicative G ≃*o H and Additive G ≃+o Additive H.

Русский

Существует эквивалентность между Multiplicative G ≃*o H и Additive G ≃+o Additive H.

LaTeX

$$$ \mathrm{toAdditiveRight}: (\mathrm{Multiplicative}\,G \simeq_o^{*} H) \to (\mathrm{Additive}\,G \simeq_o+ \mathrm{Additive}\,H) $$$

Lean4

/-- The multiplicative version of an additivized ordered monoid is order-mul-equivalent to itself.
-/
def toMultiplicative_toAdditive {G : Type*} [CommMonoid G] [PartialOrder G] : Multiplicative (Additive G) ≃*o G :=
  OrderAddMonoidIso.toMultiplicativeLeft <| OrderMonoidIso.toAdditive (.refl _)

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