English
For α, β with ordered monoid structures, the instance Mul of OrderMonoidHom α β is well-defined and respects MonoidHom structure.
Русский
Для пар α, β с упорядоченными моноидами существует корректная структура Mul для OrderMonoidHom α β, которая сохраняет структуру гомоморфизма моноида.
LaTeX
$$MonoidHom-like multiplication on OrderMonoidHom is well-defined.$$
Lean4
/-- Makes an ordered group homomorphism from a proof that the map preserves multiplication. -/
@[to_additive /-- Makes an ordered additive group homomorphism from a proof that the map preserves
addition. -/
]
def mk' (f : α → β) (hf : Monotone f) (map_mul : ∀ a b : α, f (a * b) = f a * f b) : α →*o β :=
{ MonoidHom.mk' f map_mul with monotone' := hf }
