ext_mint — Mathlib

English

Two MonoidHom from Multiplicative ℤ to a monoid M are equal if they agree on the image of ofAdd 1.

Русский

Два моноид-гомоморфизма from Multiplicative ℤ в моноид M равны, если совпадают на образе ofAdd 1.

LaTeX

$$$$ \\forall {f,g : Multiplicative \\mathbb{Z} \\to* M},\\ f(\\mathrm{ofAdd}(1)) = g(\\mathrm{ofAdd}(1)) \\Rightarrow f = g. $$$$

Lean4

@[ext]
theorem ext_mint {f g : Multiplicative ℤ →* M} (h1 : f (ofAdd 1) = g (ofAdd 1)) : f = g :=
  MonoidHom.toAdditiveRight.injective <| AddMonoidHom.ext_int <| Additive.toMul.injective h1

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