toMonoid_injective — Mathlib

English

The forgetful map from a commutative monoid to a monoid is injective.

Русский

Замещающий переход от коммутативного моноида к моноиду инъективен.

LaTeX

$$$\text{toMonoid}$ is injective on CommMonoid structures: if two CommMonoid structures have the same underlying operation, they are equal.$$

Lean4

@[to_additive]
theorem toMonoid_injective {M : Type u} : Function.Injective (@CommMonoid.toMonoid M) :=
  by
  rintro ⟨⟩ ⟨⟩ h
  congr

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