instCommMonoid — Mathlib

English

The structure on UpperSet α extends to a commutative monoid with unit 1, so UpperSet α forms a CommMonoid with 1, and 1 acts as the unit for multiplication.

Русский

Структура верхних множеств образует коммодианную моноиду с единицей 1; верхние множества образуют CommMonoid, где 1 — единица умножения.

LaTeX

$$UpperSet α forms a CommMonoid with 1, mul, and the commutative law, i.e., UpperSet.instCommMonoid.$$

Lean4

@[to_additive]
instance : CommMonoid (UpperSet α) :=
  { UpperSet.commSemigroup with
    one := 1
    one_mul := one_mul
    mul_one := fun s ↦ by
      rw [mul_comm]
      exact one_mul _ }

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