instCommMonoid — Mathlib

English

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

Русский

Структура LowerSet α образует коммутативный моноид с единицей 1; LowerSet α образует CommMonoid, где 1 является единицей умножения.

LaTeX

$$LowerSet α forms a CommMonoid with 1 and mul, satisfying commutativity and associativity.$$

Lean4

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

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