contravariant_swap_mul_of_contravariant_mul

English

If a commutative semigroup has a covariant multiplication, swapping the operands preserves covariance.

Русский

У коммутативной полугруппе ковариантность сохраняется при смене мест операндов.

LaTeX

$$$\operatorname{Covariant}(\text{swap})$ given covariance of original operation.$$

Lean4

@[to_additive]
instance contravariant_swap_mul_of_contravariant_mul [CommSemigroup N] [ContravariantClass N N (· * ·) r] :
    ContravariantClass N N (swap (· * ·)) r where
  elim := (contravariant_flip_iff N r (· * ·)).mpr ContravariantClass.elim

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