Theorems · Theorem · group theory

finprod_mul_distrib

∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] {f g : α → M},
  Function.HasFiniteMulSupport f →
    Function.HasFiniteMulSupport g → ∏ᶠ (i : α), f i * g i = (∏ᶠ (i : α), f i) * ∏ᶠ (i : α), g i

If the multiplicative supports of f and g are finite, then the product of f i * g i equals the product of f i multiplied by the product of g i.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

8 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoid