Theorems · Theorem · group theory

finprod_div_distrib

∀ {α : Type u_1} {G : Type u_4} [inst : DivisionCommMonoid G] {f g : α → G},
  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 divided by the product of g i.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionCommMonoid