Theorems · Theorem · group theory

mul_finsum

∀ {α : Type u_1} {R : Type u_7} [inst : NonUnitalNonAssocSemiring R] [NoZeroDivisors R] (f : α → R) (r : R),
  r * ∑ᶠ (a : α), f a = ∑ᶠ (a : α), r * f a

If R has no zero divisors, then multiplication commutes with finsums. See mul_finsum' for a statement assuming finiteness of support.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalNonAssocSemiringNoZeroDivisors