Theorems · Theorem · commutative algebra

Multiset.sum_smul_sum

∀ {R : Type u_5} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Multiset R}
  {t : Multiset M}, s.sum • t.sum = (Multiset.map (fun p => p.1 • p.2) (s ×ˢ t)).sum

Defined in

Mathlib.Algebra.Module.BigOperators

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule