Theorems · Theorem · commutative algebra

Finset.sum_smul

∀ {ι : Type u_1} {R : Type u_5} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {f : ι → R} {s : Finset ι} {x : M}, (∑ i ∈ s, f i) • x = ∑ i ∈ s, f i • x

Defined in

Mathlib.Algebra.Module.BigOperators

Cited by

30 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModule