Theorems · Theorem · commutative algebra

Submodule.sum_smul_mem

∀ {R : Type u} {M : Type v} {ι : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M}
  (p : Submodule R M) {t : Finset ι} {f : ι → M} (r : ι → R), (∀ c ∈ t, f c ∈ p) → ∑ i ∈ t, r i • f i ∈ p

Defined in

Mathlib.Algebra.Module.Submodule.Basic

Cited by

8 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoid