Theorems · Theorem · order theory

Submodule.sum_mem_biSup

∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_4}
  {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}, (∀ i ∈ s, f i ∈ p i) → ∑ i ∈ s, f i ∈ ⨆ i ∈ s, p i

Defined in

Mathlib.Algebra.Module.Submodule.Lattice

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule