Theorems · Theorem · linear algebra

Submodule.mem_iSup_of_chain

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (a : ℕ →o Submodule R M) (m : M), m ∈ ⨆ k, a k ↔ ∃ k, m ∈ a k

Defined in

Mathlib.LinearAlgebra.Span.Defs

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule