Theorems · Theorem · linear algebra

Submodule.mem_sSup_iff_exists_finset

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {S : Set (Submodule R M)} {m : M}, m ∈ sSup S ↔ ∃ s, ↑s ⊆ S ∧ m ∈ ⨆ i ∈ s, i

Defined in

Mathlib.LinearAlgebra.Finsupp.Span

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule