Theorems · Theorem · linear algebra

Submodule.mem_sup

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : M}
  {p p' : Submodule R M}, x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x

Defined in

Mathlib.LinearAlgebra.Span.Defs

Cited by

73 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule