Theorems · Theorem · geometry

Projectivization.Subspace.span_union

∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  (S T : Set (Projectivization K V)),
  Projectivization.Subspace.span (S ∪ T) = Projectivization.Subspace.span S ⊔ Projectivization.Subspace.span T

The supremum of two subspaces is equal to the span of their union.

Defined in

Mathlib.LinearAlgebra.Projectivization.Subspace

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule