Theorems · Theorem · geometry

Projectivization.Subspace.sup_span

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

The supremum of a subspace and the span of a set of points is equal to the span of the union of the subspace and the set of points.

Defined in

Mathlib.LinearAlgebra.Projectivization.Subspace

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule