Theorems · Theorem · geometry

Projectivization.Subspace.span_iUnion

∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Sort u_3}
  (s : ι → Set (Projectivization K V)),
  Projectivization.Subspace.span (⋃ i, s i) = ⨆ i, Projectivization.Subspace.span (s i)

The supremum of a collection of subspaces is equal to the span of the union of the collection.

Defined in

Mathlib.LinearAlgebra.Projectivization.Subspace

Cited by

0 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModule