Theorems · Theorem · geometry

Projectivization.Subspace.mem_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)} (u : Projectivization K V),
  u ∈ Projectivization.Subspace.span S ↔ ∀ (W : Projectivization.Subspace K V), S ⊆ ↑W → u ∈ W

A point in a projective space is contained in the span of a set of points if and only if the point is contained in all subspaces of the projective space which contain the set of points.

Defined in

Mathlib.LinearAlgebra.Projectivization.Subspace

Cited by

1 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModule