Theorems · Theorem · geometry

Projectivization.Subspace.span_eq_sInf

∀ {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)}, Projectivization.Subspace.span S = sInf {W | S ⊆ ↑W}

The span of a set of points in a projective space is equal to the infimum of the collection of subspaces which contain the set.

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