Theorems · Theorem · geometry

Projectivization.IsCollinear_iff_rank

∀ {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.IsCollinear S ↔ ∃ M, Module.rank K ↥(Projectivization.Subspace.submodule M) ≤ 2 ∧ S ⊆ ↑M

Defined in

Mathlib.LinearAlgebra.Projectivization.Collinear

Cited by

1 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule