Theorems · Theorem · geometry

Projectivization.dependent_pair_iff_eq

∀ {K : Type u_2} {V : Type u_3} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  (u v : Projectivization K V), Projectivization.Dependent ![u, v] ↔ u = v

Two points in a projective space are dependent if and only if they are equal.

Defined in

Mathlib.LinearAlgebra.Projectivization.Independence

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule