Theorems · Theorem · geometry

affineIndependent_iff_not_collinear_set

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {p₁ p₂ p₃ : P}, AffineIndependent k ![p₁, p₂, p₃] ↔ ¬Collinear k {p₁, p₂, p₃}

Three points are affinely independent if and only if they are not collinear.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

7 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsor