Theorems · Theorem · geometry

coplanar_iff_finrank_le_two

∀ {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] {s : Set P} [FiniteDimensional k ↥(vectorSpan k s)],
  Coplanar k s ↔ Module.finrank k ↥(vectorSpan k s) ≤ 2

A set of points, whose vectorSpan is finite-dimensional, is coplanar if and only if their vectorSpan has dimension at most 2.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

3 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorFiniteDimensional