Theorems · Theorem · geometry

Collinear.finiteDimensional_direction_affineSpan

∀ {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}, Collinear k s → FiniteDimensional k ↥(affineSpan k s).direction

The direction of the affine span of collinear points is finite-dimensional.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

0 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModuleAddTorsor