Theorems · Theorem · geometry

finite_of_fin_dim_affineIndependent

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} {ι : Type u_4} [inst : DivisionRing k] [inst_1 : AddCommGroup V]
  [inst_2 : Module k V] [inst_3 : AddTorsor V P] [FiniteDimensional k V] {p : ι → P}, AffineIndependent k p → Finite ι

An affine-independent family of points in a finite-dimensional affine space is finite.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorFiniteDimensional