Theorems · Theorem · geometry

AffineIndependent.of_set_of_injective

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} {p : ι → P},
  (AffineIndependent k fun x => ↑x) → Function.Injective p → AffineIndependent k p

If the range of an injective indexed family of points is affinely independent, so is that family.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Independent

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor