Theorems · Theorem · geometry

AffineIndependent.comp_embedding

∀ {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} {ι2 : Type u_5} (f : ι2 ↪ ι) {p : ι → P},
  AffineIndependent k p → AffineIndependent k (p ∘ ⇑f)

If a family is affinely independent, so is any subfamily given by composition of an embedding into index type with the original family.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Independent

Cited by

8 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor