Theorems · Theorem · convex and discrete geometry

ConvexIndependent.comp_embedding

∀ {𝕜 : Type u_1} {E : Type u_2} {ι : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] {ι' : Type u_4} (f : ι' ↪ ι) {p : ι → E}, ConvexIndependent 𝕜 p → ConvexIndependent 𝕜 (p ∘ ⇑f)

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

Defined in

Mathlib.Analysis.Convex.Independent

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommGroupModule