Theorems · Theorem · convex and discrete geometry

Caratheodory.minCardFinsetOfMemConvexHull_nonempty

∀ {𝕜 : Type u_1} {E : Type u} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {s : Set E} {x : E} (hx : x ∈ (convexHull 𝕜) s),
  (Caratheodory.minCardFinsetOfMemConvexHull hx).Nonempty

Defined in

Mathlib.Analysis.Convex.Caratheodory

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModule