Theorems · Theorem · convex and discrete geometry

mem_convexHull_of_exists_fintype

∀ {R : Type u_1} {E : Type u_3} {ι : Type u_5} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  [inst_3 : LinearOrder R] [IsStrictOrderedRing R] {s : Set E} {x : E} [inst_5 : Fintype ι] (w : ι → R) (z : ι → E),
  (∀ (i : ι), 0 ≤ w i) → ∑ i, w i = 1 → (∀ (i : ι), z i ∈ s) → ∑ i, w i • z i = x → x ∈ (convexHull R) s

Universe polymorphic version of the reverse implication of mem_convexHull_iff_exists_fintype.

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

3 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleLinearOrderIsStrictOrderedRingFintype