Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.iConvexComb_mem

∀ {ι : Type u_1} {R : Type u_3} {X : Type u_5} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R X] {s : Set X},
  Convexity.IsConvexSet R s →
    ∀ {w : Convexity.StdSimplex R ι} {f : ι → X}, (∀ (i : ι), w.weights i ≠ 0 → f i ∈ s) → Convexity.iConvexComb w f ∈ s

Defined in

Mathlib.Geometry.Convex.Set

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace