Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.sConvexComb_mem

∀ {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] {w : Convexity.StdSimplex R X} {s : Set X},
  Convexity.IsConvexSet R s → ↑w.weights.support ⊆ s → Convexity.sConvexComb w ∈ s

Defined in

Mathlib.Geometry.Convex.Set

Cited by

5 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace