Theorems · Theorem · convex and discrete geometry

Convex.convexHull_union

∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {s t : Set E},
  Convex 𝕜 s → Convex 𝕜 t → s.Nonempty → t.Nonempty → (convexHull 𝕜) (s ∪ t) = convexJoin 𝕜 s t

Defined in

Mathlib.Analysis.Convex.Join

Cited by

1 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModule