Theorems · Theorem · convex and discrete geometry

convexHull_insert

∀ {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 : Set E} {x : E},
  s.Nonempty → (convexHull 𝕜) (insert x s) = convexJoin 𝕜 {x} ((convexHull 𝕜) s)

Defined in

Mathlib.Analysis.Convex.Join

Cited by

2 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModule