Theorems · Theorem · convex and discrete geometry

segment_subset_convexHull

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : Module 𝕜 E] {s : Set E} {x y : E}, x ∈ s → y ∈ s → segment 𝕜 x y ⊆ (convexHull 𝕜) s

Defined in

Mathlib.Analysis.Convex.Hull

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidModule