Theorems · Theorem · convex and discrete geometry

openSegment_subset_iff

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : SMul 𝕜 E] {s : Set E} {x y : E},
  openSegment 𝕜 x y ⊆ s ↔ ∀ (a b : 𝕜), 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

2 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

SemiringPartialOrderAddCommMonoidSMul