English
If two vertices correspond under an index equality, the vertices are equal.
Русский
Если вершины соответствуют при равенстве индексов, вершины равны.
LaTeX
$$$\text{If } x = y \text{ then } \operatorname{vertex}(x) = \operatorname{vertex}(y)$$$
Lean4
/-- A set is strictly convex if the open segment between any two distinct points lies is in its
interior. This basically means "convex and not flat on the boundary". -/
def StrictConvex (𝕜 : Type*) {E : Type*} [Semiring 𝕜] [PartialOrder 𝕜] [TopologicalSpace E] [AddCommMonoid E] [SMul 𝕜 E]
(s : Set E) : Prop :=
s.Pairwise fun x y => ∀ ⦃a b : 𝕜⦄, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ interior s
