∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : AddCommMonoid β] [inst_4 : LinearOrder β] [IsOrderedAddMonoid β] [inst_6 : SMul 𝕜 E] [inst_7 : Module 𝕜 β]
  [PosSMulStrictMono 𝕜 β] {s : Set E} {f : E → β},
  StrictConcaveOn 𝕜 s f → ∀ {x y z : E}, x ∈ s → y ∈ s → x ≠ y → z ∈ openSegment 𝕜 x y → min (f x) (f y) < f z