∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : LinearOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [PosSMulMono 𝕜 E] [inst_7 : AddCommGroup β]
  [inst_8 : PartialOrder β] [IsOrderedAddMonoid β] [inst_10 : Module 𝕜 β] [PosSMulMono 𝕜 β] {e : E} {f g : E → β},
  ConcaveOn 𝕜 (Set.Iic e) f →
    ConcaveOn 𝕜 (Set.Ici e) g →
      MonotoneOn f (Set.Iic e) → AntitoneOn g (Set.Ici e) → f e = g e → ConcaveOn 𝕜 Set.univ ((Set.Iic e).piecewise f g)