∀ {k : Type u_1} {E : Type u_2} [inst : Field k] [inst_1 : AddCommGroup E] [inst_2 : Module k E]
  [inst_3 : LinearOrder k] [IsStrictOrderedRing k] [inst_5 : PartialOrder E] [IsOrderedAddMonoid E] [PosSMulMono k E]
  {f : k → E} {x y : k}, x ≤ y → (slope f x y < 0 ↔ f y < f x)