∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : TopologicalSpace E] [inst_3 : TopologicalSpace F] [inst_4 : AddCommMonoid E] [inst_5 : AddCommMonoid F]
  [inst_6 : Module 𝕜 E] [inst_7 : Module 𝕜 F] {s : Set F},
  StrictConvex 𝕜 s → ∀ {f : E → F}, IsLinearMap 𝕜 f → Continuous f → Function.Injective f → StrictConvex 𝕜 (f ⁻¹' s)