∀ {R : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
  [inst_3 : AddCommMonoid E] [inst_4 : Module R E] [inst_5 : AddCommMonoid F] [inst_6 : Module R F]
  (C : PointedCone R E) (f : E →ₗ[R] F), ↑(PointedCone.map f C) = ConvexCone.map f ↑C