∀ {A₁ : Type u_1} {A₂ : Type u_2} [inst : NonUnitalCStarAlgebra A₁] [inst_1 : NonUnitalCStarAlgebra A₂]
  [inst_2 : PartialOrder A₁] [inst_3 : PartialOrder A₂] [inst_4 : StarOrderedRing A₁] [inst_5 : StarOrderedRing A₂]
  (f g : CompletelyPositiveMap A₁ A₂), (fun f => f.toFun) f = (fun f => f.toFun) g → f = g