Structure > Faithful : Type := 
  {Faithful_functor :> Functor C D;
   Prf_isFaithful :> Faithful_law Faithful_functor}.Structure > Faithful : Type := 
  {Faithful_functor :> Functor C D;
   Prf_isFaithful :> Faithful_law Faithful_functor}.Structure > Faithful : Type := 
  {Faithful_functor :> Functor C D;
   Prf_isFaithful :> Faithful_law Faithful_functor}.

Lemma IsFaithful_comp : Faithful_law F -> Faithful_law G -> Faithful_law (F o_F G).