Section comp_functor_prop.
Variables (C D E : Category) (F : Functor C D) (G : Functor D E).
Variables (F1 : forall a b : C, (F a --> F b) -> (a --> b))
(G1 : forall a b : D, (G a --> G b) -> (a --> b)).

Lemma IsFull_comp :
Full_law F1 ->
Full_law G1 ->
let H1 := fun (a b : C) (h : G (F a) --> G (F b)) => F1 (G1 h) in
Full_law (F:=F o_F G) H1.