proposition: Lemma lift_F_compose (X Y Z:Set) (g:X->Y) (f:Y->Z) fx: (fun fx0 => lift_F_ Y Z f (lift_F_ X Y g fx0)) fx = lift_F_ X Z (fun x => f (g x)) fx.
proof: Proof. destruct fx as [fa|fb]; unfold lift_F_; [ rewrite FA.lift_F_compose | rewrite FB.lift_F_compose] ; reflexivity. Qed.