induction F;intros A B C H;simpl;auto.
apply IHF;auto.
Qed.

Theorem compose3 :
forall hyps F (A B C D:Prop),
(A -> B -> C -> D) ->
(interp_ctx hyps F A) ->
(interp_ctx hyps F B) ->
(interp_ctx hyps F C) ->
(interp_ctx hyps F D).