proposition: Lemma BDDcompare_succ : forall a : BDDvar, BDDcompare a (ad_S a) = Datatypes.Lt.
proof: Proof. simple induction a. simpl in |- *. trivial. simpl in |- *. intro p. cut (nat_of_P p < nat_of_P (Pos.succ p)). intro H. apply nat_of_P_lt_Lt_compare_complement_morphism. assumption. cut (nat_of_P (Pos.succ p) = 1 + nat_of_P p). intro H. rewrite H. simpl in |- *. unfold lt in |- *. trivial. unfold nat_of_P in |- *. apply Pmult_nat_succ_morphism. Qed.
imports: Bool Sumbool Arith ZArith NArith Nnat Ndec Ndigits IntMap(Allmaps)