End BDDreplace_results.
Fixpoint BDDreplacel (cfg : BDDconfig) (ul : list ad)
(node : ad) (lx ly : list BDDvar) {struct ly} : BDDconfig * ad :=
match lx, ly with
| nil, _ => (cfg, node)
| _ :: _, nil => (cfg, node)
| x :: lx', y :: ly' =>
match BDDreplacel cfg ul node lx' ly' with
| (cfg1, node1) => BDDreplace cfg1 (node1 :: ul) node1 x y
end
end.

(* Specifications: *)
Lemma BDDreplacel_lemma :
forall (lx ly : list ad) (cfg : BDDconfig) (ul : list ad) (node : ad),
BDDconfig_OK cfg ->
used_list_OK cfg ul ->
used_node' cfg ul node ->
ad_list_neq lx ly = true ->
BDDconfig_OK (fst (BDDreplacel cfg ul node lx ly)) /\
config_node_OK (fst (BDDreplacel cfg ul node lx ly))
(snd (BDDreplacel cfg ul node lx ly)) /\
used_nodes_preserved cfg (fst (BDDreplacel cfg ul node lx ly)) ul /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDreplacel cfg ul node lx ly))
(snd (BDDreplacel cfg ul node lx ly)))
(bool_fun_replacel (bool_fun_of_BDD cfg node) lx ly).