Definition bool_fun_var (x : BDDvar) : bool_fun :=
  fun vb : var_binding => vb x.

(* Specifications: *)
Lemma BDDvar_make_is_var : forall (cfg : BDDconfig) (x : BDDvar), BDDconfig_OK cfg -> bool_fun_eq (bool_fun_of_BDD (fst (BDDvar_make cfg x)) (snd (BDDvar_make cfg x))) (bool_fun_var x).