Definition bool_fun_impl (bf1 bf2 : bool_fun) : bool_fun :=
  fun vb : var_binding => implb (bf1 vb) (bf2 vb).

Lemma BDDimpl_is_impl : forall (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo) (node1 node2 : ad), BDDconfig_OK cfg -> BDDneg_memo_OK_2 cfg negm -> BDDor_memo_OK cfg orm -> config_node_OK cfg node1 -> config_node_OK cfg node2 -> bool_fun_eq (bool_fun_of_BDD (fst (BDDimpl cfg negm orm node1 node2)) (fst (snd (BDDimpl cfg negm orm node1 node2)))) (bool_fun_impl (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).