Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Inductive bool_expr : Set :=
  | Zero : bool_expr
  | One : bool_expr
  | Var : BDDvar -> bool_expr
  | Neg : bool_expr -> bool_expr
  | Or : bool_expr -> bool_expr -> bool_expr
  | ANd : bool_expr -> bool_expr -> bool_expr
  | Impl : bool_expr -> bool_expr -> bool_expr
  | Iff : bool_expr -> bool_expr -> bool_expr.Fixpoint bool_fun_of_bool_expr (be : bool_expr) : bool_fun :=
  match be with
  | Zero => bool_fun_zero
  | One => bool_fun_one
  | Var x => bool_fun_var x
  | Neg be' => bool_fun_neg (bool_fun_of_bool_expr be')
  | Or be1 be2 =>
      bool_fun_or (bool_fun_of_bool_expr be1) (bool_fun_of_bool_expr be2)
  | ANd be1 be2 =>
      bool_fun_and (bool_fun_of_bool_expr be1) (bool_fun_of_bool_expr be2)
  | Impl be1 be2 =>
      bool_fun_impl (bool_fun_of_bool_expr be1) (bool_fun_of_bool_expr be2)
  | Iff be1 be2 =>
      bool_fun_iff (bool_fun_of_bool_expr be1) (bool_fun_of_bool_expr be2)
  end.Fixpoint BDDof_bool_expr (cfg : BDDconfig) (negm : BDDneg_memo)
 (orm : BDDor_memo) (be : bool_expr) {struct be} :
 BDDconfig * (ad * (BDDneg_memo * BDDor_memo)) :=
  match be with
  | Zero => (cfg, (BDDzero, (negm, orm)))
  | One => (cfg, (BDDone, (negm, orm)))
  | Var x =>
      match BDDvar_make cfg x with
      | (cfg', node) => (cfg', (node, (negm, orm)))
      end
  | Neg be' =>
      match BDDof_bool_expr cfg negm orm be' with
      | (cfg', (node, (negm', orm'))) =>
          match BDDneg cfg' negm' node with
          | (cfg'', (node', negm'')) => (cfg'', (node', (negm'', orm')))
          end
      end
  | Or be1 be2 =>
      match BDDof_bool_expr cfg negm orm be1 with
      | (cfg', (node1, (negm', orm'))) =>
          match BDDof_bool_expr cfg' negm' orm' be2 with
          | (cfg'', (node2, (negm'', orm''))) =>
              match BDDor cfg'' orm'' node1 node2 with
              | (cfg''', (node, orm''')) =>
                  (cfg''', (node, (negm'', orm''')))
              end
          end
      end
  | ANd be1 be2 =>
      match BDDof_bool_expr cfg negm orm be1 with
      | (cfg', (node1, (negm', orm'))) =>
          match BDDof_bool_expr cfg' negm' orm' be2 with
          | (cfg'', (node2, (negm'', orm''))) =>
              BDDand cfg'' negm'' orm'' node1 node2
          end
      end
  | Impl be1 be2 =>
      match BDDof_bool_expr cfg negm orm be1 with
      | (cfg', (node1, (negm', orm'))) =>
          match BDDof_bool_expr cfg' negm' orm' be2 with
          | (cfg'', (node2, (negm'', orm''))) =>
              BDDimpl cfg'' negm'' orm'' node1 node2
          end
      end
  | Iff be1 be2 =>
      match BDDof_bool_expr cfg negm orm be1 with
      | (cfg', (node1, (negm', orm'))) =>
          match BDDof_bool_expr cfg' negm' orm' be2 with
          | (cfg'', (node2, (negm'', orm''))) =>
              BDDiff cfg'' negm'' orm'' node1 node2
          end
      end
  end.

(* Specifications: *)
Lemma BDDof_bool_expr_correct : forall (be : bool_expr) (cfg : BDDconfig) (negm : BDDneg_memo) (orm : BDDor_memo), BDDconfig_OK cfg -> BDDneg_memo_OK_2 cfg negm -> BDDor_memo_OK cfg orm -> BDDconfig_OK (fst (BDDof_bool_expr cfg negm orm be)) /\ config_node_OK (fst (BDDof_bool_expr cfg negm orm be)) (fst (snd (BDDof_bool_expr cfg negm orm be))) /\ BDDneg_memo_OK_2 (fst (BDDof_bool_expr cfg negm orm be)) (fst (snd (snd (BDDof_bool_expr cfg negm orm be)))) /\ BDDor_memo_OK (fst (BDDof_bool_expr cfg negm orm be)) (snd (snd (snd (BDDof_bool_expr cfg negm orm be)))) /\ nodes_preserved cfg (fst (BDDof_bool_expr cfg negm orm be)) /\ bool_fun_eq (bool_fun_of_BDD (fst (BDDof_bool_expr cfg negm orm be)) (fst (snd (BDDof_bool_expr cfg negm orm be)))) (bool_fun_of_bool_expr be).