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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
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(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Inductive capa : Set :=
| Read : capa
| Write : capa
| Both : capa
| Nil : capa.
Inductive capst : capa -> capa -> Prop :=
| capst_refl : forall c : capa, capst c c
| capst_nil : forall c : capa, capst c Nil
| capst_both : forall c : capa, capst Both c.
Parameter type : Set.
Parameter getcap : type -> capa.
Parameter getobj : type -> type.
Parameter typest : type -> type -> Prop.
Axiom
typest_trans :
forall t t' : type,
typest t t' -> forall t'' : type, typest t' t'' -> typest t t''.

Theorem capst_trans :
forall c c' c'' : capa, capst c c' -> capst c' c'' -> capst c c''.