(* This program is free software; you can redistribute it and/or      *)
(* 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.             *)
(*                                                                    *)
(* 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.                       *)
(*                                                                    *)
(* 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.(* This program is free software; you can redistribute it and/or      *)
(* 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.             *)
(*                                                                    *)
(* 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.                       *)
(*                                                                    *)
(* 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.(* This program is free software; you can redistribute it and/or      *)
(* 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.             *)
(*                                                                    *)
(* 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.                       *)
(*                                                                    *)
(* 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.(* This program is free software; you can redistribute it and/or      *)
(* 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.             *)
(*                                                                    *)
(* 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.                       *)
(*                                                                    *)
(* 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.(* This program is free software; you can redistribute it and/or      *)
(* 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.             *)
(*                                                                    *)
(* 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.                       *)
(*                                                                    *)
(* 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.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.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.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_refl : forall t : type, typest t t.Axiom
  typest_trans :
    forall t t' : type,
    typest t t' -> forall t'' : type, typest t' t'' -> typest t t''.

(* Specifications: *)
Theorem capst_trans : forall c c' c'' : capa, capst c c' -> capst c' c'' -> capst c c''.