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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(*                           --- while.v ---                                *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
Global Set Asymmetric Patterns.
Section while_do.
Variable St : Set. (* states *)
Variable postcond : St -> Prop.
Variable precond : St -> Prop.
Variable Invar : St -> Prop.
Variable term_order : St -> St -> Prop.
Variable LoopExit : St -> Prop.
Hypothesis
LoopExit_dec : forall s : St, Invar s -> {LoopExit s} + {~ LoopExit s}.
Hypothesis
Onestep :
forall s : St,
~ LoopExit s -> Invar s -> {s' : St | Invar s' /\ term_order s' s}.
Hypothesis LoopExit_ok : forall s : St, LoopExit s -> Invar s -> postcond s.
Hypothesis loopstart : forall s : St, precond s -> Invar s.
Hypothesis Termi : well_founded term_order.
Remark loopexec :
forall s : St, Invar s -> {s' : St | Invar s' /\ LoopExit s'}.

(* Specifications: *)
Lemma startloop :
forall s : St, precond s -> {s' : St | Invar s' /\ LoopExit s'}.
Lemma while_not : forall s : St, precond s -> {s' : St | postcond s'}.
End while_do.