fact: Fixpoint synt_wp (prog: ImpProg) : Pred -> Pred := fun post e => match prog with | Iskip => post e | (Iset A x expr) => post (E.upd x (E.eval expr e) e) | (Iif cond p1 p2) => ((E.eval cond e)=true -> (synt_wp p1 post e)) /\ ((E.eval cond e)=false -> (synt_wp p2 post e)) | (Iseq p1 p2) => synt_wp p1 (synt_wp p2 post) e | (Iwhile cond p) => exists inv:Pred, (inv e) /\ (forall e', (inv e') -> (E.eval cond e')=false -> (post e')) /\ (forall e', (inv e') -> (E.eval cond e')=true -> (synt_wp p inv e')) end.
imports: hoarelogicsemantics