reserve Values for Values_with_Bool;
reserve a, a1, a2 for Element of the carrier of Values;
reserve S for Events_structure over Values;
reserve p, p1, p2 for Process of S;
reserve x, x1, x2 for Location of S;
reserve tr, tr1, tr2 for trace of S;
reserve e, e0, e1, e2, e3, e4, e5 for Event of S;
reserve E for EventSet of S;
reserve DS for DistributedSysWithSharedMem of Values;
reserve p, p1, p2 for Process of DS;
reserve x, x1, x2, flag1, flag2, turn for Location of DS;
reserve tr, tr1, tr2 for trace of DS;
reserve e, e0, e1, e2, e3, e4, e5 for Event of DS;
reserve E for EventSet of DS;

theorem
  (e1,e2) interval_in (p,tr) c= (e1,e2) inter
proof
  let o be object such that O1: o in (e1,e2) interval_in (p,tr);
  consider e such that O2: e = o & e1 < e & e < e2 & e in p,tr by O1;
  thus thesis by O2;
end;
