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 thEvStrictPrec:
  e1 in p & e2 in p & e1 < e2 implies e1 << e2
proof
  assume A1: e1 in p & e2 in p;
  assume A2: e1 < e2;
  DS is consistent;
  then DS is pr-ordered;
  then not e1 <= e2 or not e2 <= e1 by A1, A2;
  hence thesis by A2, ORDERS_2:def 6;
end;
