reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;
reserve D for non empty set;
reserve p,q,r for PartialPredicate of D;

theorem Th9:
  x in dom p & x in dom q & PP_or(p,q).x = TRUE implies
   p.x = TRUE or q.x = TRUE
  proof
    assume that
A1: x in dom p and
A2: x in dom q and
A3: PP_or(p,q).x = TRUE;
    p.x <> FALSE or q.x <> FALSE by A1,A2,A3,Def4;
    hence thesis by A1,A2,Th3;
  end;
