reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th16:
  X c= Z & Y c= Z implies X (\/) Y c= Z
proof
  assume
A1: X c= Z & Y c= Z;
  let i be object;
  assume
A2: i in I;
  then X.i c= Z.i & Y.i c= Z.i by A1;
  then X.i \/ Y.i c= Z.i by XBOOLE_1:8;
  hence thesis by A2,Def4;
end;
