theorem Th5:
  Z c= [:X,Y:] implies proj1 Z c= X & proj2 Z c= Y
proof
  assume Z c= [:X,Y:];
  then
A1: proj1 Z c= proj1 [:X,Y:] & proj2 Z c= proj2 [:X,Y:] by XTUPLE_0:8,9;
  proj1 [:X,Y:] c= X & proj2 [:X,Y:] c= Y by Th4;
  hence thesis by A1;
end;
