reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

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;
