reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem
  for X1 being Subset of X, Y1 being Subset of Y st [:X1,Y1:] <> {}
  holds Pr1(X,Y). [:X1,Y1:] = X1 & Pr2(X,Y). [:X1,Y1:] = Y1 by EQREL_1:50;
