theorem Th18:
  Px(a,|.4*x+y.|), Px(a,|.y.|) are_congruent_mod Px(a,|.x.|)
proof
A1: Px(a,|.2*x+y.|) * (-1),(- Px(a,|.y.|))*(-1)
  are_congruent_mod Px(a,|.x.|) by Th17,INT_4:11;
  Px(a,|.2*x+(2*x+y).|),- Px(a,|.2*x+y.|)
  are_congruent_mod Px(a,|.x.|) by Th17;
  hence thesis by A1,INT_1:15;
end;
