
theorem RNS4:
  for x,y be Real, x1,y1 be Point of RNS_Real
    st x=x1 & y=y1 holds x-y = x1-y1
proof
  let x,y be Real, x1,y1 be Point of RNS_Real;
  assume AS: x=x1 & y=y1; then
P1: -y = -y1 by RNS3;
  x-y = x + -y;
  hence x-y = x1-y1 by AS,BINOP_2:def 9,P1;
end;
