
theorem Th1:
  for x,y being odd Element of NAT holds x < y iff x + 2 <= y
proof
  let x,y be odd Element of NAT;
  hereby
    assume x < y;
    then x + 1 <= y by NAT_1:13;
    then x + 1 < y by XXREAL_0:1;
    then x + 1 + 1 < y + 1 by XREAL_1:8;
    hence x + 2 <= y by NAT_1:13;
  end;
  assume x + 2 <= y;
  then x + 2 - 2 < y - 0 by XREAL_1:15;
  hence thesis;
