reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  a <> b implies 0 < a-b or 0 < b-a
proof
  assume a <> b;
  then per cases by XXREAL_0:1;
  suppose a < b;
    then 0 + a < b;
    hence thesis by Lm19;
  end;
  suppose b < a;
    then 0 + b < a;
    hence thesis by Lm19;
  end;
end;
