
theorem
  for a,b be Real st sgn a > sgn b holds a > b
  proof
    let a,b be Real;
    assume
    A1: sgn a > sgn b;
    a > 0 or a = 0 or a < 0; then
    A2: sgn a = 1 or sgn a = 0 or sgn a = -1 by ABSVALUE:def 2;
    b > 0 or b = 0 or b < 0;
    hence thesis by A1,A2,ABSVALUE:def 2;
  end;
