
theorem
  for a be heavy positive Real,c be light positive Real, b,d be positive Real
  holds
  log (a,b) <= log (c,d) & a < b implies c > d
  proof
    let a be heavy positive Real, c be light positive Real,
        b,d be positive Real;
    assume
    A2: log (a,b) <= log (c,d) & a < b; then
    log (a,b) > 1 by AG2; then
    log (c,d) > 1 by A2,XXREAL_0:2;
    hence thesis by AM2;
  end;
