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