
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 AM1; then
    log (c,d) < 1 by A2,XXREAL_0:2;
    hence thesis by AG1;
  end;
