
theorem
  for a,b be heavy positive Real holds
  log (a,b) > log (b,a) >= 1 implies a > b
  proof
    let a,b be heavy positive Real;
    A1: a > 1 & b > 1 by TA1;
    assume
    A2: log (a,b) > log (b,a);
    assume log (b,a) >= 1; then
    B2: log (b,a) >= log (b,b) by A1,POWER:52;
    B4: a <> b by A2;
    a >= b by A1,B2,POWER:57;
    hence thesis by B4,XXREAL_0:1;
  end;
