
theorem
  for a,b be heavy positive Real holds
  log (b,a) < 1 implies a < b
  proof
    let a,b be heavy positive Real;
    A1: a > 1 & b > 1 by TA1;
    assume
    B1: log (b,a) < 1; then
    B2: log (b,a) < log (b,b) by A1,POWER:52;
    a <= b by A1,B2,POWER:57;
    hence thesis by B1,AZ1,XXREAL_0:1;
  end;
