
theorem AM1:
  for a be light positive Real, b be positive Real holds
  a < b iff log (a,b) < 1
  proof
    let a be light positive Real, b be positive Real;
    1/a > 1/b iff log (1/a,1/b) < 1  by AG1;
    hence thesis by XREAL_1:76,ABO,XREAL_1:118;
  end;
