
theorem
  for a,b be non weightless positive Real st
  log (a,b) <= -1 holds 0 > log (b,a) >= -1
  proof
    let a,b be non weightless positive Real;
    assume
    A2: log (a,b) <= -1;
    A4: log (b,a) = 1/log (a,b) by ABA;
    (log (a,b))/(log (a,b)) >= (-1)/(log (a,b)) by A2,XREAL_1:73; then
    1 >= -(1/log (a,b)) by A2,XCMPLX_1:60;
    hence thesis by A4,A2,XREAL_1:26;
  end;
