
theorem CPOWER57:
  for a,b,c be Real st 1 < a & 0 < b & b <= c holds
    log(a,b) <= log(a,c)
  proof
    let a,b,c be Real;
    assume AS: 1 < a & 0 < b & b <= c;
    now per cases by AS,XXREAL_0:1;
      case b < c;
        hence log(a,b) < log(a,c) by POWER:57,AS;
      end;
      case b = c;
        hence log(a,b) =log(a,c);
      end;
    end;
    hence thesis;
  end;
