theorem Th1:
  for L st 0<L & L<1 holds for n,m st n<=m holds L to_power m <= L to_power n
proof
  let L such that
A1: 0<L & L<1;
  let n,m such that
A2: n<=m;
  per cases by A2,XXREAL_0:1;
  suppose n<m;
    hence thesis by A1,POWER:40;
  end;
  suppose n=m;
    hence thesis;
  end;
end;
