reserve x1,x2,y1,a,b,c for Real;

theorem Th1:
  a >= 0 & a < b & c > 0 implies a to_power c < b to_power c
proof
  a = 0 & c > 0 implies a to_power c = 0 by POWER:def 2;
  hence thesis by POWER:34,37;
end;
