
theorem POWER37:
  for a,b be non negative Real, c be positive Real holds
  a >= b iff a to_power c >= b to_power c
  proof
    let a,b be non negative Real, c be positive Real;
    b = 0 implies b to_power c = 0 by POWER:def 2; then
    A1: a > b implies a to_power c >= b to_power c by POWER:37;
    a = 0 implies a to_power c = 0 by POWER:def 2;
    hence thesis by A1,XXREAL_0:1,POWER:37;
  end;
