
theorem Th7:
  for n being Nat, r being Real st n is odd & r < 0 holds
    r to_power n < 0
  proof
    let n be Nat;
    let r be Real;
    assume A1: n is odd;
    assume A2: r < 0;
A3: r to_power n = (--r) to_power n .= - ((-r) to_power n) by Th4,A1,A2;
    (-r) to_power n > 0 by A2,POWER:34;
    hence thesis by A3;
  end;
