
theorem Th6:
  for n being Nat, r being non zero Real st n is even holds
    r to_power n > 0
  proof
    let n be Nat;
    let r be non zero Real;
    assume A1: n is even;
    per cases;
    suppose r > 0;
      hence thesis by POWER:34;
    end;
    suppose A2: r < 0;
      r to_power n = (-r) to_power n by Th3,A1;
      hence thesis by A2,POWER:34;
    end;
  end;
