
theorem ThNS:
for F being finite Field
holds F is (PrimeField F)-normal (PrimeField F)-separable
                                      FieldExtension of (PrimeField F)
proof
let F be finite Field;
consider p being Prime, n being non zero Nat such that
A: Char F = p & order F = p|^n by finex2;
reconsider E = F as SplittingField of X^(p|^n,PrimeField F) by A,split;
E is (PrimeField F)-normal FieldExtension of (PrimeField F);
hence thesis;
end;
