
theorem FA1:
for F being finite Field holds
F is (PrimeField F)-finite FieldExtension of (PrimeField F)
proof
let F be finite Field;
set P = PrimeField F;
reconsider E = F as FieldExtension of P by FIELD_4:7;
the carrier of E = the carrier of VecSp(E,P) by FIELD_4:def 6;
then [#]VecSp(E,P) is finite;
then VecSp(E,P) is finite-dimensional by RANKNULL:4;
hence thesis by FIELD_4:def 8;
end;
