
theorem
for p being Prime
for n being non zero Nat
for F being Field st card F = p|^n holds (Frob F)`^n = id F
proof
let p be Prime, n be non zero Nat, F be Field;
set g = (Frob F)`^n;
assume AS: card F = p|^n; then
I: Char F = p by T5;
now let a be Element of F;
  thus g.a = a|^(p|^n) by I,T4 .= (id F).a by AS,thX0;
  end;
hence thesis;
end;
