
theorem thX1:
for p being Prime
for n being non zero Nat
for F being p-characteristic Field st card F = p|^n
for a being Element of F holds eval(X^(p|^n,F),a) = 0.F
proof
let p be Prime, n be non zero Nat, F be p-characteristic Field;
assume A: card F = p|^n;
let a be Element of F;
a|^(p|^n) = a by A,thX0;
then a is_a_root_of X^(p|^n,F) by thXX;
hence thesis;
end;
