
theorem cof2:
for F being Field
for E being FieldExtension of F
for p being non zero Polynomial of E
st Coeff p c= the carrier of F holds p is non zero Polynomial of F
proof
let F be Field, E be FieldExtension of F, p be non zero Polynomial of E;
assume Coeff p c= the carrier of F; then
reconsider q = p as Polynomial of F by cof1;
p <> 0_.(E);
then q <> 0_.(F) by FIELD_4:12;
hence thesis by UPROOTS:def 5;
end;
