
theorem alg3:
for f being ascending Field-yielding sequence
for p being Polynomial of (SeqField f)
ex i being Element of NAT st p is Polynomial of (f.i)
proof
let f be ascending Field-yielding sequence, p be Polynomial of (SeqField f);
consider i being Element of NAT such that
H: Coeff p c= the carrier of (f.i) by alg3a;
take i;
f.i is Subfield of SeqField f by Fsub;
then SeqField f is FieldExtension of f.i by FIELD_4:7;
hence thesis by H,FIELD_7:11;
end;
