
theorem lift6:
for F1,F2 being Field
for p being non zero Polynomial of F1
st F1 == F2 holds p is non zero Polynomial of F2
proof
let F1,F2 be Field, p be non zero Polynomial of F1;
assume AS: F1 == F2; then
reconsider p1 = p as Polynomial of F2 by lift6a;
now assume p1 is zero;
  then p1 = 0_.(F2) by UPROOTS:def 5
         .= 0_.(F1) by AS,lift6b;
  hence contradiction;
  end;
hence thesis;
end;
