
theorem lift4:
for F1,F2 being Field, E being AlgebraicClosure of F1
st F1 == F2 holds E is AlgebraicClosure of F2
proof
let F1,F2 be Field, E be AlgebraicClosure of F1;
assume F1 == F2; then
reconsider E3 = E as F2-algebraic FieldExtension of F2 by lift5;
E3 is algebraic-closed;
hence thesis by defAC;
end;
