
theorem lemBas0:
for F being Field,
    E being FieldExtension of F
for a being Element of E st a^2 in F holds a is F-algebraic
proof
let F be Field, E be FieldExtension of F, a be Element of E;
assume a^2 in F; then
reconsider b = a^2 as Element of F;
Ext_eval(X^2-b,a) = 0.E by lemBas00;
hence thesis by FIELD_6:43;
end;
