
theorem u10:
for F being Field,
    E being FieldExtension of F
for a being Element of E
holds hom_Ext_eval(a,F) is Function of (Polynom-Ring F),RAdj(F,{a})
proof
let F be Field, E be FieldExtension of F; let a be Element of E;
reconsider E1 = E as (Polynom-Ring F)-homomorphic Field;
reconsider f = hom_Ext_eval(a,F) as Homomorphism of (Polynom-Ring F),E1;
RAdj(F,{a}) = Image f by FIELD_6:44;
then rng f = the carrier of RAdj(F,{a}) by RING_2:def 6;
hence thesis by FUNCT_2:6;
end;
