
theorem 
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),FAdj(F,{a})
proof
let F be Field, E be FieldExtension of F; let a be Element of E;
RAdj(F,{a}) is Subring of FAdj(F,{a}) by FIELD_6:39; then
A: the carrier of RAdj(F,{a}) c= the carrier of FAdj(F,{a}) by C0SP1:def 3;
hom_Ext_eval(a,F) is Function of (Polynom-Ring F),RAdj(F,{a}) by u10;
hence thesis by A,FUNCT_2:7;
end;
