
theorem u1:
for F being Field,
    E being FieldExtension of F
for a being F-algebraic Element of E 
holds 0.FAdj(F,{a}) = Ext_eval(0_.F,a) & 1.FAdj(F,{a}) = Ext_eval(1_.F,a)
proof
let F be Field, E be FieldExtension of F;
let a be F-algebraic Element of E;
H: F is Subring of E by FIELD_4:def 1;
thus 0.FAdj(F,{a}) = 0.E by FIELD_6:def 6
                  .= Ext_eval(0_.F,a) by ALGNUM_1:13;
thus 1.FAdj(F,{a}) = 1.E by FIELD_6:def 6
                  .= Ext_eval(1_.F,a) by H,ALGNUM_1:14;
end;
