
theorem lemphi5:
for F being Field,
    E being (Polynom-Ring F)-homomorphic FieldExtension of F
for a being Element of E
holds the carrier of RAdj(F,{a})
    = the set of all Ext_eval(p,a) where p is Polynomial of F
proof
let F be Field, E be (Polynom-Ring F)-homomorphic FieldExtension of F;
let a be Element of E;
thus the carrier of RAdj(F,{a})
   = the carrier of Image hom_Ext_eval(a,F) by lemphi4
  .= rng hom_Ext_eval(a,F) by RING_2:def 6
  .= the set of all Ext_eval(p,a) where p is Polynomial of F by lemphi1;
end;
