 reserve n for Nat;
 reserve F for Field,
         p for irreducible Element of the carrier of Polynom-Ring F,
         f for Element of the carrier of Polynom-Ring F,
         a for Element of F;

theorem Th43:
   KrRoot p is_a_root_of emb(p,p)
   proof
A1:   p - 0.(Polynom-Ring F) in {p}-Ideal by IDEAL_1:66;
     eval(emb(p,p),KrRoot p)
     = Class(EqRel(Polynom-Ring F,{p}-Ideal),p) by Th42
     .= Class(EqRel(Polynom-Ring F,{p}-Ideal),0.(Polynom-Ring F))
       by A1,RING_1:6
     .= 0.KroneckerField(F,p) by RING_1:def 6;
     hence thesis by POLYNOM5:def 7;
   end;
