
theorem Kr2:
for F being Field
for g being bijective Function of (nonConstantPolys F),card(nonConstantPolys F)
for I being maxIdeal of nonConstantPolys(g,F)-Ideal
for p being Element of the carrier of Polynom-Ring F
for m being Ordinal st m in card(nonConstantPolys F)
holds eval((PolyHom emb(F,I,g)).p,KrRoot(I,m)) =
      Class(EqRel(Polynom-Ring(card(nonConstantPolys F),F),I), Poly(m,p))
proof
let F be Field;
let g be bijective Function of (nonConstantPolys F),card(nonConstantPolys F);
let I be maxIdeal of nonConstantPolys(g,F)-Ideal;
let p be Element of the carrier of Polynom-Ring F;
let m be Ordinal;
assume A0: m in card(nonConstantPolys F);
per cases;
suppose p is constant;
  hence thesis by Kr2a;
  end;
suppose p is non constant;
  hence thesis by A0,Kr3;
  end;
end;
