
theorem npl0:
for F being Field holds NormPolynomial(0_.(F)) = 0_.(F)
proof
let F be Field;
set q = 0_.(F); set p = NormPolynomial q;
now let x be object;
  assume x in NAT;
  then reconsider i = x as Element of NAT;
  p.i = q.i / q.(len q-'1) by POLYNOM5:def 11
     .= 0.F * (q.(len q-'1))" by FUNCOP_1:7
     .= q.i by FUNCOP_1:7;
  hence p.x = q.x;
  end;
hence thesis by FUNCT_2:12;
end;
