reserve n for Nat;

theorem pf2:
for R being domRing,
    B being non zero bag of the carrier of R,
    p being Ppoly of R,B holds BRoots(p) = B
proof
let R be domRing, B be non zero bag of the carrier of R,
    p be Ppoly of R,B;
set b = BRoots p;
now let o be object;
  assume o in the carrier of R;
  then reconsider a = o as Element of the carrier of R;
  B.a = multiplicity(p,a) by dpp .= b.a by UPROOTS:def 9;
  hence b.o = B.o;
  end;
hence thesis by PBOOLE:3;
end;
