
theorem Th18:
  for L being domRing
  for p being non-zero Polynomial of L
  for B being bag of the carrier of L
  for E being Enumeration of Roots p st Roots p = {}
  holds B(++)E = {}
  proof
    let L be domRing;
    let p be non-zero Polynomial of L;
    let B be bag of the carrier of L;
    let E be Enumeration of Roots p such that
A1: Roots p = {};
A2: len(B(++)E) = len E by Def1;
    rng E = Roots p by RLAFFIN3:def 1;
    then E = {} by A1;
    hence thesis by A2;
  end;
