
theorem ZZ1f:
for R being non degenerated comRing
for p,q being Polynomial of R holds Roots p c= Roots(p *' q)
proof
let F be non degenerated comRing, p,q be Polynomial of F;
now let o be object;
  assume A: o in Roots p;
  then reconsider a = o as Element of F;
  a is_a_root_of p by A,POLYNOM5:def 10;
  then a is_a_root_of p *' q by ro1;
  hence o in Roots(p *' q) by POLYNOM5:def 10;
  end;
hence thesis;
end;
