
theorem
  for L being Field
  for a,c being Element of L
  for b,d being non zero Element of L holds
  Roots(<%a,b%>*'<%c,d%>) = {-a/b,-c/d}
  proof
    let L be Field;
    let a,c be Element of L;
    let b,d be non zero Element of L;
    Roots(<%a,b%>) = {-a/b} & Roots(<%c,d%>) = {-c/d} by Th10;
    hence {-a/b,-c/d} = Roots(<%a,b%>) \/ Roots(<%c,d%>) by ENUMSET1:1
    .= Roots(<%a,b%>*'<%c,d%>) by UPROOTS:23;
  end;
