theorem Th40:
  for L being add-associative right_zeroed right_complementable
      non empty addLoopStr
  for p,q being Polynomial of L st deg p > deg q holds
  deg(p+q) = deg p
  proof
    let L be add-associative right_zeroed right_complementable
        non empty addLoopStr;
    let p,q be Polynomial of L;
    assume
A1: deg p > deg q;
    then deg(p+q) = max(deg(p),deg(q)) by HURWITZ:21;
    hence thesis by A1,XXREAL_0:def 10;
  end;
