
theorem
  for F being commutative associative well-unital almost_left_invertible
right_zeroed non empty doubleLoopStr for f being Function of F,NAT
holds f is DegreeFunction of F
proof
  let F be commutative associative well-unital almost_left_invertible
  right_zeroed non empty doubleLoopStr;
  let f be Function of F,NAT;
  for a,b being Element of F st b <> 0.F ex q,r being Element of F
  st a = q * b + r & (r = 0.F or f.r < f.b) by Lm4;
  hence thesis by Def9;
end;
