
theorem Th22:
  for L being add-associative right_zeroed right_complementable
  distributive non empty doubleLoopStr, p, q being (Polynomial of L), pc, qc
  being (Element of Polynom-Ring L) st p= pc & q = qc holds p-q = pc-qc
proof
  let L be add-associative right_zeroed right_complementable distributive non
  empty doubleLoopStr, p,q be (Polynomial of L), pc,qc be (Element of
  Polynom-Ring L) such that
A1: p = pc and
A2: q = qc;
  -q = -qc by A2,Th21;
  hence thesis by A1,POLYNOM3:def 10;
end;
