
theorem
  for L be Abelian add-associative right_zeroed right_complementable
unital distributive non empty doubleLoopStr for p,q be Polynomial of L for x
  be Element of L holds eval(p-q,x) = eval(p,x) - eval(q,x)
proof
  let L be Abelian add-associative right_zeroed right_complementable unital
  distributive non empty doubleLoopStr;
  let p,q be Polynomial of L;
  let x be Element of L;
  thus eval(p-q,x) = eval(p,x) + eval(-q,x) by Th19
    .= eval(p,x) +- eval(q,x) by Th20
    .= eval(p,x) - eval(q,x) by RLVECT_1:def 11;
end;
