
theorem
  for n being Ordinal, L being Abelian left_zeroed right_zeroed
  add-associative right_complementable well-unital associative commutative
  distributive non trivial doubleLoopStr, p being Polynomial of n,L, a being
Element of L, x being Function of n,L holds eval(p*'(a |(n,L)),x) = eval(p,x) *
  a
proof
  let n be Ordinal, L be left_zeroed right_zeroed add-associative
right_complementable well-unital associative commutative Abelian distributive
non trivial doubleLoopStr, p be Polynomial of n,L, a be Element of L, x being
  Function of n,L;
  thus eval(p*'(a |(n,L)),x) = eval(p,x) * eval(a |(n,L),x) by POLYNOM2:25
    .= eval(p,x) * a by Th25;
end;
