
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(a*p,x) = a * eval(p,x)
proof
  let n be Ordinal, L be Abelian left_zeroed right_zeroed add-associative
  right_complementable well-unital associative commutative distributive non
  trivial doubleLoopStr, p be Polynomial of n,L, a be Element of L, x be
  Function of n,L;
  thus eval(a*p,x) = eval((a |(n,L)) *' p,x) by Th27
    .= a * eval(p,x) by Lm4;
end;
