
theorem
  for C being non empty set, D being complex-membered non empty set
  for f being Function of C,D, r being Complex
  for c being Element of C holds
  (r+f).c = r + f.c
proof
  let C be non empty set;
  let D be complex-membered non empty set;
  let f be Function of C,D, r be Complex;
  dom(r+f) = C by FUNCT_2:def 1;
  hence thesis by Def2;
end;
