
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 g being Function of C,
  COMPLEX st for c being Element of C holds g.c = r * f.c holds g = r(#)f
proof
  let C be non empty set, D be complex-membered non empty set;
  let f be Function of C,D, r be Complex;
  let g be Function of C,COMPLEX such that
A1: for c being Element of C holds g.c = r * f.c;
  let x be Element of C;
  thus g.x = r*f.x by A1
    .= (r(#)f).x by Th6;
end;
