theorem
  for F being Function of X,Y, A being Subset of X, B being Subset of Z
  holds [:F,id Z:].:[:A,B:] = [:F.:A,B:]
proof
  let F be Function of X,Y, A be Subset of X, B be Subset of Z;
  thus [:F,id Z:].:[:A,B:] = [:F.:A, (id Z).:B:] by FUNCT_3:72
    .= [:F.:A,B:] by FUNCT_1:92;
end;
