
theorem Th12:
  for X being set, f being Function holds X-indexing ((id X)+*f) = X-indexing f
proof
  let X be set, f be Function;
  thus X-indexing ((id X)+*f) = (id X)+*(((id X)|X)+*(f|X)) by FUNCT_4:71
    .= (id X)+*((id X)+*(f|X))
    .= (id X)+*(id X)+*(f|X) by FUNCT_4:14
    .= X-indexing f;
end;
