
theorem Th8:
  for X being non empty set, f being Function, x being Element of X
  holds (X-indexing f).x = ((id X) +* f).x
proof
  let X be non empty set, f be Function, x be Element of X;
  ((id X) +* f)|X = (id X)|X +* f|X by FUNCT_4:71
    .= (id X)|(dom id X) +* f|X
    .= X-indexing f;
  hence thesis by FUNCT_1:49;
end;
