
theorem
  for X being set, f being Function st X c= dom f holds X-indexing f = f |X
proof
  let X be set, f be Function;
  assume X c= dom f;
  then
A1: dom (f|X) = X by RELAT_1:62;
  thus X-indexing f = X-indexing (f|X)
    .= f|X by A1,Th10;
end;
