
theorem Th17:
  for X,Y being set, f being Function st X c= Y holds (Y-indexing
  f)|X = X-indexing f
proof
  let X,Y be set, f be Function;
  assume
A1: X c= Y;
  then
A2: (f|Y)|X = f|X by RELAT_1:74;
  (id Y)|X = id X by A1,FUNCT_3:1;
  hence thesis by A2,FUNCT_4:71;
end;
