reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  for f being PartFunc of X,Y holds Z|`f is PartFunc of X,Z
proof
  let f be PartFunc of X,Y;
  dom(Z|`f) c= X & rng(Z|`f) c= Z by RELAT_1:85;
  hence thesis by RELSET_1:4;
end;
