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 Function holds Z|`<:f,X,Y:> = <:f,X,Z /\ Y:>
proof
  let f be Function;
  thus Z|`<:f,X,Y:> = Z|`(Y|`(f|X)) by RELAT_1:109
    .= (Z /\ Y)|`(f|X) by RELAT_1:96
    .= <:f,X,Z /\ Y:> by RELAT_1:109;
end;
