reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;

theorem
  for f being Function, A,B being set holds f|(A \/ B) = f|A +* f|B
proof
  let f be Function, A,B be set;
A1: f|(A \/ B)|B = f|((A \/ B) /\ B) by RELAT_1:71
    .= f|B by XBOOLE_1:21;
A2: dom (f|(A \/ B)) c= A \/ B by RELAT_1:58;
  f|(A \/ B)|A = f|((A \/ B) /\ A) by RELAT_1:71
    .= f|A by XBOOLE_1:21;
  hence thesis by A1,A2,Th70;
end;
