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;
