reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem
  (A \+\ B)` = A /\ B \/ A` /\ B`
proof
  A in bool E by Def1;
  then
A1: A c= E by ZFMISC_1:def 1;
  thus (A \+\ B)` = E \ (A \/ B) \/ E /\ A /\ B by XBOOLE_1:102
    .= A /\ B \/ (E \ (A \/ B)) by A1,XBOOLE_1:28
    .= A /\ B \/ (A`) /\ (B`) by XBOOLE_1:53;
end;
