reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

theorem
  for E being non empty set, e being Singleton of E, A being Event of E
  holds e misses A or e /\ A = e
proof
  let E be non empty set, e be Singleton of E, A be Event of E;
  e /\ E = e & A \/ A` = [#] E by SUBSET_1:10,XBOOLE_1:28;
  then e = e /\ A \/ e /\ A` by XBOOLE_1:23;
  then e /\ A c= e by XBOOLE_1:7;
  then e /\ A = {} or e /\ A = e by Th1;
  hence thesis;
end;
