theorem Th79:
  (for X st X in A holds X misses B) implies union A misses B
proof
  assume
A1: for X st X in A holds X misses B;
  assume union(A) meets B;
  then consider z such that
A2: z in union(A) /\ B by XBOOLE_0:4;
  z in union(A) by A2,XBOOLE_0:def 4;
  then consider X such that
A3: z in X and
A4: X in A by TARSKI:def 4;
  z in B by A2,XBOOLE_0:def 4;
  then z in X /\ B by A3,XBOOLE_0:def 4;
  hence contradiction by A1,A4,XBOOLE_0:4;
end;
