theorem Th34:
  x in B^C implies ex b,c st b in B & c in C & x = b \/ c
proof
  assume x in B^C;
  then x in { s \/ t: s in B & t in C } by XBOOLE_0:def 4;
  then ex s,t st x = s \/ t & s in B & t in C;
  hence thesis;
end;
