reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];
reserve a for Element of [:Fin X, Fin X:];
reserve A for set;
reserve x,y for Element of [:Fin X, Fin X:],
  a,b for Element of DISJOINT_PAIRS X;
reserve A for set,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t for Element of DISJOINT_PAIRS A,
  B,C,D for Element of Fin DISJOINT_PAIRS A;
reserve K,L,M for Element of Normal_forms_on A;

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;
