reserve x,z for set;
reserve k for Element of NAT;
reserve D for non empty set;
reserve X for set;
reserve p,r for relation;
reserve a,a1,a2,b for FinSequence;
reserve a,b for FinSequence of D;
reserve p,r for Element of relations_on D;
reserve u,v,w for boolean object;

theorem
  (v '&' w = TRUE iff v = TRUE & w = TRUE) & (v '&' w = FALSE iff v =
  FALSE or w = FALSE) by XBOOLEAN:101,140;
