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
  (not FALSE in X iff ALL(X) = TRUE) & (FALSE in X iff ALL(X) = FALSE)
  by Def15;
