As shown by Dyson in his famous paper "Missed Opportunities", it follows even from purely mathematical considerations that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Then the usual explanation of why in particle physics Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators$M_{4mu}$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{muu}$ ($mu,u=0,1,2,3$).We explicitly show that this is the case in the Flato-Fronsdal approach where elementary particles in the standard theory are bound states of two Dirac singletons.