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Degeneracies in the dispersion can be lifted by coupling the edge states as in Fig.10(b), and this then leads to annihilate certain edge states as in Fig.10(c). Due to the adiabatic deformation, the two counter-propagating modes have to be annihilate in pairs, as required by TRS. So this obviously shows that the change in number of edge states are pairs of pairs, or should be integer multiples of four. But there is a special case we can discuss in the Fig.10(c). That is the TRIM point in the Brillouin zone. If the annihilation took place at this point, the decrease of number of states is 2 instead of 4. However, this situation is forbidden. Since the Kramer's theorem indicated that the eigenstates have to be doubly degenerate at the TRIM. This is the reason why we said the edge states are protected by the time-reversal symmetry.