If "m" ≥ "n", the Clos network is "rearrangeably nonblocking", meaning that an unused input on an ingress switch can always be connected to an unused output on an egress switch, but for this to take place, existing calls may have to be rearranged by assigning them to different centre stage switches in the Clos network. To prove this, it is sufficient to consider "m" = "n", with the Clos network fully utilised; that is, "r"×"n" calls in progress. The proof shows how any permutation of these "r"×"n" input terminals onto "r"×"n" output terminals may be broken down into smaller permutations which may each be implemented by the individual crossbar switches in a Clos network with "m" = "n".