Since n − m = 1 mod p x m and x n lie in different adjacently labelled sets A iand A i+1 for some 1 ≤ i ≤ p, so by the contractive condition[1 − α(d(x n ,x m ))]ρ < [1 − α(d(x n ,x m ))]d(x n ,x m )≤ d(x n ,x n+1 ) + d(x m ,x m+1 ).
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