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In particular ''d'' defines a metric on ''D''.
The chain rule
:<math>\displaystyle{(g\circ f)^\prime(z)=g^\prime(f(z))g^\prime(z)}</math>
implies that
:<math>\displaystyle{\alpha(f(z),f^\prime(z)v)\le \alpha(z,v)}</math>
and hence ''f'' satisfies
:<math>\displaystyle{d(f(x),f(y))\le d(x,y).}</math>
==References==
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