Lemma 5.3 . [02CG]

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Lemma 5.3.

For any $p_{1},p_{2}\in Y^{reg}$ , if $p_{1}(t),p_{2}(t)$ are both defined on some interval $[0,T]$ , then $f(t)=d(p_{1}(t),p_{2}(t))$ is independent of $t$ .