[see also: information, detail, evidence, proof, actually, more]
A stronger result is in fact true.
We note that $H$ is in fact not Lipschitz continuous if this condition is violated.
In fact, we can do even better, and prescribe finitely many derivatives at each point of $A$.
Now, just the fact that $F$ is a homeomorphism lets us prove that ......
The advantage of applying ...... lies in the fact that ......
Observe that (1) just uses the fact that $m$ is unary.
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