Lemma 17.10.58`DB740351ED65`

Lemma 17.10.58.DB740351ED65 Let $(E,d,\land )$ be a rooftop metric space. Let $x,y,x',y'\in E$. Then

4.61

\begin{equation} d(x\land y,x'\land y')\leq d(x,x')+d(y,y'). \end{equation}

Proof. We compute

\[ d(x\land y,x'\land y')\leq d(x\land y,x\land y')+d(x\land y',x'\land y')\leq d(x,x')+d(y,y'). \]

This completes the proof. $\square$

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BibTeX citation

@misc{pome-tag-DB740351ED65,
  author = {{Pome contributors}},
  title = {Lemma 17.10.58},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/DB740351ED65/}
}

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Lemma 17.10.58DB740351ED65

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Lemma 17.10.58`DB740351ED65`