Proof
(related to Proposition: Limit of the Identity Function)
Context
 Let $a\in\mathbb R.$
 Let $f:\mathbb R\to\mathbb R,$ $f(x)=x$ be the identity function.
Hypothesis
Implications
 Then for $\delta:=\epsilon$ it holds that for all $x$ with $0 < xa < \delta$ we have that $f(x)a=xa < \epsilon.$
Conclusion
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References
Bibliography
 Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016