I am searching for a reference about the following theorem:
Let $M \xrightarrow{i_{0}} \mathbb{R}^{k},\,\,$ $M \xrightarrow{i_{1}} \mathbb{R}^{l}$ be two embeddings of the manifold $M$. We know by the tubular neighborhood theorem that these embeddings extend to embeddings of the normal bundles $E(\nu_{0})\xrightarrow{j_{0}}\mathbb{R}^{k},\,\,E(\nu_{1})\xrightarrow{j_{0}}\mathbb{R}^{l}$. Show that there exists an $m>k,l$ such that, if $i_{o}',i_{1}'\,\,$ are the embeddings $i_{0}':M \xrightarrow{i_{0}} \mathbb{R}^{k}\subset \mathbb{R}^{m},\,\,$ $i_{1}':M \xrightarrow{i_{1}} \mathbb{R}^{l}\subset \mathbb{R}^{m}$ with extensions to the normal bundles $E(\nu_{0}')\xrightarrow{j_{0}'}\mathbb{R}^{m},\,\,E(\nu_{1}')\xrightarrow{j_{1}'}\mathbb{R}^{m},\,\,\,$ then $j_{0}',j_{1}'$ are isotopic as embeddings.
Do you know any book that states the theorem in this form? I have checked in many books ( for example in Hirsch, Lang) but I can't find the theorem in this form, everyone states the theorem for a given embedding rather than for two different embeddings.
Thank you a lot.