I would like to know whether there's any way to include some text in one of the lines of some aligned output but that exists "outside" of the alignment. (In case it makes a difference, I am asking this about a document I'm writing in Overleaf.) Here a sample code:
\begin{enumerate \item \-\hspace{4cm} $\tan^{-1} x + tan^{-1} y = \frac{\pi}{4} \Longleftrightarrow (x+1)(y+1) = 2$ Proof: \begin{align*} \tan^{-1}x + tan^{-1}y = \frac{\pi}{4} & \Longleftrightarrow \tan \left(\tan^{-1}x + tan^{-1}y\right) = 1 \\[2mm] & \Longleftrightarrow \frac{x+y}{1-xy} = 1 \\[2mm] & \Longleftrightarrow (x+1)(y+1) = 2 \end{align*} \end{enumerate}} This yields the following output:
I would like to have the word "Proof" be part of the first line of the proof but not be affected by the align environment. I tried including the "Proof" in the first line with it's own set of &'s, but that indented the word much more than I liked:
\begin{enumerate} \item \-\hspace{4cm} $\tan^{-1}x + tan^{-1}y = \frac{\pi}{4} \Longleftrightarrow (x+1)(y+1) = 2$ \begin{align*} &\text{Proof:}&\tan^{-1}x+tan^{-1}y=\frac{\pi}{4}&\Longleftrightarrow\tan\left(\tan^{-1}x+tan^{-1}y\right)=1\\[2mm] &&& \Longleftrightarrow \frac{x+y}{1-xy} = 1 \\[2mm] &&& \Longleftrightarrow (x+1)(y+1) = 2 \end{align*} \end{enumerate} 
Ideally I'd like the "Proof" to be as far left as it is in the first image, just a bit to the right of the number 1, but still part of the first line as in the second image. If that's possible, perhaps I could also align the top line with the first line of the proof without having to push it to the right separately with the -\hspace as I did.
I did search the site for answers, the closest thing I found to what I want is \intertext, but that adds a separate line outside the \align environment; is there something similar that I can use but that puts the text in one of the lines that's aligned?
