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I am new to LaTeX and have been trying to format my proofs in the following style in the photo. However, the page How to correctly format (and align) a LaTeX proof? on this site has not been effective in forming this format. I have tried using {equation}, {aligned},{proof} and {align} environments but so far the proof has not come out in the format below. Any help would be greatly appreciated.

Please note, the working in this photo is an example from online.

proof

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    Welcome to TeX.SE. For future reference, it would be helpful if you compose a fully compilable MWE including \documentclass and the appropriate packages that sets up the problem. While solving problems can be fun, setting them up is not. Then, those trying to help can simply cut and paste your MWE and get started on solving the problem. It also shows what you have tried and increases the chances that the proposed solutions will actually be help you as they will be based on your stating point. – Peter Grill Apr 21 '17 at 8:51
  • I find that style difficult to read, because the comment associated to each line is so far to the right. I would need a ruler to read a whole book in that style. Isn't it easier to write: "A is bounded, so lies in a ball, and B lies in A, so lies in the same ball."? – Benjamin McKay Apr 21 '17 at 9:17
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First of all, welcome to LaTeX! The following answer contains an example of how I handled your problem. As you're new I will list every step I took, perhaps a bit too detailed, but then you see what I am thinking.

Output:

enter image description here


Explanation

The code block is at the end of this answer. Here I explain what I did or used within.

  1. The first thing I did was make sure I had an Itemization that started with (a). I used this answer in my code and added a package in the preamble. I did change the \Alph* into (\alph*), which adds brackets and doesn't capitalise the letters. Then I used the regular itemize structure of LaTeX. This is where the enumitem package is used.
  2. For bold text I used the LaTeX \textbf{} command.
  3. For writing math, I wrote it in the parts between the slashes with opening and closing parentheses: \( ... \). For any symbols, I used this pdf and this online source. For the R symbol, I used the amssymb package that gave me the \mathbb{R} command.
  4. To get part of the text aligned to the right side, I used the \hfill command. This means horizontal fill and will, as expected, fill the line up horizontally. Any text you write after that, LaTeX will put aligned to the right because it's filling up the space between! Simple and easy.
  5. To get the powered + in the third line, I just used the normal power notation in LaTeX math mode, a hat character ^ followed by the +. Due to a habit of mine I always put brackets {} after the hat character, which tells LaTeX to only use the characters inside the brackets, but could be left out in this code. I am just being explicit there.
  6. In the end, I added some spacing between parts of the math by using \quad. For more info on spacing, I suggest reading this easy to follow page.

All of that combined together, gave me the output as seen above. Hope this helps you further!


Complete Code

\documentclass{article}

\usepackage{enumitem}
\usepackage{amssymb}

\begin{document}


\begin{enumerate}[label=(\alph*)]
    \item   \textbf{Claim.} If \(A \subseteq \mathbb{R} \) is bounded, and \( B \subseteq A \), then \( B \) is bounded.

            \textbf{Proof.} Assume \( A \) is bounded. \hfill Premise

            \( \exists K \in \mathbb{R}^{+} \quad   \forall a \in A \quad   |a| \leq K \) \hfill Def. bounded

            Assume \(B \subseteq A\) \hfill Premise

            Let \( b \in B \) be arbitrary.

            Then \( b \in A \). \hfill Def. \( \subseteq \)
\end{enumerate}


\end{document}
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    Would be perfect if you would consider tex.stackexchange.com/a/513/124577. – TeXnician Apr 21 '17 at 8:18
  • Using LaTeX for 6 years now and never knew. Adjusted my answer accordingly. Thanks for the info! – JiyuuSensei Apr 21 '17 at 8:41
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    @TeXnician - I believe it's quite unhelpful to conflate the issues of using \(...\) vs. $...$ on the one hand with the issues of using \[...\] vs. $$...$$ on the other. Since you appear to be fond of the answer at tex.stackexchange.com/a/513/124577, you may want to take to heart Frank Mittelbach's comment on this subject, esp. as it has attracted 50 upvotes. For one, I believe that @Dima's claim that "\( ... \) will give less obscure error messages [than $...$]" is not valid in general. For instance, in my answer I provide a specific example of the opposite being true. – Mico Apr 21 '17 at 9:11
  • @TeXnician We have more than enough of brackets and parentheses already. Introducing yet another pair of brackets only hinders the readability of code. – TZakrevskiy Apr 21 '17 at 13:13

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