[Tex/LaTex] Writing a natural deduction proof in Latex

proof-package

I have checked the other questions, before anyone asks, but the style of proof appears to be subtly different and I would be expected to stick to the convention that I am using.

My question is how to create a proof in Latex like the one in the image attached:

(Apologies for the lighting, it is late for me)

This is not a Fitch-style proof, as no indentation is present, or those bars. I could use ordered lists, but I am wondering if there is a package that allows me to auto-indent lines and the side-notes/operations as that can be fiddly with raw lists (although if anyone has any pointers on this I would be happy to hear them).

Any ideas? I am quite surprised I wasn't able to find any packages that use this kind of proof, it is the style used in Mendelson's Introduction to Mathematical Logic, so perhaps it is old-school. Appreciate any guidance people can provide.

Best Answer

Another solution, based on listliketab:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{listliketab}

\begin{document}

\storestyleof{enumerate}
\begin{listliketab}%
\newcounter{tabenum}\setcounter{tabenum}{0}
\newcommand{\step}{\refstepcounter{tabenum}\thetabenum.}
\noindent \begin{tabular}{L >{$}l <{$}@{\hskip4em}l}
\multicolumn{2}{c}{$ \vdash P\lor\lnot P $} \\
\step & \lnot(P\land\lnot P) & Hyp \\
\step & P & {Hyp}\\
\step & P\lor\lnot P & 2, $\lor$-introduction \\
\step & \bot & 1, 3, contradiction \\
\step & \lnot P & 2, 4, negation-introduction \\
\step & P\lor\lnot P & 5, $\lor$-introduction \\
\step & \bot & 1, 6, contradiction \\
\step & \lnot\lnot(P\lor\lnot P) & 1, 7, negation-introduction \\
\step & P\lor\lnot P & 8, double negation elimination
\end{tabular}
\end{listliketab}

\end{document}

Related Solutions

[Tex/LaTex] Problem with proof environment

The proof environment is not defined so you get the error

! LaTeX Error: Environment proof undefined.

a common way to define it is to load amsthm when you get a proof heading and qed box at the end.

\documentclass[12pt]{report}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{graphicx}
\usepackage{float}
\usepackage{framed}
\usepackage[hang,flushmargin]{footmisc}

\usepackage{amsthm}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}{Definition}[section]

\begin{document} 
\begin{proof}
    Assume that $R$ decides $\mathrm{HALT}_{\mathrm{TM}}$, and obtain a contradiction. Construct $S$ to decide $A_{\mathrm{TM}}$, where $S$ operates as follows: 

    $S={}$ ``On input $\langle M, w \rangle$, an encoding of a TM $M$ and a string $w$:
    \begin{enumerate}
    \item Run TM $r$ on input $\langle M, w \rangle$.
    \item If $R$ rejects, reject
    \item If $R$ accepts, accept
    \item If $M$ has accepted, accept; if $M$ has rejected, reject."
    \end{enumerate}

     If $R$ decides $\mathrm{HALT}_{\mathrm{TM}}$, then $S$ decides $A_{\mathrm{TM}}$. Because $A_{\mathrm{TM}}$ is undecidable, $\mathrm{HALT}_{\mathrm{TM}}$ must also be undecidable. 
    \end{proof}
\end{document}

[Tex/LaTex] Square at the end of proof without “proof” at the beginning

... I don't want the [word] "Proof" to be in italic ... I want [a colon] after "Proof" ...

Assuming you employ the amsthm package to set up and typeset theorem-like environments, you may achieve your formatting objective by modifying the macros \proofname and \qedsymbol.

\documentclass{article}
\usepackage{amssymb}  % for '\blacksquare' macro
\usepackage{amsthm}   % for 'proof' environment 
\renewcommand\proofname{\textup{Proof:}} % default is 'Proof.' 
\renewcommand\qedsymbol{$\blacksquare$}

\begin{document}
\begin{proof}
Bla bla bla\dots
\end{proof}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Problem with proof environment

[Tex/LaTex] Square at the end of proof without “proof” at the beginning

Related Question