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% proofeg.tex (An example file for proof.sty)
%
% Mar 6, 1997
% Makoto Tatsuta
%
% I hope you can learn how to use proof figure macros easily
% by these examples.
\def\imp{\to}
\def\land{\mathbin\&}
\documentstyle[proof]{article}
% for LaTeX 2e naitive mode.
%\documentclass[]{article}
%\usepackage{proof}
\begin{document}
\section*{Examples of proof.sty}
\verb|\infer| draws beautiful proof figures easily:
\noindent (1)
$$
\infer{A}{
\infer{B}{
B11\land B12\land B13
&
B21\land B22\land B23
}
&
C
}
$$
\noindent (2)
$$
\infer{A1\land A2\land A3\land A4\land A5\land A6}{
\infer{B}{
B11\land B12\land B13
&
B21\land B22\land B23
}
&
C
}
$$
\noindent (3)
$$
\infer{A1\land A2\land A3\land A4\land A5\land A6}{
C
&
\infer{B}{
B11\land B12\land B13
&
B21\land B22\land B23
}
}
$$
You can use also some variations:
\noindent (4)
$$
\infer[(1)]{A}{
\infer*{B}{
B11\land B12\land B13
&
B21\land B22\land B23
}
&
C
}
$$
\noindent (5)
$$
\infer*[(1)]{A1\land A2\land A3\land A4\land A5\land A6}{
\deduce[{\displaystyle \sum}]{B}{
B11\land B12\land B13
&
B21\land B22\land B23
}
&
\deduce{C}{(2)}
}
$$
\noindent (6)
$$
\infer={A}{A \land B \land C}
$$
Here are more practical examples:
\noindent (7)
$$
\infer[(\land I)]{A \land B}{A & B}
\qquad
\infer[(\land E_l)]A{A\land B}
\qquad
\infer[(\land E_r)]B{A\land B}
$$
$$
\infer[(\imp I)]{A \imp B}{
\infer*{B}{[A]}
}
\qquad
\infer[(\imp E)]{B}{
A \imp B
&
A
}
$$
Some techniques:
Use \verb|\vcenter| for an equation of proofs.
\noindent (8)
$$
\pi = \vcenter{
\infer{E}{
A
&
\infer{D}{B & C}
}
}
$$
Use \verb|\kern| to adjust the form of a proof.
\noindent (9)
$$
\infer{E}{
A
&
\infer{D}{B & C} \kern 0.5cm
}
$$
\end{document}
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