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% proof.sty (Proof Figure Macros)
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%
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% version 3.0 (for both LaTeX 2.09 and LaTeX 2e)
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% Mar 6, 1997
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% Copyright (C) 1990 -- 1997, Makoto Tatsuta (tatsuta@kusm.kyoto-u.ac.jp)
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%
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% This program is free software; you can redistribute it or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation; either versions 1, or (at your option)
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% any later version.
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%
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% This program is distributed in the hope that it will be useful
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% Usage:
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% In \documentstyle, specify an optional style `proof', say,
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% \documentstyle[proof]{article}.
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%
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% The following macros are available:
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%
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% In all the following macros, all the arguments such as
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% <Lowers> and <Uppers> are processed in math mode.
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%
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% \infer<Lower><Uppers>
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% draws an inference.
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%
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% Use & in <Uppers> to delimit upper formulae.
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% <Uppers> consists more than 0 formulae.
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%
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% \infer returns \hbox{ ... } or \vbox{ ... } and
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% sets \@LeftOffset and \@RightOffset globally.
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%
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% \infer[<Label>]<Lower><Uppers>
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% draws an inference labeled with <Label>.
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%
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% \infer*<Lower><Uppers>
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% draws a many step deduction.
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%
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% \infer*[<Label>]<Lower><Uppers>
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% draws a many step deduction labeled with <Label>.
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%
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% \infer=<Lower><Uppers>
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% draws a double-ruled deduction.
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%
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% \infer=[<Label>]<Lower><Uppers>
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% draws a double-ruled deduction labeled with <Label>.
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%
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% \deduce<Lower><Uppers>
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% draws an inference without a rule.
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%
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% \deduce[<Proof>]<Lower><Uppers>
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% draws a many step deduction with a proof name.
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%
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% Example:
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% If you want to write
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% B C
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% -----
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% A D
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% ----------
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% E
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% use
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% \infer{E}{
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% A
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% &
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% \infer{D}{B & C}
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% }
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%
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% Style Parameters
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\newdimen\inferLineSkip \inferLineSkip=2pt
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\newdimen\inferLabelSkip \inferLabelSkip=5pt
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\def\inferTabSkip{\quad}
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% Variables
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\newdimen\@LeftOffset % global
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\newdimen\@RightOffset % global
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\newdimen\@SavedLeftOffset % safe from users
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\newdimen\UpperWidth
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\newdimen\LowerWidth
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\newdimen\LowerHeight
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\newdimen\UpperLeftOffset
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\newdimen\UpperRightOffset
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\newdimen\UpperCenter
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\newdimen\LowerCenter
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\newdimen\UpperAdjust
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\newdimen\RuleAdjust
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\newdimen\LowerAdjust
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\newdimen\RuleWidth
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\newdimen\HLabelAdjust
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\newdimen\VLabelAdjust
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\newdimen\WidthAdjust
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\newbox\@UpperPart
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\newbox\@LowerPart
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\newbox\@LabelPart
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\newbox\ResultBox
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% Flags
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\newif\if@inferRule % whether \@infer draws a rule.
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\newif\if@DoubleRule % whether \@infer draws doulbe rules.
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\newif\if@ReturnLeftOffset % whether \@infer returns \@LeftOffset.
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\newif\if@MathSaved % whether inner math mode where \infer or
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% \deduce appears.
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% Special Fonts
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\def\DeduceSym{\vtop{\baselineskip4\p@ \lineskiplimit\z@
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\vbox{\hbox{.}\hbox{.}\hbox{.}}\hbox{.}}}
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% Math Save Macros
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%
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% \@SaveMath is called in the very begining of toplevel macros
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% which are \infer and \deduce.
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% \@RestoreMath is called in the very last before toplevel macros end.
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% Remark \infer and \deduce ends calling \@infer.
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\def\@SaveMath{\@MathSavedfalse \ifmmode \ifinner
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\relax $\relax \@MathSavedtrue \fi\fi }
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\def\@RestoreMath{\if@MathSaved \relax $\relax\fi }
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% Macros
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% Renaming @ifnextchar and @ifnch of LaTeX2e to @IFnextchar and @IFnch.
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\def\@IFnextchar#1#2#3{%
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\let\reserved@e=#1\def\reserved@a{#2}\def\reserved@b{#3}\futurelet
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\reserved@c\@IFnch}
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\def\@IFnch{\ifx \reserved@c \@sptoken \let\reserved@d\@xifnch
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\else \ifx \reserved@c \reserved@e\let\reserved@d\reserved@a\else
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\let\reserved@d\reserved@b\fi
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\fi \reserved@d}
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\def\@ifEmpty#1#2#3{\def\@tempa{\@empty}\def\@tempb{#1}\relax
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\ifx \@tempa \@tempb #2\else #3\fi }
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\def\infer{\@SaveMath \@IFnextchar *{\@inferSteps}{\relax
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\@IFnextchar ={\@inferDoubleRule}{\@inferOneStep}}}
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\def\@inferOneStep{\@inferRuletrue \@DoubleRulefalse
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\@IFnextchar [{\@infer}{\@infer[\@empty]}}
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\def\@inferDoubleRule={\@inferRuletrue \@DoubleRuletrue
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\@IFnextchar [{\@infer}{\@infer[\@empty]}}
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\def\@inferSteps*{\@IFnextchar [{\@@inferSteps}{\@@inferSteps[\@empty]}}
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\def\@@inferSteps[#1]{\@deduce{#1}[\DeduceSym]}
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\def\deduce{\@SaveMath \@IFnextchar [{\@deduce{\@empty}}
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{\@inferRulefalse \@infer[\@empty]}}
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% \@deduce<Proof Label>[<Proof>]<Lower><Uppers>
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\def\@deduce#1[#2]#3#4{\@inferRulefalse
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\@infer[\@empty]{#3}{\@SaveMath \@infer[{#1}]{#2}{#4}}}
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% \@infer[<Label>]<Lower><Uppers>
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% If \@inferRuletrue, it draws a rule and <Label> is right to
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% a rule. In this case, if \@DoubleRuletrue, it draws
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% double rules.
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%
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% Otherwise, draws no rule and <Label> is right to <Lower>.
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\def\@infer[#1]#2#3{\relax
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% Get parameters
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\if@ReturnLeftOffset \else \@SavedLeftOffset=\@LeftOffset \fi
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\setbox\@LabelPart=\hbox{$#1$}\relax
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\setbox\@LowerPart=\hbox{$#2$}\relax
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%
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\global\@LeftOffset=0pt
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\setbox\@UpperPart=\vbox{\tabskip=0pt \halign{\relax
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\global\@RightOffset=0pt \@ReturnLeftOffsettrue $##$&&
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\inferTabSkip
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\global\@RightOffset=0pt \@ReturnLeftOffsetfalse $##$\cr
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#3\cr}}\relax
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% Here is a little trick.
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% \@ReturnLeftOffsettrue(false) influences on \infer or
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% \deduce placed in ## locally
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% because of \@SaveMath and \@RestoreMath.
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\UpperLeftOffset=\@LeftOffset
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\UpperRightOffset=\@RightOffset
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% Calculate Adjustments
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\LowerWidth=\wd\@LowerPart
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\LowerHeight=\ht\@LowerPart
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\LowerCenter=0.5\LowerWidth
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%
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\UpperWidth=\wd\@UpperPart \advance\UpperWidth by -\UpperLeftOffset
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\advance\UpperWidth by -\UpperRightOffset
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\UpperCenter=\UpperLeftOffset
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\advance\UpperCenter by 0.5\UpperWidth
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%
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\ifdim \UpperWidth > \LowerWidth
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% \UpperCenter > \LowerCenter
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\UpperAdjust=0pt
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\RuleAdjust=\UpperLeftOffset
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\LowerAdjust=\UpperCenter \advance\LowerAdjust by -\LowerCenter
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\RuleWidth=\UpperWidth
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\global\@LeftOffset=\LowerAdjust
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%
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\else % \UpperWidth <= \LowerWidth
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\ifdim \UpperCenter > \LowerCenter
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%
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\UpperAdjust=0pt
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\RuleAdjust=\UpperCenter \advance\RuleAdjust by -\LowerCenter
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\LowerAdjust=\RuleAdjust
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\RuleWidth=\LowerWidth
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\global\@LeftOffset=\LowerAdjust
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%
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\else % \UpperWidth <= \LowerWidth
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% \UpperCenter <= \LowerCenter
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%
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\UpperAdjust=\LowerCenter \advance\UpperAdjust by -\UpperCenter
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\RuleAdjust=0pt
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\LowerAdjust=0pt
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\RuleWidth=\LowerWidth
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\global\@LeftOffset=0pt
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%
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\fi\fi
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% Make a box
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\if@inferRule
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%
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\setbox\ResultBox=\vbox{
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\moveright \UpperAdjust \box\@UpperPart
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\nointerlineskip \kern\inferLineSkip
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\if@DoubleRule
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\moveright \RuleAdjust \vbox{\hrule width\RuleWidth
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\kern 1pt\hrule width\RuleWidth}\relax
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\else
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\moveright \RuleAdjust \vbox{\hrule width\RuleWidth}\relax
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\fi
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\nointerlineskip \kern\inferLineSkip
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\moveright \LowerAdjust \box\@LowerPart }\relax
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%
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\@ifEmpty{#1}{}{\relax
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%
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\HLabelAdjust=\wd\ResultBox \advance\HLabelAdjust by -\RuleAdjust
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\advance\HLabelAdjust by -\RuleWidth
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\WidthAdjust=\HLabelAdjust
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\advance\WidthAdjust by -\inferLabelSkip
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\advance\WidthAdjust by -\wd\@LabelPart
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\ifdim \WidthAdjust < 0pt \WidthAdjust=0pt \fi
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%
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\VLabelAdjust=\dp\@LabelPart
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\advance\VLabelAdjust by -\ht\@LabelPart
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\VLabelAdjust=0.5\VLabelAdjust \advance\VLabelAdjust by \LowerHeight
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\advance\VLabelAdjust by \inferLineSkip
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%
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\setbox\ResultBox=\hbox{\box\ResultBox
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\kern -\HLabelAdjust \kern\inferLabelSkip
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\raise\VLabelAdjust \box\@LabelPart \kern\WidthAdjust}\relax
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%
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}\relax % end @ifEmpty
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%
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\else % \@inferRulefalse
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%
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\setbox\ResultBox=\vbox{
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\moveright \UpperAdjust \box\@UpperPart
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\nointerlineskip \kern\inferLineSkip
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\moveright \LowerAdjust \hbox{\unhbox\@LowerPart
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\@ifEmpty{#1}{}{\relax
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\kern\inferLabelSkip \unhbox\@LabelPart}}}\relax
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\fi
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%
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\global\@RightOffset=\wd\ResultBox
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\global\advance\@RightOffset by -\@LeftOffset
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\global\advance\@RightOffset by -\LowerWidth
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\if@ReturnLeftOffset \else \global\@LeftOffset=\@SavedLeftOffset \fi
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%
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\box\ResultBox
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\@RestoreMath
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}
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