summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/tex/latex/prftree/prftree.sty
blob: 2bec5c8f07af5e18176ad3fd80aa8e8c1b9a76d7 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
%
% prftree.sty
% by Marco Benini - 31st October 2015
% v1.2
%
% A package to typeset natural deduction proofs, or sequent proofs, or
% tableau proofs
%
% This package is distributed under the GNU General Public License
%

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{prftree}[2015/10/31 Natural Deduction Proofs]

% Package options: deactivated by default
\newif\ifprf@NDOption\prf@NDOptionfalse
\newif\ifprf@SEQOption\prf@SEQOptionfalse
\newif\ifprfIMPOption\prfIMPOptionfalse

\DeclareOption{ND}{\prf@NDOptiontrue}
\DeclareOption{SEQ}{\prf@SEQOptiontrue}
\DeclareOption{IMP}{\prfIMPOptiontrue}
\ProcessOptions\relax

%--------------------------------------------------------------------
% A proof tree is composed by a generic cell:
%  A1 A2 A3
% ---------- R
%      C
% We call A1, A2, A3. ... assumptions, C the conclusion and R the rule
% name. The line dividing the assumptions from the conclusion is
% called the proof line. A proof tree with no assumptions is an axiom.
% An assumption which is not a proof tree is a pure assumption.
%
% A proof tree is typeset by
% \prftree[<options>]...[<options>]
%         {<assumption1>}...{<assumptionN>}
%         {<conclusion>}
% The possible options are:
%   r             : the first argument after the options is the rule
%                   name, typeset in text mode
%   rule          : synonym for 'r'
%   by rule       : synonym for 'r'
%   by            : synonym for 'r'
%   right         : synonym for 'r'
%   l             : the first argument after the options is the rule
%                   label, typeset in text mode; if there is also a
%                   rule name, the label is the second argument
%   label         : synonym for 'l'
%   left          : synonym for 'l'
%   straight      : the proof line will be a solid line (default) 
%   straight line : synonym for 'l'
%   straightline  : synonym for 'l'
%   dotted        : the proof line will be a dotted line
%   dotted line   : synonym for 'dotted'
%   dottedline    : synonym for 'dotted'
%   dashed        : the proof line will be a dashed line
%   dashed line   : synonym for 'dashed'
%   dashedline    : synonym for 'dashed'
%   f             : the proof line will be fancy
%   fancy         : synonym for 'f'
%   fancy line    : synonym for 'f'
%   fancyline     : synonym for 'f'
%   s             : the proof line will be single, not double (default)
%   single        : synonym for 's'
%   single line   : synonym for 's'
%   singleline    : synonym for 's'
%   d             : the proof line will be double, not single
%   double        : synonym for 'd'
%   double line   : synonym for 'd'
%   doubleline    : synonym for 'd'
%   noline        : suppresses the proof line (prevails over all other
%                   line options)
%   summary       : renders the proof line as the summary symbol
%                   (prevails over all other line options except
%                   noline) 
% 
% The format of options is [<opt1>,...,<optM>]; it is correct to have
% empty options. Options are parsed left-to-right: in case of
% conflicting options, the latest prevails.
%
% If present, the rule name is typeset in text style, while the
% conclusion and the assumptions are typeset in display math mode.
% The result is a box with the correct height and width, whose
% conclusion is aligned with the current baseline.
%
% Notice that the conclusion must be present, while the assumptions
% may be absent.
%
% If there are no assumptions, i.e., if the proof tree represents an
% axiom, you may use the following commands:
%  \prfaxiom{<axiom>}
%  \prfbyaxiom{<label>}{<axiom>}
% the latter includes also the axiom name.
%
% A pure assumption is just a proof tree composed by the conclusion
% only. It uses an option to suppress the drawing of the proof line.
% The commands are:
%   \prfassumption<reference>{<formula>}
%   \prfboundedassumption<reference>{<formula>}
% the second command discharges the assumption.
%
% A proof summary is just a proof tree whose proof line is bizarre. It
% uses an option to specify the type of summary.
% The command is:
%   \prfsummary<reference>[<label>]
%              {<assumption1>}...{<assumptionN>} 
%              {<conclusion>}
% The label is optional. The shape of the summary is controlled by the
% global option \prfsummarystyle.
%
% The <reference> field above is used for labelling and
% referencing, as explained in the documentation.
%--------------------------------------------------------------------

%--------------------------------------------------------------------
% Parameters
% These values can be safely used to configure the behaviour of the
% macros in the package. Beware to modify them only outside a proof
% tree as the order in which a proof tree is typeset may vary in
% future version of the package.
%--------------------------------------------------------------------

% \prflinepad                default 0.3ex
% the space between the baseline of assumptions and the proof line and
% also the space between the proof line and the top of the conclusion
\newdimen\prflinepad\prflinepad.3ex

% \prflineextra              default 0.3em 
% the length which extends on the left and on the right the proof line
% so that it is slightly longer than the largest between the
% conclusion and the list of (direct) assumptions
\newdimen\prflineextra\prflineextra.3em

% \prflinethickness          default 0.2pt
% the thickness of the proof line
\newdimen\prflinethickness\prflinethickness.2pt

% \prfemptylinethickness     default 4 times the linethickness
% the thickness of the proof line which has to be drawn but it is empty
\newdimen\prfemptylinethickness\prfemptylinethickness4\prflinethickness

% \prfrulenameskip           default 0.2em
% the space between the proof line and the rule name
\newdimen\prfrulenameskip\prfrulenameskip.2em

% \prflabelskip           default 0.2em
% the space between the label and the proof line
\newdimen\prflabelskip\prflabelskip.2em

% \prfinterspace             default .6em
% the space between two subsequent assumptions
\newdimen\prfinterspace\prfinterspace.6em

% \prfdoublelineinterspace   default 1.2pt
% the space between a double line
\newdimen\prfdoublelineinterspace\prfdoublelineinterspace1.2pt

% \prfboundedstyle           default 0
% defines the style of bounded (discharged) assumptions:
% 0 = [<formula>]
% 1 = <formula> cancelled by a horizontal line
% >1 = uses the custom \prfdiscargedassumption command
\newcount\prfboundedstyle\prfboundedstyle0

% \prfsummarystyle           default 0
% defines the style for the summary box. The argument takes the
% following values
% 0 = a vertical dotted line (default)
% 1 = a huge \Pi
% 2 = \prod
% 3 = a calligraphic D
% >3 = uses the custom \prffancysummarybox command
\newcount\prfsummarystyle\prfsummarystyle0

% \prffancyline
% the command to draw "fancy" lines
\def\prffancyline{\cleaders\hbox to .63em%
  {\hss\raisebox{-.5ex}[.2ex][0pt]{$\sim$}\hss}\hfill}

% \prfConclusionBox
% the command to draw the conclusion box
\def\prfConclusionBox#1{%
  \hbox{$\displaystyle\begingroup#1\endgroup\mathstrut$}}

% \prfAssumptionBox
% the command to draw the assumption box
\def\prfAssumptionBox#1{%
  \hbox{$\displaystyle\begingroup#1\endgroup\mathstrut$}}

% \prfRuleNameBox
% the command to draw the rule name box.
\def\prfRuleNameBox#1{\hbox{\begingroup#1\endgroup\strut}}

% \prfLabelBox
% the command to draw the label box.
\def\prfLabelBox#1{\hbox{\begingroup#1\endgroup\strut}}

% \prfdiscargedassumption
% the command to draw a discharged assumption in a custom way.
% Users may consider the cancel.sty package
\def\prfdiscargedassumption#1{\left\langle{#1}\right\rangle}

% \prffancysummarybox
% the command to draw the body of a custom summary
\newbox\prf@@fancysummarybox
\newdimen\prf@@fancysymmarylen
\def\prffancysummarybox{%
  \sbox{\prf@@fancysummarybox}{\Huge$\bigtriangledown$}%
  \prf@@fancysymmarylen\ht\prf@@fancysummarybox%
  \advance\prf@@fancysymmarylen\dp\prf@@fancysummarybox%
  \sbox{\prf@@fancysummarybox}{%
    \raisebox{.25\prf@@fancysymmarylen}[.8\prf@@fancysymmarylen]%
    [0pt]{\usebox{\prf@@fancysummarybox}}}%
  \prf@@fancysymmarylen\wd\prf@summary@label%
  \ifdim\prf@@fancysymmarylen>\z@\relax%
    \prf@@fancysymmarylen\wd\prf@@fancysummarybox%
    \wd\prf@summary@label.4em%
    \hbox to\prf@@fancysymmarylen{%
      \usebox\prf@@fancysummarybox}\kern-.4em%
      \box\prf@summary@label%
  \else\usebox\prf@@fancysummarybox\fi}

%====================================================================

%--------------------------------------------------------------------
% What follows is intended for internal use of the package.
% It shouldn't be used in documents and may vary in future versions.
%
% Notice that we use temporary registers shared with TeX & LaTeX, and
% that some registers are shared also inside the drawing procedure!
%--------------------------------------------------------------------

% Lengths
\newskip\prf@Lassum%     space between the left border of the
                   %     assumption box and the left border of the
                   %     conclusion of the first assumption;
\newskip\prf@Rassum%     space between the right border of the
                   %     assumption box and the right border of the
                   %     conclusion of the last assumption 
\skipdef\prf@assumline1%
\skipdef\prf@concline3%
\skipdef\prf@linewd5%
\skipdef\prf@lineht3%
\skipdef\prf@linedp1%
\skipdef\prf@temp7%
\skipdef\prf@tmp7%
\skipdef\prf@Aval9%

% Boxes
\newbox\prf@assumptionsbox%   Assumptions
\newbox\prf@conclusionbox%    Conclusion
\newbox\prf@rulenamebox%      Rule name
\newbox\prf@labelbox%         Label
\newbox\prf@linebox%          Proof line
\newbox\prf@summarybox%       Summary
\newbox\prf@fancybox%         To compute the fancy line

%--------------------------------------------------------------------
% Stack implementation
%--------------------------------------------------------------------
%% End-of-stack, wrapper and stack declaration 
\def\prf@eos{\noexpand\prf@eos}
\def\prf@cons{\noexpand\prf@cons}
\let\prf@stack\prf@eos

%% Pushing a value puts the (decorated) value in front
%% of the stack list
\def\prf@push#1{\expandafter\edef\expandafter\prf@stack%
  {\prf@cons{#1}\prf@stack}}

%% Top retrieves the topmost value in the stack
\def\prf@@top\prf@cons#1#2\prf@eos{#1}
\def\prf@top{\expandafter\prf@@top\prf@stack}

%% Pop discards the topmost value in the stack
\def\prf@@pop\prf@cons#1#2\prf@eos{%
  \expandafter\edef\expandafter\prf@stack{#2\prf@eos}}
\def\prf@pop{\expandafter\prf@@pop\prf@stack}

%--------------------------------------------------------------------
% Checks whether two strings are equal
% \prf@streq{A}{B} if A = B then the boolean value \ifprf@same is 
% true otherwise false 
%
% There is also \prf@strlisteq{A}{L} which checks whether A is equal
% to any element in the comma-separated list L of strings
%--------------------------------------------------------------------
\newif\ifprf@same

\newcommand{\prf@streq}[2]{%
  \global\prf@samefalse\begingroup\def\1{#1}\def\2{#2}%
  \ifx\1\2\global\prf@sametrue\fi\endgroup}

\def\prf@strlisteq#1#2{\prf@@strlisteq{#1}#2,@}
\def\prf@@strlisteq#1#2,{\prf@streq{#1}{#2}%
  \ifprf@same\expandafter\prf@@strlistignore%
  \else\expandafter\prf@@@strlisteq\fi{#1}}
\def\prf@@strlistignore#1@{\relax}
\def\prf@@@strlisteq#1#2{%
  \begingroup\def\1{@}\def\2{#2}%
  \ifx\1\2\prf@@@strlistignore\else\prf@hop\fi\endgroup{#1}#2}
\def\prf@hop\fi\endgroup#1#2{\fi\endgroup\prf@@strlisteq{#1}#2}
\def\prf@@@strlistignore\else\prf@hop\fi\endgroup#1@{\fi\endgroup}

% -------------------------------------------------------------------
% Labelling and referencing
% The following commands implement the reference mechanism to allow to
% label and then refer to assumptions and summaries of proofs
% -------------------------------------------------------------------

% The counter to keep track of assumptions
\newcounter{prfassumptioncounter}
\setcounter{prfassumptioncounter}{0}

% The counter to keep track of summaries
\newcounter{prfsummarycounter}
\setcounter{prfsummarycounter}{0}

% To keep track of the options
\newif\ifprf@lbl@arabic\prf@lbl@arabictrue
\newif\ifprf@lbl@roman\prf@lbl@romanfalse
\newif\ifprf@lbl@Roman\prf@lbl@Romanfalse
\newif\ifprf@lbl@alph\prf@lbl@alphfalse
\newif\ifprf@lbl@Alph\prf@lbl@Alphfalse
\newif\ifprf@lbl@fnsymbol\prf@lbl@fnsymbolfalse
\newif\ifprf@lbl@label\prf@lbl@labelfalse

% The prooftree environment is used to define the scope of the
% assumption references
\newenvironment{prooftree}%
  {\setcounter{prfassumptioncounter}{0}}%
  {\setcounter{prfassumptioncounter}{0}}

% Test whether a reference is defined
\def\ifprf@undefref<#1>{%
  \expandafter\ifx\csname prf@ref@@#1\endcsname\relax}

% Test whether a reference has been written in the .aux file
\def\ifprf@unwrittenref<#1>{%
  \expandafter\ifx\csname prf@w@ref@#1\endcsname\relax}

% Write a reference
\protected\def\prfref<#1>{%
  \ifprf@undefref<#1>\relax\mbox{??}%
    \PackageWarningNoLine{prftree}{Undefined reference <#1>}\relax%
  \else\csname prf@ref@@#1\endcsname\relax\fi\relax} 

% Create the anchor from what stored in the .aux file
\def\prfauxlabel#1#2{%
  \ifprf@undefref<#1>%
    \expandafter\gdef\csname prf@ref@@#1\endcsname{{#2}}\fi}

% Write the newly created label in the .aux file
\def\prf@auxwrite<#1>#2{%
  \ifprf@unwrittenref<#1>%
    \protected@write\@auxout{}{\string\prfauxlabel{#1}{#2}}%
    \expandafter\gdef\csname prf@w@ref@#1\endcsname{0}\fi}

% Generate an assumption label
\def\prf@assum@lbl<#1>{\prf@generic@lbl<#1>{prfassumptioncounter}}

% Generate a summary label 
\def\prf@summary@lbl<#1>{\prf@generic@lbl<#1>{prfsummarycounter}}

% Generate a label on a given counter
\def\prf@generic@lbl<#1>#2{%
  \prf@warningtrue\stepcounter{#2}%
  \ifprf@lbl@arabic\prf@warningfalse%
    \prf@auxwrite<#1>{\arabic{#2}}\fi%
  \ifprf@lbl@roman\prf@warningfalse%
    \prf@auxwrite<#1>{\roman{#2}}\fi%
  \ifprf@lbl@Roman\prf@warningfalse%
    \prf@auxwrite<#1>{\Roman{#2}}\fi%
  \ifprf@lbl@alph\prf@warningfalse%
    \prf@auxwrite<#1>{\alph{#2}}\fi%
  \ifprf@lbl@Alph\prf@warningfalse%
    \prf@auxwrite<#1>{\Alph{#2}}\fi%
  \ifprf@lbl@fnsymbol\prf@warningfalse%
    \prf@auxwrite<#1>{\fnsymbol{#2}}\fi%
  \ifprf@warning\prf@auxwrite<#1>{\arabic{#2}}\fi}

% Parsing of the labelled assumption options
\def\prf@lblopt#1{%
  \prf@warningtrue%
  \global\prf@lbl@arabicfalse% 
  \global\prf@lbl@romanfalse% 
  \global\prf@lbl@Romanfalse%
  \global\prf@lbl@alphfalse%
  \global\prf@lbl@Alphfalse%
  \global\prf@lbl@fnsymbolfalse%
  \global\prf@lbl@labelfalse%
  \prf@strlisteq{#1}{n,number,arabic}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@arabictrue\fi%
  \prf@strlisteq{#1}{r,roman}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@romantrue\fi%
  \prf@strlisteq{#1}{R,Roman}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@Romantrue\fi%
  \prf@strlisteq{#1}{a,alph,alpha,alphabetic}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@alphtrue\fi%
  \prf@strlisteq{#1}{A,Alph,Alpha,Alphabetic}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@Alphtrue\fi
  \prf@strlisteq{#1}{f,s,function,symbol,function symbol}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@fnsymboltrue\fi%
  \prf@strlisteq{#1}{l,label}%
  \ifprf@same\prf@warningfalse\global\prf@lbl@labeltrue\fi%
  \ifprf@warning%
    \PackageWarning{prftree}{Unrecognised option #1}\fi}

% How a labelled assumption is graphically rendered
\def\prflabelledassumptionbox#1#2{%
  \setbox\prf@fancybox\hbox{${#1}$}%
  % \prf@tmp\wd\prf@fancybox% CHANGED FROM v1.0
  \setbox\prf@fancybox\hbox{$\box\prf@fancybox^{#2}$}%
  % \wd\prf@fancybox\prf@tmp% CHANGED FROM v1.0
  \prf@assumption{\box\prf@fancybox}}

% How a discharged fancy labelled assumption is graphically rendered
\def\prflabelleddiscargedassumption#1#2{%
  \prflabelledassumptionbox{\left\langle{#1}\right\rangle}{#2}}

%--------------------------------------------------------------------
% \prfassumption{<formula>}
% \prfboundedassumption{<formula>}
% 
% Commands to draw a pure assumption: the former draws a pure
% assumption, while the latter draws a pure assumption which is
% discharged. The way to mark discharging is controlled by the global
% option \prfboundedstyle
%--------------------------------------------------------------------
\def\prfassumption{\@ifnextchar<{\prf@assum@one}{\prf@assumption}}
\def\prf@assum@one<#1>{\global\prf@lbl@labelfalse\prf@assum@two#1>}
\def\prf@assum@two{\@ifnextchar[{\prf@assum@three}{\prf@assum@four}}
\def\prf@assum@three[#1]{\prf@lblopt{#1}\prf@assum@four}
\def\prf@assum@four#1>#2{%
  \ifprf@unwrittenref<#1>\relax%
  \else\ifprf@lbl@label\relax\else%
    \global\prf@lbl@labeltrue%
    \PackageWarningNoLine{prftree}{Label <#1> is [label]!}\fi\fi%
  \ifprf@lbl@label\relax\else\prf@assum@lbl<#1>\fi%
  \prflabelledassumptionbox{#2}{\prfref<#1>}}
\def\prf@assumption#1{\prftree[noline]{#1}\relax}

\def\prfboundedassumption{%
  \@ifnextchar<{\prf@bassum@one}{\prf@boundedassumption}}
\def\prf@bassum@one<#1>{\global\prf@lbl@labelfalse\prf@bassum@two#1>}
\def\prf@bassum@two{\@ifnextchar[{\prf@bassum@three}{\prf@bassum@four}}
\def\prf@bassum@three[#1]{\prf@lblopt{#1}\prf@bassum@four}
\def\prf@bassum@four#1>#2{%
  \ifprf@unwrittenref<#1>\relax%
  \else\ifprf@lbl@label\relax\else%
    \global\prf@lbl@labeltrue%
    \PackageWarningNoLine{prftree}{Label <#1> is [label]!}\fi\fi%
  \ifprf@lbl@label\relax\else\prf@assum@lbl<#1>\fi%
  \prftree[noline]{\prf@labelledbounded{#2}{#1}}\relax}
\def\prf@boundedassumption#1{\prftree[noline]{\prf@bounded{#1}}\relax}
\def\prf@bounded#1{%
  \ifnum\prfboundedstyle=0\left[{#1}\right]%
  \else\ifnum\prfboundedstyle=1%
      \setbox\prf@conclusionbox\prfConclusionBox{#1}%
      \prf@tmp\wd\prf@conclusionbox%
      \prf@linedp.5\ht\prf@conclusionbox%
      \advance\prf@linedp-.5\dp\prf@conclusionbox%
      \prf@lineht\prf@linedp\advance\prf@lineht\prflinethickness%
      \edef\prf@cancel{\hskip-\prf@tmp%
        \vrule width\prf@tmp height\prf@lineht depth-\prf@linedp}%
      {#1}\prf@cancel%
    \else\prfdiscargedassumption{#1}\fi\fi}  
\def\prf@labelledbounded#1#2{%
  \ifnum\prfboundedstyle=0%
    \prflabelledassumptionbox{\left[{#1}\right]}{\prfref<#2>}%
  \else\ifnum\prfboundedstyle=1%
      \setbox\prf@conclusionbox\prfConclusionBox{#1}%
      \prf@tmp\wd\prf@conclusionbox%
      \prf@linedp.5\ht\prf@conclusionbox%
      \advance\prf@linedp-.5\dp\prf@conclusionbox%
      \prf@lineht\prf@linedp\advance\prf@lineht\prflinethickness%
      \edef\prf@cancel{\hskip-\prf@tmp%
        \vrule width\prf@tmp height\prf@lineht depth-\prf@linedp}%
      \prflabelledassumptionbox{{#1}\prf@cancel}{\prfref<#2>}%
    \else\prflabelleddiscargedassumption{#1}{\prfref<#2>}\fi\fi}  

%--------------------------------------------------------------------
% \prfaxiom{<axiom>}
% \prfbyaxiom{<label>}{<axiom>}
%
% Commands to draw an axiom: the former draws the axiom, while the
% latter includes also a rule name for the axiom.
%--------------------------------------------------------------------
\def\prfaxiom#1{\prftree[single,straight]{#1}\relax}
\def\prfbyaxiom#1#2{\prftree[single,straight,rule]{#1}{#2}\relax}

%--------------------------------------------------------------------
% \prfsummary[<label>]
%            {<assumption1>}...{<assumptionN>} 
%            {<conclusion>}
%
% Command to draw a proof summary, i.e., a structure with assumptions
% 1 to N and a conclusion which stands for a complex proof not
% explicited. The label is optional.
% The shape of the summary is controlled by the global option
% \prfsummarystyle 
%--------------------------------------------------------------------
\def\prfsummary{\@ifnextchar<{\prf@summary@one}{\prf@summary}}
\def\prf@summary@one<#1>{%
  \global\prf@lbl@labelfalse\prf@summary@four#1>}
\def\prf@summary@four{%
  \@ifnextchar[{\prf@summary@five}{\prf@summary@six}}
\def\prf@summary@five[#1]#2>{%
  \prf@lblopt{#1}%
  \ifprf@unwrittenref<#2>\relax%
  \else\ifprf@lbl@label\relax\else%
    \global\prf@lbl@labeltrue%
    \PackageWarningNoLine{prftree}{Label <#2> is [label]!}\fi\fi%
  \ifprf@lbl@label\relax\else\prf@summary@lbl<#2>\fi%
  \setbox\prf@summary@label\hbox{\scriptsize\prfref<#2>}%
  \prf@summary}
\def\prf@summary@six#1>{%
  \ifprf@lbl@label\relax\else\prf@summary@lbl<#1>\fi%
  \setbox\prf@summary@label\hbox{\scriptsize\prfref<#1>}%
  \prf@summary}
\def\prf@summary{\@ifnextchar[{\prf@summary@two}{\prf@summary@three}}
\def\prf@summary@two[#1]{\prftree[summary,rule]{#1}}
\def\prf@summary@three{\prftree[summary]}

\newbox\prf@summary@label
\def\prf@@summarystyle{%
  \ifnum3=\prfsummarystyle\relax%
    \setbox\prf@summarybox\hbox{$\mathcal{D}$}%
    %\prf@tmp\wd\prf@summarybox%
    \setbox\prf@summarybox\hbox{$\mathcal{D}%
      \hbox{\box\prf@summary@label}\mathstrut$}%
    %\wd\prf@summarybox\prf@tmp%
  \else\ifnum2=\prfsummarystyle\relax%
    \setbox\prf@summarybox\hbox{$\prod$}%
    %\prf@tmp\wd\prf@summarybox%
    \setbox\prf@summarybox\hbox{$\prod\hbox{\box\prf@summary@label}$}% 
    %\wd\prf@summarybox\prf@tmp%
  \else\ifnum1=\prfsummarystyle\relax%
    \setbox\prf@summarybox\hbox{\hbox{\Huge$\Pi$}}%
    %\prf@tmp\wd\prf@summarybox%
    \setbox\prf@summarybox\hbox{\hbox{\Huge$\Pi$}%
      \hbox{\box\prf@summary@label}}%
    %\wd\prf@summarybox\prf@tmp%
  \else\ifnum0=\prfsummarystyle\relax%
    \setbox\prf@summarybox\hbox{$\cdot$}%
    %\prf@tmp\wd\prf@summarybox%
    \setbox\prf@summarybox%
      \vbox to5.2ex{\cleaders\hbox{$\cdot$}\vfill}%
    \setbox\prf@summarybox\hbox{\usebox{\prf@summarybox}%
      \hbox{\ \box\prf@summary@label}}%
    %\wd\prf@summarybox\prf@tmp%
  \else\setbox\prf@summarybox\hbox{\prffancysummarybox}\fi\fi\fi\fi% 
  \prf@tmp.5\ht\prf@summarybox%
  \advance\prf@tmp-.5\dp\prf@summarybox%
  \setbox\prf@summarybox%
    \hbox{\lower\prf@tmp\hbox{\box\prf@summarybox}}}%

%--------------------------------------------------------------------
% \prftree[<options>]...[<options>]
%         {<assumption1>}...{<assumptionN>}
%         {<conclusion>}
% 
% The format of options is [<opt1>,...,<optM>]; it is correct to have
% empty options. Options are parsed left-to-right: in case of
% conflicting options, the latest prevails. See the documentation for
% their description.
%
% If present, the rule name is typesetted in text style, while the
% conclusion and the assumptions are typesetted in math mode.
% The result is a box with the correct height and width, whose
% conclusion is aligned with the current baseline.
%
% Notice that the conclusion must be present, while the assumptions
% may be absent.
%
% Options and the way things are drawn can be modified via the global
% settings of the package (see above). Notice that changing these
% settings inside a proof tree may lead to impredictable results, as
% the typesetting may proceed in an arbitrary order.
%--------------------------------------------------------------------
\newif\ifprf@rule%
\newif\ifprf@label%
\newif\ifprf@noline%
\newif\ifprf@doubleline%
\newif\ifprf@straightline%
\newif\ifprf@dottedline%
\newif\ifprf@dashedline%
\newif\ifprf@fancyline%
\newif\ifprf@summary%
\newif\ifprf@first%
\newif\ifprf@warning%
\newif\ifprf@assum

% The real parsing command is \prf@Ntree; the external command sets
% the right values for the various switches controlling the options
\def\prftree{\prf@init\prf@Ntree}
\def\prf@init{%
  \global\prf@rulefalse%
  \global\prf@labelfalse%
  \global\prf@nolinefalse%
  \global\prf@doublelinefalse%
  \global\prf@straightlinetrue%
  \global\prf@dottedlinefalse%
  \global\prf@dashedlinefalse%
  \global\prf@fancylinefalse%
  \global\prf@summaryfalse}

% If there are options then parse them, eventually setting the
% booleans to their appropriate values. Then, expand \prf@@tree
\def\prf@Ntree{\@ifnextchar[{\prf@options}{\prf@@tree}}

% Parses a block [<opt>,...,<opt>] of options one by one, left to
% right 
\def\prf@options[#1]{\prf@opts#1,]\prf@Ntree}
\def\prf@opts#1,{\prf@opt#1,\@ifnextchar]{\prf@optsskip}{\prf@opts}} 
\def\prf@optsskip]{\relax} % to consume the final ]

% Parses a single option eventually setting the appropriate flag 
\def\prf@opt#1,{\prf@warningtrue%
  \prf@strlisteq{#1}{r,by rule,rule,by,right}%
  \ifprf@same\prf@warningfalse\global\prf@ruletrue\fi%
  \prf@strlisteq{#1}{l,label,left}%
  \ifprf@same\prf@warningfalse\global\prf@labeltrue\fi%
  \prf@strlisteq{#1}{s,single line,single,singleline}%
  \ifprf@same\prf@warningfalse\global\prf@doublelinefalse\fi%
  \prf@strlisteq{#1}{d,double line,double,doubleline}%
  \ifprf@same\prf@warningfalse\global\prf@doublelinetrue\fi%
  \prf@strlisteq{#1}{straight,straight line,straightline}%
  \ifprf@same\prf@warningfalse%
  \global\prf@straightlinetrue\global\prf@dottedlinefalse%
  \global\prf@dashedlinefalse\global\prf@fancylinefalse\fi%
  \prf@strlisteq{#1}{dotted,dotted line,dottedline}%
  \ifprf@same\prf@warningfalse%
  \global\prf@straightlinefalse\global\prf@dottedlinetrue%
  \global\prf@dashedlinefalse\global\prf@fancylinefalse\fi%
  \prf@strlisteq{#1}{dashed,dashed line,dashedline}%
  \ifprf@same\prf@warningfalse%
  \global\prf@straightlinefalse\global\prf@dottedlinefalse%
  \global\prf@dashedlinetrue\global\prf@fancylinefalse\fi%
  \prf@strlisteq{#1}{f,fancy line,fancy,fancyline}%
  \ifprf@same\prf@warningfalse%
  \global\prf@straightlinefalse\global\prf@dottedlinefalse%
  \global\prf@dashedlinefalse\global\prf@fancylinetrue\fi%
  \prf@strlisteq{#1}{noline}%
  \ifprf@same\prf@warningfalse\global\prf@nolinetrue\fi%
  \prf@strlisteq{#1}{summary}%
  \ifprf@same\prf@warningfalse\global\prf@summarytrue\fi%
  \ifprf@warning\PackageWarning{prftree}%
                               {Unrecognised option #1}\fi}%

% At this point, options have been parsed. So, we process them
% preparing the right parameters for the drawing procedure. 
% We start from the proof line options:
%   0 = single straight line
%   1 = double straight line 
%   2 = single dotted line
%   3 = double dotted line
%   4 = single dashed line
%   5 = double dashed line
%   6 = single fancy line
%   7 = double fancy line
%   8 = no line
%   9 = summary
\def\prf@@tree{%
  \countdef\prf@linetype1\prf@linetype0%
  \ifprf@dottedline\prf@linetype2\fi%
  \ifprf@dashedline\prf@linetype4\fi%
  \ifprf@fancyline\prf@linetype6\fi%
  \ifprf@doubleline\advance\prf@linetype1\fi%
  \ifprf@noline\prf@linetype8\fi%
  \ifprf@summary\prf@linetype9\fi\relax%
  \expandafter\prf@@Ntree\the\prf@linetype}

% If there is no rule name, we put an empty one in place 
% #1 the line options
\def\prf@@Ntree#1{%
  \edef\prf@choice{\ifprf@rule{#1}\else{#1}{}\fi}%
  \expandafter\prf@@NNtree\prf@choice}

% If there is no label, we put an empty one in place 
% #1 the line options
% #2 the rule name
\def\prf@@NNtree#1#2{%
  \edef\prf@choice{\ifprf@label{#1}{#2}\else{#1}{#2}{}\fi}%
  \expandafter\prf@tree\prf@choice}

% We collect the first assumption, if any, or the conclusion otherwise
% and we look if there is another argument. If not, we draw the proof.
% #1 the line options' value
% #2 the rule name
% #3 the label
% #4 the conclusion or the first assumption 
\def\prf@tree#1#2#3#4{\@ifnextchar\bgroup%
  {\prf@assumptions{#1}{#2}{#3}{\prf@preprf{#4}}}%
  {\prf@draw{#1}{#2}{#3}{#4}{\prf@preprf}{}}}

% We examine assumptions from left to right. If we hit the last
% argument, it is the conclusion and the proof is ready to be drawn. 
% #1 the line options' value
% #2 the rule name
% #3 the label
% #4 the first assumptions
% #5 the current argument
\def\prf@assumptions#1#2#3#4#5{\@ifnextchar\bgroup%
  {\prf@assumenext{#1}{#2}{#3}{#4}{\prf@interprf{#5}}}%
  {\prf@draw{#1}{#2}{#3}{#5}{#4}{}}}

% An intermediate assumption is added to the assumptions' box, until
% the last assumption has been collected. Then the proof is drawn.
% #1 the line options' value
% #2 the rule name
% #3 the label
% #4 the first assumption
% #5 the complete list of assumptions
% #6 the new argument
\def\prf@assumenext#1#2#3#4#5#6{\@ifnextchar\bgroup%
  {\prf@assumenext{#1}{#2}{#3}{#4}{{#5}\prf@interprf{#6}}}%
  {\prf@draw{#1}{#2}{#3}{#6}{#4}{#5}}}

% We need to reset some internal variables during the generation of
% the assumptions
\def\prf@preprf{\global\prf@Lassum\z@\global\prf@Rassum\z@}

% We need to put some space between assumptions when generating them 
\def\prf@interprf{\hskip\prfinterspace}

%--------------------------------------------------------------------
% The drawing procedure, i.e., the "core" of the package
% #1 the line options' value
% #2 the rule name
% #3 the label 
% #4 the conclusion
% #5 the first assumption
% #6 the list of assumptions
%--------------------------------------------------------------------

\def\prf@draw#1#2#3#4#5#6{%
  % We construct the boxes which will constitute the proof
  \ifprf@first\prf@push{1}\else\prf@push{0}\fi%
  \global\prf@firsttrue%
  \setbox\prf@assumptionsbox\prfAssumptionBox{#5}%
  \prf@push{\the\prf@Lassum}%
  \global\prf@firstfalse%
  \ifdim\wd\prf@assumptionsbox>\z@\relax\prf@assumtrue%
    \setbox\prf@assumptionsbox%
      \hbox{\box\prf@assumptionsbox\prfAssumptionBox{#6}}%
  \else\prf@assumfalse%
    \setbox\prf@assumptionsbox\hbox{}\fi%
  \prf@push{\the\prf@Rassum}%
  \setbox\prf@conclusionbox\prfConclusionBox{#4}%
  \setbox\prf@rulenamebox\prfRuleNameBox{#2}%
  \setbox\prf@labelbox\prfLabelBox{#3}%
  % We set up the flags needed to format the proof tree box
  \prf@nolinefalse\prf@doublelinefalse\prf@straightlinetrue%
  \prf@dottedlinefalse\prf@dashedlinefalse\prf@fancylinefalse%
  \prf@summaryfalse\prf@rulefalse\prf@labelfalse%
  \ifcase#1\relax\or%
  \prf@doublelinetrue\or%
  \prf@dottedlinetrue\prf@straightlinefalse\or%
  \prf@doublelinetrue\prf@dottedlinetrue\prf@straightlinefalse\or%
  \prf@dashedlinetrue\prf@straightlinefalse\or%
  \prf@doublelinetrue\prf@dashedlinetrue\prf@straightlinefalse\or%
  \prf@fancylinetrue\prf@straightlinefalse\or%
  \prf@doublelinetrue\prf@fancylinetrue\prf@straightlinefalse\or%
  \prf@nolinetrue\prf@straightlinefalse\or%
  \prf@summarytrue\prf@straightlinefalse\fi%
  \ifdim\wd\prf@rulenamebox>\z@\relax\prf@ruletrue%
  \else\prf@rulefalse\fi%
  \ifdim\wd\prf@labelbox>\z@\relax\prf@labeltrue%
  \else\prf@labelfalse\fi%
  \ifdim\wd\prf@assumptionsbox>\z@\relax\prf@assumtrue%
  \else\prf@assumfalse\fi%
  % Now, we retrieve the right values for Lassum and Rassum
  % since box construction may have overwritten them. Also, we need to
  % know if this proof is the first of a list of assumptions
  \edef\prf@tok{\prf@top}\prf@pop\global\prf@Rassum\prf@tok%
  \edef\prf@tok{\prf@top}\prf@pop\global\prf@Lassum\prf@tok%
  \edef\prf@tok{\prf@top}\prf@pop\global\prf@firstfalse%
  \ifnum\prf@tok=1\global\prf@firsttrue\fi%
  % The assumptions' box has the following shape
  %  --------------------------------
  % |<---------------------wd------->|
  % | -----------       ------------ |
  % ||<-->       |     |      <---->||
  % || Lassum    | ... |   Rassum   ||
  % ||   |       |     |      |     ||
  % ||   V       |     |      V     ||
  % | -----------       ------------ |
  %  --------------------------------
  % The assumptions' line is composed by the conclusions of the
  % proofs which are the antecedents of the application of the
  % inference rule
  % The final box will be something like
  %  --------------------------------
  % |<---------------------wd------->|
  % | -----------       ------------ |
  % ||<-->       |     |      <---->||
  % || Lassum    | ... |   Rassum   ||
  % ||   |       |     |      |     ||
  % ||   V       |     |      V     ||
  % | -----------       ------------ |
  %  --------------------------------
  %     ========================   rule name
  %             conclusion
  % <--Lassum-->          <-----Rassum----->
  % 
  % We calculate the length of the assumptions' line:
  %   assumline = assumptionsbox - Lassum - Rassum
  % if there are no assumption, assumline = 0
  % (for efficiency reasons, we actually calculate 1/2assumline)
  \ifprf@assum\prf@assumline.5\wd\prf@assumptionsbox%
    \advance\prf@assumline-.5\prf@Lassum%
    \advance\prf@assumline-.5\prf@Rassum%
    \else\prf@assumline\z@\fi%
  % The length of the conclusionbox
  % (for efficiency reasons, we actually calculate 1/2concline)
  \prf@concline.5\wd\prf@conclusionbox%
  % The length of the proof line is 
  %   linewd = if summary then width of summary box else
  %               max(concline,assumline)
  %   if there is a line, we add 2extra
  % (for efficiency reasons, we actually calculate 1/2linewd)
  \ifprf@summary\prf@@summarystyle\prf@linewd.5\wd\prf@summarybox%
  \else\prf@linewd\prf@assumline%
    \ifdim\prf@assumline<\prf@concline\prf@linewd\prf@concline\fi% 
    \ifprf@noline\relax\else\advance\prf@linewd\prflineextra\fi\fi%
  % We calculate the proofline without label and rule name.
  \ifprf@noline\setbox\prf@fancybox\hbox{\hskip2\prf@linewd}%
  \else\ifprf@summary\setbox\prf@fancybox\copy\prf@summarybox%
  \else\ifprf@fancyline%
      \setbox\prf@fancybox\hbox to2\prf@linewd{\prffancyline}\else%
      \ifprf@dashedline%
      \setbox\prf@fancybox%
      \hbox to2\prf@linewd{\cleaders\hbox to.5em{\hss\_\hss}\hfill}\else%
      \ifprf@dottedline%
      \setbox\prf@fancybox%
      \hbox to2\prf@linewd{\cleaders\hbox to.33em{\hss.\hss}\hfill}\else% 
   % it must be a straight line!
      \setbox\prf@fancybox\hbox{\vrule width2\prf@linewd%
        height\prflinethickness}\fi\fi\fi%
  % If the line is double, we draw it twice with enough
  % (doublelineinterspace) space between the two copies. 
    \ifprf@doubleline%
      \setbox\prf@fancybox\hbox{\vbox{\copy\prf@fancybox%
         \nointerlineskip\vskip\prfdoublelineinterspace\nointerlineskip%
         \box\prf@fancybox}}\fi\fi\fi%
  \prf@tmp\dp\prf@fancybox%
  \setbox\prf@fancybox\hbox{\raise\prf@tmp\box\prf@fancybox}%
  % Let A = max(1/2assumline + Lassum, 1/2conclusionbox, 1/2linewd +
  % delta), where delta is 0 if there is no label, and it is the width
  % of the label box plus prflabelskip otherwise.
  % Then
  %   Assumptions shift         = A - (1/2assumline + Lassum)
  %   Rule line shift           = A - (1/2linewd + delta)
  %   Lassum = Conclusion shift = A - 1/2conclusionbox
  % And, so, we can prepare the assumptions box and the conclusion box 
  \prf@Aval\prf@assumline\advance\prf@Aval\prf@Lassum%
  \prf@tmp\prf@linewd\relax%
  \ifprf@label\advance\prf@tmp\wd\prf@labelbox%
    \advance\prf@tmp\prflabelskip\fi%
  \ifdim\prf@Aval<\prf@tmp\prf@Aval\prf@tmp\fi%
  \ifdim\prf@Aval<\prf@concline\prf@Aval\prf@concline\fi%
  \prf@temp\prf@Aval\advance\prf@temp-\prf@assumline%
  \advance\prf@temp-\prf@Lassum%
  \setbox\prf@assumptionsbox%
    \hbox{\hskip\prf@temp\box\prf@assumptionsbox}%
  \prf@temp\prf@Aval\advance\prf@temp-\prf@concline%
  \setbox\prf@conclusionbox%
    \hbox{\hskip\prf@temp\box\prf@conclusionbox}%
  \global\prf@Lassum\prf@temp%
  % Rassum will be the width of the composition of all boxes (but we
  % still have to cope with heigths...) minus (concline + conclusion
  % shift) 
  \global\prf@Rassum-2\prf@concline%
  \global\advance\prf@Rassum-\prf@temp%
  % Then, if there is a rule name, the line is raised to align with
  % the centre of the rule name and the rule box gets attached to the
  % proof line box.
  \prf@linedp\z@%
  \ifprf@noline\setbox\prf@fancybox\hbox to2\prf@linewd{}\fi%
  \ifprf@rule\advance\prf@linedp.5\ht\prf@fancybox%
    \advance\prf@linedp-.5\ht\prf@rulenamebox%
    \advance\prf@linedp.5\dp\prf@rulenamebox%
    \setbox\prf@linebox%
      \hbox{\copy\prf@fancybox\hskip\prfrulenameskip%
        \raise\prf@linedp\box\prf@rulenamebox}%
  \else\setbox\prf@linebox\copy\prf@fancybox\fi%
  \setbox\prf@linebox\hbox{\raise\dp\prf@linebox\box\prf@linebox}%
  % Then, if there is a label, the line is raised to align with
  % the centre of the label and the label box gets attached to the
  % proof line box.
  \prf@linedp\z@%
  \prf@temp\prf@Aval\advance\prf@temp-\prf@linewd%
  \ifprf@label\advance\prf@linedp.5\ht\prf@linebox%
    \advance\prf@linedp-.5\ht\prf@labelbox%
    \advance\prf@linedp.5\dp\prf@labelbox%
    \advance\prf@temp-\prflabelskip%
    \advance\prf@temp-\wd\prf@labelbox%
    \setbox\prf@linebox%
      \hbox{\raise\prf@linedp\box\prf@labelbox%
        \hskip\prflabelskip\box\prf@linebox}\fi%
  \setbox\prf@linebox%
    \hbox{\hskip\prf@temp\raise\dp\prf@linebox\box\prf@linebox}%
  % We need to calculate the distance between the assumptions and the
  % proofline: if there are no assumptions, it is zero; if there are
  % assumptions but no rule name, it is \prflinepad; otherwise it is
  % \linepad plus half of the "real" line's height
  \prf@tmp\z@%
  \ifprf@assum%
    \ifprf@rule\prf@tmp-.5\ht\prf@linebox%
      \advance\prf@tmp.5\ht\prf@fancybox%
      \advance\prf@tmp.5\dp\prf@fancybox\fi\relax%
    \ifprf@label\ifprf@rule\relax\else%
      \prf@tmp-.5\ht\prf@linebox%
      \advance\prf@tmp.5\ht\prf@fancybox%
      \advance\prf@tmp.5\dp\prf@fancybox\fi\fi%
    \advance\prf@tmp\prflinepad%
    \setbox\prf@assumptionsbox%
      \vbox{\box\prf@assumptionsbox\nointerlineskip\vskip\prf@tmp}\fi%
  % We need to calculate the distance between the proofline and the
  % conclusion: it is slightly complex to explain... try to draw the
  % whole thing to make it clear!! 
  \prf@temp\prflinepad%
  \ifprf@noline%
    \ifprf@assum%
      \advance\prf@temp\prfemptylinethickness\fi%
    \advance\prf@temp-\prflinepad\fi%
  \ifprf@rule%
    \advance\prf@temp-.5\ht\prf@linebox%
    \advance\prf@temp.5\ht\prf@fancybox%
    \advance\prf@temp.5\dp\prf@fancybox\fi%
  \ifprf@label\ifprf@rule\relax\else%
    \advance\prf@temp-.5\ht\prf@linebox%
    \advance\prf@temp.5\ht\prf@fancybox%
    \advance\prf@temp.5\dp\prf@fancybox\fi\fi%
  \setbox\prf@conclusionbox%
    \vbox{\vskip\prf@temp\box\prf@conclusionbox}%
  % And, finally, we can prepare the proof box and we can calculate
  % the right value from Rassum. At the very end, we can output the
  % result (!!) 
  \setbox\prf@rulenamebox%
    \vbox{\box\prf@assumptionsbox\nointerlineskip%
      \box\prf@linebox\nointerlineskip%
      \box\prf@conclusionbox\nointerlineskip}%
  \global\advance\prf@Rassum\wd\prf@rulenamebox%
  \hbox{$\box\prf@rulenamebox$}}

% -------------------------------------------------------------------
% The following macros are used to simplify the writing of proofs in
% natural deduction, and they roughly follow the format of proofs as
% in Troelstra, Schwichtenberg "Basic Proof Theory".
% 
% Since they may conflict with other packages, they are controlled by
% options in the package. 
% -------------------------------------------------------------------

% -------------------------------------------------------------------
% Natural deduction systems
%
% Package option [ND]
% -------------------------------------------------------------------

\ifprf@NDOption%
  \def\NDA{\prfassumption}
  \def\NDD{\prfboundedassumption}
  \def\NDAL#1{\prfassumption<#1>}
  \def\NDDL#1{\prfboundedassumption<#1>}
  \def\NDP{\prftree}
  \def\NDANDI{\prftree[by]{$\scriptstyle\mathord{\wedge}%
      \noexpand\textup{I}$}}
  \def\NDANDEL{\prftree[by]{$\scriptstyle\mathord{\wedge}%
      \noexpand\textup{E}_1$}}
  \def\NDANDER{\prftree[by]{$\scriptstyle\mathord{\wedge}%
      \noexpand\textup{E}_2$}}
  \def\NDANDE{\prftree[by]{$\scriptstyle\mathord{\wedge}%
      \noexpand\textup{E}$}}
  \def\NDORIL{\prftree[by]{$\scriptstyle\mathord{\vee}%
      \noexpand\textup{I}_1$}}
  \def\NDORIR{\prftree[by]{$\scriptstyle\mathord{\vee}%
      \noexpand\textup{I}_2$}}
  \def\NDORI{\prftree[by]{$\scriptstyle\mathord{\vee}%
      \noexpand\textup{I}$}}
  \def\NDORE{\prftree[by]{$\scriptstyle\mathord{\vee}%
      \noexpand\textup{E}$}}
  \def\NDOREL#1{\prftree[by]{$\scriptstyle{\vee}%
      {\noexpand\textup{E}}^{\noexpand\prfref<#1>}$}}
  \ifprfIMPOption
    \def\NDIMPI{\prftree[by]{$\scriptstyle\mathord{\supset}%
        \noexpand\textup{I}$}}
    \def\NDIMPE{\prftree[by]{$\scriptstyle\mathord{\supset}%
        \noexpand\textup{E}$}}
    \def\NDIMPIL#1{\prftree[by]{$\scriptstyle\mathord{\supset}%
        \noexpand\textup{I}^{\noexpand\prfref<#1>}$}}
  \else
    \def\NDIMPI{\prftree[by]{$\scriptstyle\mathord{\rightarrow}%
        \noexpand\textup{I}$}}
    \def\NDIMPE{\prftree[by]{$\scriptstyle\mathord{\rightarrow}%
        \noexpand\textup{E}$}}
    \def\NDIMPIL#1{%
      \prftree[by]{$\scriptstyle\mathord{\rightarrow}%
        \noexpand\textup{I}^{\noexpand\prfref<#1>}$}}\fi
  \def\NDNOTI{\prftree[by]{$\scriptstyle\mathord{\neg}%
      \noexpand\textup{I}$}}
  \def\NDNOTIL#1{\prftree[by]{$\scriptstyle{\neg}%
      \noexpand\textup{I}^{\noexpand\prfref<#1>}$}}
  \def\NDNOTE{\prftree[by]{$\scriptstyle\mathord{\neg}%
      \noexpand\textup{E}$}}
  \def\NDALLI{\prftree[by]{$\scriptstyle\mathord{\forall}%
      \noexpand\textup{I}$}}
  \def\NDALLE{\prftree[by]{$\scriptstyle\mathord{\forall}%
      \noexpand\textup{E}$}}
  \def\NDEXI{\prftree[by]{$\scriptstyle\mathord{\exists}%
      \noexpand\textup{I}$}}
  \def\NDEXE{\prftree[by]{$\scriptstyle\mathord{\exists}%
      \noexpand\textup{E}$}}
  \def\NDEXEL#1{%
    \prftree[by]{$\scriptstyle\mathord{\exists}%
      \noexpand\textup{E}^{\noexpand\prfref<#1>}$}}
  \def\NDTI{\prftree[by]{$\scriptstyle\mathord{\top}%
      \noexpand\textup{I}$}}
  \def\NDFE{\prftree[by]{$\scriptstyle\mathord{\bot}%
      \noexpand\textup{E}$}}
  \def\NDLEM{\prftree[by]{$\scriptstyle\noexpand\textup{lem}$}}
  \def\NDAX{\prftree[by]{$\scriptstyle\noexpand\textup{ax}$}}
\fi

% -------------------------------------------------------------------
% Sequent systems
%
% Package option [SEQ]
% -------------------------------------------------------------------

\ifprf@SEQOption%
  \def\SEQA{\prfassumption}
  \def\SEQD{\prfboundedassumption}
  \def\SEQP{\prftree}
  \def\SEQAX{\prftree[by]{$\scriptstyle\noexpand\textup{Ax}$}}
  \def\SEQLF{\prftree[by]{$\scriptstyle\noexpand\textup{L}\bot$}}
  \def\SEQLW{\prftree[by]{$\scriptstyle\noexpand\textup{LW}$}}
  \def\SEQRW{\prftree[by]{$\scriptstyle\noexpand\textup{RW}$}}
  \def\SEQLC{\prftree[by]{$\scriptstyle\noexpand\textup{LC}$}}
  \def\SEQRC{\prftree[by]{$\scriptstyle\noexpand\textup{RC}$}}
  \def\SEQLAND{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
      \mathord{\wedge}$}}
  \def\SEQRAND{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
      \mathord{\wedge}$}}
  \def\SEQLOR{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
      \mathord{\vee}$}}
  \def\SEQROR{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
      \mathord{\vee}$}}
  \ifprfIMPOption
    \def\SEQLIMP{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
        \mathord{\supset}$}}
    \def\SEQRIMP{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
        \mathord{\supset}$}}
  \else
    \def\SEQLIMP{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
        \mathord{\rightarrow}$}}
    \def\SEQRIMP{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
        \mathord{\rightarrow}$}}
  \fi
  \def\SEQLALL{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
      \mathord{\forall}$}} 
  \def\SEQRALL{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
      \mathord{\forall}$}}
  \def\SEQLEX{\prftree[by]{$\scriptstyle\noexpand\textup{L}%
      \mathord{\exists}$}}
  \def\SEQREX{\prftree[by]{$\scriptstyle\noexpand\textup{R}%
      \mathord{\exists}$}}
  \def\SEQCUT{\prftree[by]{$\scriptstyle\noexpand\textup{Cut}$}}
\fi

% -------------------------------------------------------------------