; TeX output 1995.10.03:1353l'&DDtGGcmr17Build7tprosoftreeforNaturalDeduction,SequenqtCalculus,7tetc.dYXQ cmr12PraulTVaylortDepartmenrtofComputing,5ImpSerialCollege,RLondonSW72BZ'+44715895111!@ cmti12ext50572߆T cmtt12]‰OctobSer3,1995"ԆNK`y cmr10UsingUUmyProGofT*reemacros,youcanproGduceMA+0 ?-o cmr9[(/ cmsy99.5" cmmi9yR:(#(n9n:x;cmmi6n=y)7?^8qy)Lg>)8^(8w>:(#(n9n:xn=w)9)pw)T$)] p?c獑g^1E3;9yR:(#(n9n:xn=y)7?^8qy)Jb*[(9yR:(#(n9n:xn=y)7?^8qy)Lg>)8^(8w>:(#(n9n:xn=w)9)pw)T$)] pJb*c獑g^2Eq8w>:(#(n9n:xn=w)9)pw)pq՟cDg8E|(9n:xn=yR))pyFC[(9n:xn=yR)8^qy] pFCMwg^1EXw9n:xn=yp|\g) cEWpy@[(9n:xn=yR)8^qy] pW׍g^Ilpy`^8((9n:xn=yR)^qy)pcq;g9Ic9zc:pzq^8(( ?( 9n:xn=z);,Z^8qRz)P#)p3;Rg9E 9zc:pzq^8(( ?( 9n:xn=z);,Z^8qRz)P#)p}`\3&g) cI }`(9yR:(#(n9n:xn=y)7?^8qy)Lg>)8^(8w>:(#(n9n:xn=w)9)pw)T$))(9zc:pzq^8(( ?( 9n:xn=z);,Z^8qRz)P#)S)N ABUUusingUUtheTU>'ExXorL5ffٓRcmr7A͉TU>'EXcoGdej?B cmmi10A Bp̀g.$s !", cmsy10^ IõA8^B큍?ThehypGothesesmaythemselvesbGeprooftrees(enclosedinB\[::: UOB\])andthe?purpGose_ofthemacrosistoadjustthelengthofthehorizontal\deduction"line.2 l'?WhenthehypGothesesareprooftrees,)suitablespaceisputbetweenthem,)butof ?courseϯthismustbGesuppliedbyhandforsimpleformulae.E;TheB\thicknessand?B\shiftrightҿcommandsare,ofcourse,optional;stheyapplytothehorizontal?lineRandtothepGositioningoftheconclusionrelativetoit.]F*oradoubleline,?useUUB\JustifiesinsteadofB\justifies.NNoticetheoverloadingoftheB\[::: UOB\];theoutermostproGoftreemustbe?enclosedwithB\begin{prooftree}andB\end{prooftree}orB\prooftreeand?B\endprooftree.NT*oUUgetaverticalstringofdotsinsteadoftheproGofrule,do?B\[?[A]?\using?\pi?\proofdotseparation=1.2ex?\proofdotnumber=4?\leadsto?B?\]񽍑?toUUgetc[A]1xUX*@VB1NAllMofofthekeywordsMexceptB\prooftreeandB\endprooftreeareoptional?andmayappGearinanyorder.1TheymayalsobGecombinedinB\newcommands,?forUUexample?B\newcommand\Cut{\using\sf?cut\thickness.08em\justifies}?withUUtheabbreviation?B\[?A\vdashB\qquadNB?\vdashCI\CutNA?\vdashC?\]N\thickness`spGeci esthebreadthoftheruleinanyunits,althoughfont-?relative.unitssuchasexoremarepreferable.ItmayoptionallybGefollowed?by=.B\proofrulebreadth=.08emorB\setlength\proofrulebreadth{.08em}?maygalsobGeusedeitherinplaceofB\thicknessorglobally;vthedefaultis0.04em.?B\proofdotseparationвandB\proofdotnumbercontrolthesizeofthestringof?dots.NIfproGoftreesandformulaearemixed,someexplicitspacingisneeded,but?don'tputanythingtotheleftoftheleft-most(ortherightoftheright-most)3l'?hypGothesis,zor@@putitinbraces,bGecausethiswillcausetheindentationtobe ?lost.NByEdefaulttheconclusioniscenteredwrttheleft-mostandright-mostim-?mediate5hypGotheses(nottheirproofs);2B\shiftrightorB\shiftleftmoves5it?relativeZtothispGosition.(Notsureaboutthisspeci cationorhowitshould?a ectUUspreadingofproGoftree.)4:;lD': cmti10B cmmi10K`y cmr10ٓRcmr7V