% D. Roegel, 20/5/2001 input metaobj % Proof from % David, Nour, Raffalli: Introduction à la logique, Paris: Dunod, 2001 % p. 197 verbatimtex \newcount\pntcnt \pntcnt=0 \def\npoints#1{\pntcnt=#1\vbox{\offinterlineskip\kern5pt\npointsa}} \def\npointsa{\ifnum\pntcnt>0\hbox{$.$}\kern5pt\advance\pntcnt-1 \expandafter\npointsa\fi} etex beginfig(1); % setObjectDefaultOption("PTree")("treemode")("U"); % default is down newAssumption.pi1(btex $\Pi_1$ etex); newConclusion.pi1c1(btex \npoints3 etex); newPTreeR.pi1proof(pi1c1)(pi1)("") "rule(0)"; newConclusion.pi1c2(btex $\Gamma,B \vdash \Delta$ etex); newPTreeR.a1(pi1c2)(pi1proof)("") "rule(0)"; newAssumption.pi2(btex $\Pi_2$ etex); newConclusion.pi2c1(btex \npoints3 etex); newPTreeR.pi2proof(pi2c1)(pi2)("") "rule(0)"; newConclusion.pi2c2(btex $\Gamma,C \vdash \Delta$ etex); newPTreeR.a2(pi2c2)(pi2proof)("") "rule(0)"; newConclusion.c1(btex $\Gamma,B\lor C \vdash \Delta$ etex); newPTreeR.proof1(c1)(a1,a2)(btex $\lor_g$ etex); newAssumption.pi3(btex $\Pi_3$ etex); newConclusion.pi3c1(btex \npoints3 etex); newPTreeR.pi3proof(pi3c1)(pi3)("") "rule(0)"; newConclusion.pi3c2(btex $\Gamma' \vdash B,C, \Delta'$ etex); newPTreeR.a3(pi3c2)(pi3proof)("") "rule(0)"; newConclusion.c2 (btex $\Gamma_A,\Gamma'\vdash B,C,\Delta,\Delta'_A$ etex); newPTreeR.proof2(c2)(proof1,a3)(btex {\it mix\/}$(1)$ etex); newConclusion.c2points (btex $\npoints{12}$ etex); newPTreeR.proof2a(c2points)(proof2)("") "rule(0)"; duplicateObj(a4,a1); duplicateObj(a5,a3); newConclusion.c3(btex $\Gamma' \vdash B\lor C, \Delta'$ etex); newPTreeR.proof3(c3)(a5)(btex $\lor_d$ etex); newConclusion.c4(btex $\Gamma_A,\Gamma',B \vdash \Delta, \Delta'_A$ etex); newPTreeR.proof4(c4)(a4,proof3)(btex {\it mix\/}$(2)$ etex); newConclusion.c5(btex $\Gamma_A,\Gamma',\Gamma_A,\Gamma' \vdash C,\Delta, \Delta'_A,\Delta, \Delta'_A$ etex); newHRazor.hr1(-4cm); newPTreeR.proof5(c5)(proof2a,hr1,proof4)(btex {\it mix\/}$(3)$ etex); duplicateObj(a6,a2); duplicateObj(proof3a,proof3); newConclusion.c7(btex $\Gamma_A,\Gamma',C \vdash \Delta, \Delta'_A$ etex); newPTreeR.proof3b(c7)(a6,proof3a)(btex {\it mix\/}$(4)$ etex); newConclusion.c8(btex $\Gamma_A,\Gamma',\Gamma_A,\Gamma',\Gamma_A,\Gamma' \vdash \Delta, \Delta'_A,\Delta, \Delta'_A,\Delta, \Delta'_A$ etex); newPTreeR.proof3d(c8)(proof5,proof3b)(btex {\it mix\/}$(5)$ etex) "hsep(5mm)"; newConclusion.c9(btex $\Gamma_A,\Gamma'\vdash \Delta, \Delta'_A$ etex); newPTreeR.proof3E(c9)(proof3d)(btex contr$_g$,contr$_d$ etex); %yscaleObj(proof3E,2); %reflectObj(proof3E,(0,0),(0,1)); %slantObj(proof3E,0.2); proof3E.c=origin; drawObj(proof3E); endfig; clearObj pi,a,c,proof,hr; beginfig(2); setObjectDefaultOption("PTree")("treemode")("U"); % default is down newAssumption.pi1(btex $\Pi_1$ etex); newConclusion.pi1c1(btex \npoints3 etex); newPTreeR.pi1proof(pi1c1)(pi1)("") "rule(0)"; newConclusion.pi1c2(btex $\Gamma,B \vdash \Delta$ etex); newPTreeR.a1(pi1c2)(pi1proof)("") "rule(0)"; newAssumption.pi2(btex $\Pi_2$ etex); newConclusion.pi2c1(btex \npoints3 etex); newPTreeR.pi2proof(pi2c1)(pi2)("") "rule(0)"; newConclusion.pi2c2(btex $\Gamma,C \vdash \Delta$ etex); newPTreeR.a2(pi2c2)(pi2proof)("") "rule(0)"; newConclusion.c1(btex $\Gamma,B\lor C \vdash \Delta$ etex); newPTreeR.proof1(c1)(a1,a2)(btex $\lor_g$ etex); newAssumption.pi3(btex $\Pi_3$ etex); newConclusion.pi3c1(btex \npoints3 etex); newPTreeR.pi3proof(pi3c1)(pi3)("") "rule(0)"; newConclusion.pi3c2(btex $\Gamma' \vdash B,C, \Delta'$ etex); newPTreeR.a3(pi3c2)(pi3proof)("") "rule(0)"; newConclusion.c2 (btex $\Gamma_A,\Gamma'\vdash B,C,\Delta,\Delta'_A$ etex); newPTreeR.proof2(c2)(proof1,a3)(btex {\it mix\/}$(1)$ etex); newConclusion.c2points (btex $\npoints{12}$ etex); newPTreeR.proof2a(c2points)(proof2)("") "rule(0)"; duplicateObj(a4,a1); duplicateObj(a5,a3); newConclusion.c3(btex $\Gamma' \vdash B\lor C, \Delta'$ etex); newPTreeR.proof3(c3)(a5)(btex $\lor_d$ etex); newConclusion.c4(btex $\Gamma_A,\Gamma',B \vdash \Delta, \Delta'_A$ etex); newPTreeR.proof4(c4)(a4,proof3)(btex {\it mix\/}$(2)$ etex); newConclusion.c5(btex $\Gamma_A,\Gamma',\Gamma_A,\Gamma' \vdash C,\Delta, \Delta'_A,\Delta, \Delta'_A$ etex); newHRazor.hr1(-4cm); newPTreeR.proof5(c5)(proof2a,hr1,proof4)(btex {\it mix\/}$(3)$ etex); duplicateObj(a6,a2); duplicateObj(proof3a,proof3); newConclusion.c7(btex $\Gamma_A,\Gamma',C \vdash \Delta, \Delta'_A$ etex); newPTreeR.proof3b(c7)(a6,proof3a)(btex {\it mix\/}$(4)$ etex); newConclusion.c8(btex $\Gamma_A,\Gamma',\Gamma_A,\Gamma',\Gamma_A,\Gamma' \vdash \Delta, \Delta'_A,\Delta, \Delta'_A,\Delta, \Delta'_A$ etex); newPTreeR.proof3d(c8)(proof5,proof3b)(btex {\it mix\/}$(5)$ etex) "hsep(5mm)"; newConclusion.c9(btex $\Gamma_A,\Gamma'\vdash \Delta, \Delta'_A$ etex); newPTreeR.proof3E(c9)(proof3d)(btex contr$_g$,contr$_d$ etex); %yscaleObj(proof3E,2); %reflectObj(proof3E,(0,0),(0,1)); %slantObj(proof3E,0.2); proof3E.c=origin; drawObj(proof3E); endfig; end