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Diffstat (limited to 'Master/texmf-dist/metapost/metaobj/proofex.mp')
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1 files changed, 153 insertions, 0 deletions
diff --git a/Master/texmf-dist/metapost/metaobj/proofex.mp b/Master/texmf-dist/metapost/metaobj/proofex.mp new file mode 100644 index 00000000000..02d61b7df91 --- /dev/null +++ b/Master/texmf-dist/metapost/metaobj/proofex.mp @@ -0,0 +1,153 @@ +% 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 |