Logiweb aspects of prop lemma doubly conditioned join conjuncts in pyk

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The predefined "pyk" aspect

define pyk of prop lemma doubly conditioned join conjuncts as text unicode start of text unicode small p unicode small r unicode small o unicode small p unicode space unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small d unicode small o unicode small u unicode small b unicode small l unicode small y unicode space unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode small e unicode small d unicode space unicode small j unicode small o unicode small i unicode small n unicode space unicode small c unicode small o unicode small n unicode small j unicode small u unicode small n unicode small c unicode small t unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop lemma doubly conditioned join conjuncts as text unicode start of text unicode capital j unicode small o unicode small i unicode small n unicode capital c unicode small o unicode small n unicode small j unicode small u unicode small n unicode small c unicode small t unicode small s unicode left parenthesis unicode two unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop lemma doubly conditioned join conjuncts as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar end define

The user defined "the proof aspect" aspect

define proof of prop lemma doubly conditioned join conjuncts as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar infer metavar var b end metavar infer prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar modus ponens metavar var a end metavar modus ponens metavar var b end metavar conclude metavar var c end metavar cut prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar modus ponens metavar var a end metavar modus ponens metavar var b end metavar conclude metavar var d end metavar cut prop lemma join conjuncts modus ponens metavar var c end metavar modus ponens metavar var d end metavar conclude not0 metavar var c end metavar imply not0 metavar var d end metavar cut all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar infer metavar var b end metavar infer not0 metavar var c end metavar imply not0 metavar var d end metavar conclude metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar cut metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar conclude metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar end quote state proof state cache var c end expand end define