define pyk of lemma pair subset0 as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small p unicode small a unicode small i unicode small r unicode space unicode small s unicode small u unicode small b unicode small s unicode small e unicode small t unicode zero unicode end of text end unicode text end text end define
define tex of lemma pair subset0 as text unicode start of text unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode capital p unicode small a unicode small i unicode small r unicode capital s unicode small u unicode small b unicode small s unicode small e unicode small t unicode end of text end unicode text end text end define
define statement of lemma pair subset0 as system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar end define
define proof of lemma pair subset0 as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var s end metavar zermelo is metavar var x end metavar infer lemma =transitivity modus probans quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote modus ponens metavar var s end metavar zermelo is metavar var x end metavar modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude metavar var s end metavar zermelo is metavar var y end metavar cut prop lemma weaken or second modus ponens metavar var s end metavar zermelo is metavar var y end metavar conclude not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var w end metavar indeed 1rule deduction modus ponens all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var s end metavar zermelo is metavar var x end metavar infer not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar conclude quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,