define pyk of lemma same singleton 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 s unicode small a unicode small m unicode small e unicode space unicode small s unicode small i unicode small n unicode small g unicode small l unicode small e unicode small t unicode small o unicode small n unicode end of text end unicode text end text end define
define tex of lemma same singleton as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital s unicode small i unicode small n unicode small g unicode small l unicode small e unicode small t unicode small o unicode small n unicode end of text end unicode text end text end define
define statement of lemma same singleton as system zf infer all metavar var x end metavar indeed all metavar var y end metavar indeed 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end define
define proof of lemma same singleton as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var x end metavar indeed all metavar var y end metavar indeed 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer lemma same pair 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 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 probans quote object var var t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote modus probans quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote modus ponens metavar var x end metavar zermelo is metavar var y end metavar modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair cut 1rule repetition modus ponens zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair conclude zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,