define pyk of lemma equivalence nec condition 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 e unicode small q unicode small u unicode small i unicode small v unicode small a unicode small l unicode small e unicode small n unicode small c unicode small e unicode space unicode small n unicode small e unicode small c 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 end of text end unicode text end text end define
define tex of lemma equivalence nec condition as text unicode start of text unicode capital e unicode small q unicode capital n unicode small e unicode small c unicode small e unicode small s unicode small s unicode small a unicode small r unicode small y unicode end of text end unicode text end text end define
define statement of lemma equivalence nec condition as system zf infer all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var big set end metavar end quote endorse metavar var x end metavar zermelo in metavar var big set end metavar infer metavar var y end metavar zermelo in metavar var big set end metavar infer not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar infer zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar imply the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set zermelo is the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar end set end define
define proof of lemma equivalence nec condition as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var r end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var big set end metavar indeed quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var big set end metavar end quote endorse metavar var x end metavar zermelo in metavar var big set end metavar infer metavar var y end metavar zermelo in metavar var big set end metavar infer not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar infer lemma equivalence nec condition0 modus probans quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var big set end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote modus probans quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote modus probans quote object var var u end var end quote avoid zero quote metavar var big set end metavar end quote conclude metavar var x end metavar zermelo in metavar var big set end metavar imply metavar var y end metavar zermelo in metavar var big set end metavar imply not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar imply the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set zermelo is the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar end set cut prop lemma mp3 modus ponens metavar var x end metavar zermelo in metavar var big set end metavar imply metavar var y end metavar zermelo in metavar var big set end metavar imply not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar imply the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set zermelo is the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar end set modus ponens metavar var x end metavar zermelo in metavar var big set end metavar modus ponens metavar var y end metavar zermelo in metavar var big set end metavar modus ponens not0 not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply not0 for all objects object var var s end var indeed for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var u end var end pair end pair zermelo in metavar var r end metavar conclude zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar imply the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var x end metavar end pair end pair zermelo in metavar var r end metavar end set zermelo is the set of ph in metavar var big set end metavar such that zermelo pair zermelo pair placeholder-var var a end var comma placeholder-var var a end var end pair comma zermelo pair placeholder-var var a end var comma metavar var y end metavar end pair end pair zermelo in metavar var r end metavar end set end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,