define pyk of lemma same union 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 u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define tex of lemma same union as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define statement of lemma same union 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 metavar var x end metavar zermelo is metavar var y end metavar infer union metavar var x end metavar end union zermelo is union metavar var y end metavar end union end define
define proof of lemma same union 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 metavar var x end metavar zermelo is metavar var y end metavar infer lemma union subset 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 conclude metavar var x end metavar zermelo is metavar var y end metavar imply object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union cut 1rule mp modus ponens metavar var x end metavar zermelo is metavar var y end metavar imply object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union cut lemma =symmetry 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 x end metavar zermelo is metavar var y end metavar conclude metavar var y end metavar zermelo is metavar var x end metavar cut lemma union subset 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 conclude metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union cut 1rule mp modus ponens metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union modus ponens metavar var y end metavar zermelo is metavar var x end metavar conclude object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union cut lemma set equality suff condition modus ponens object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union modus ponens object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union conclude union metavar var x end metavar end union zermelo is union metavar var y end metavar end union end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,