define pyk of lemma power set is subset 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 o unicode small w unicode small e unicode small r unicode space unicode small s unicode small e unicode small t unicode space unicode small i unicode small s unicode space unicode small 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 tex of lemma power set is subset as text unicode start of text unicode capital p unicode small o unicode small w unicode small e unicode small r unicode capital i unicode small s unicode capital s unicode small u unicode small b unicode end of text end unicode text end text end define
define statement of lemma power set is subset as system zf infer all metavar var s end metavar indeed all metavar var x 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 metavar var s end metavar zermelo in power metavar var x end metavar end power infer object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar end define
define proof of lemma power set is subset 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 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 metavar var s end metavar zermelo in power metavar var x end metavar end power infer axiom power definition conclude not0 metavar var s end metavar zermelo in power metavar var x end metavar end power imply for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in power metavar var x end metavar end power cut prop lemma iff second modus ponens not0 metavar var s end metavar zermelo in power metavar var x end metavar end power imply for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in power metavar var x end metavar end power modus ponens metavar var s end metavar zermelo in power metavar var x end metavar end power conclude for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar cut lemma power set is subset0 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 conclude for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar cut 1rule mp modus ponens for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar modus ponens for all objects object var var s end var indeed object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar conclude object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar cut 1rule repetition modus ponens object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar conclude object var var s end var zermelo in metavar var s end metavar imply object var var s end var zermelo in metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,