define pyk of lemma power set is 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 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 zero unicode end of text end unicode text end text end define
define tex of lemma power set is 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 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 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 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 for all objects object var var s end var indeed object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar end define
define proof of lemma power set is subset0 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 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar infer 1rule repetition modus ponens object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar conclude object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar cut all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar infer object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar conclude 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 for all objects object var var s end var indeed object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,