define pyk of lemma empty 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 e unicode small m unicode small p unicode small t unicode small y 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 empty set is subset as text unicode start of text unicode backslash unicode capital o unicode left brace unicode right brace unicode small i unicode small s unicode capital 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 statement of lemma empty set is subset as system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed metavar var s end metavar zermelo in zermelo empty set imply metavar var s end metavar zermelo in metavar var x end metavar end define
define proof of lemma empty 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 metavar var s end metavar zermelo in zermelo empty set infer axiom empty set conclude not0 metavar var s end metavar zermelo in zermelo empty set cut prop lemma from contradiction modus ponens metavar var s end metavar zermelo in zermelo empty set modus ponens not0 metavar var s end metavar zermelo in zermelo empty set conclude metavar var s end metavar zermelo in metavar var x end metavar cut all metavar var s end metavar indeed all metavar var x end metavar indeed 1rule deduction modus ponens all metavar var s end metavar indeed all metavar var x end metavar indeed metavar var s end metavar zermelo in zermelo empty set infer metavar var s end metavar zermelo in metavar var x end metavar conclude metavar var s end metavar zermelo in zermelo empty set imply metavar var s end metavar 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,