define pyk of lemma same separation 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 s unicode small e unicode small p unicode small a unicode small r unicode small a 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 same separation as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital s unicode small e unicode small p unicode small a unicode small r unicode small a unicode small t 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 separation as system zf infer all metavar var a end metavar indeed all metavar var b 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 metavar var x end metavar zermelo is metavar var y end metavar infer not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar infer the set of ph in metavar var x end metavar such that metavar var a end metavar end set zermelo is the set of ph in metavar var y end metavar such that metavar var b end metavar end set end define
define proof of lemma same separation as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var a end metavar indeed all metavar var b 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 metavar var x end metavar zermelo is metavar var y end metavar infer not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar infer lemma separation 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 not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set cut prop lemma mp2 modus ponens metavar var x end metavar zermelo is metavar var y end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set modus ponens metavar var x end metavar zermelo is metavar var y end metavar modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar conclude object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set 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 prop lemma iff commutativity modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar conclude not0 metavar var b end metavar imply metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar cut lemma separation 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 not0 metavar var b end metavar imply metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set cut prop lemma mp2 modus ponens metavar var y end metavar zermelo is metavar var x end metavar imply not0 metavar var b end metavar imply metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set modus ponens metavar var y end metavar zermelo is metavar var x end metavar modus ponens not0 metavar var b end metavar imply metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar conclude object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set cut lemma set equality suff condition modus ponens object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set modus ponens object var var s end var zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set imply object var var s end var zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set conclude the set of ph in metavar var x end metavar such that metavar var a end metavar end set zermelo is the set of ph in metavar var y end metavar such that metavar var b 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,