Logiweb aspects of lemma same separation in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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