Logiweb aspects of lemma reflexivity in pyk

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The predefined "pyk" aspect

define pyk of lemma reflexivity 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 r unicode small e unicode small f unicode small l unicode small e unicode small x unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma reflexivity as text unicode start of text unicode capital r unicode small e unicode small f unicode small l unicode small e unicode small x unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma reflexivity as system zf infer all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var big set end metavar indeed quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set 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 big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar infer metavar var s end metavar zermelo in metavar var big set end metavar infer zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var s end metavar end pair end pair zermelo in metavar var r end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma reflexivity as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var big set end metavar indeed quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var big set 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 big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar infer metavar var s end metavar zermelo in metavar var big set end metavar infer lemma reflexivity0 modus probans quote object var var s end var end quote avoid zero quote metavar var r end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var big set 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 big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply metavar var s end metavar zermelo in metavar var big set end metavar imply zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var s end metavar end pair end pair zermelo in metavar var r end metavar cut prop lemma mp2 modus ponens for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar imply metavar var s end metavar zermelo in metavar var big set end metavar imply zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var s end metavar end pair end pair zermelo in metavar var r end metavar modus ponens for all objects object var var s end var indeed object var var s end var zermelo in metavar var big set end metavar imply zermelo pair zermelo pair object var var s end var comma object var var s end var end pair comma zermelo pair object var var s end var comma object var var s end var end pair end pair zermelo in metavar var r end metavar modus ponens metavar var s end metavar zermelo in metavar var big set end metavar conclude zermelo pair zermelo pair metavar var s end metavar comma metavar var s end metavar end pair comma zermelo pair metavar var s end metavar comma metavar var s end metavar end pair end pair zermelo in metavar var r end metavar end quote state proof state cache var c end expand end define