Logiweb aspects of lemma transitivity0 in pyk

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The predefined "pyk" aspect

define pyk of lemma transitivity0 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 t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode zero unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma transitivity0 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 t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t 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 transitivity0 as system zf infer all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var t end metavar indeed all metavar var u 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 quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u 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 for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u 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 metavar var t end metavar zermelo in metavar var big set end metavar imply metavar var u 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 t end metavar end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair metavar var t end metavar comma metavar var t end metavar end pair comma zermelo pair metavar var t end metavar comma metavar var u end metavar end pair end pair zermelo in metavar var r 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 u 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 transitivity0 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 big set end metavar indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u end var end pair end pair zermelo in metavar var r end metavar infer 1rule repetition modus ponens object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u end var end pair end pair zermelo in metavar var r end metavar conclude object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u end var end pair end pair zermelo in metavar var r end metavar cut all metavar var r end metavar indeed all metavar var s end metavar indeed all metavar var t end metavar indeed all metavar var u end metavar indeed all metavar var big set end metavar indeed 1rule deduction modus ponens all metavar var r end metavar indeed all metavar var big set end metavar indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u end var end pair end pair zermelo in metavar var r end metavar infer object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u end var end pair end pair zermelo in metavar var r end metavar conclude 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 quote object var var t end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var big set end metavar end quote endorse quote object var var u end var end quote avoid zero quote metavar var r end metavar end quote endorse quote object var var u 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 for all objects object var var t end var indeed for all objects object var var u end var indeed object var var s end var zermelo in metavar var big set end metavar imply object var var t end var zermelo in metavar var big set end metavar imply object var var u 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 t end var end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair object var var t end var comma object var var t end var end pair comma zermelo pair object var var t end var comma object var var u end var end pair end pair zermelo in metavar var r 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 u 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 metavar var t end metavar zermelo in metavar var big set end metavar imply metavar var u 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 t end metavar end pair end pair zermelo in metavar var r end metavar imply zermelo pair zermelo pair metavar var t end metavar comma metavar var t end metavar end pair comma zermelo pair metavar var t end metavar comma metavar var u end metavar end pair end pair zermelo in metavar var r 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 u 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