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 equal sign 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 backslash unicode exclamation mark unicode left brace unicode right brace unicode equal sign unicode backslash unicode exclamation mark unicode left brace unicode right brace 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 s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z 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 quote object var var s end var end quote avoid zero quote metavar var z end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var y end metavar zermelo is metavar var z end metavar imply metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var z 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 s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z 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 quote object var var s end var end quote avoid zero quote metavar var z end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var y end metavar zermelo is metavar var z end metavar infer metavar var s end metavar zermelo in metavar var x end metavar infer lemma set equality nec condition 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 modus ponens metavar var s end metavar zermelo in metavar var x end metavar conclude metavar var s end metavar zermelo in metavar var y end metavar cut lemma set equality nec condition 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 z end metavar end quote modus ponens metavar var y end metavar zermelo is metavar var z end metavar modus ponens metavar var s end metavar zermelo in metavar var y end metavar conclude metavar var s end metavar zermelo in metavar var z end metavar cut all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 1rule deduction modus ponens all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z 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 quote object var var s end var end quote avoid zero quote metavar var z end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var y end metavar zermelo is metavar var z end metavar infer metavar var s end metavar zermelo in metavar var x end metavar infer metavar var s end metavar zermelo in metavar var z end metavar conclude 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 quote object var var s end var end quote avoid zero quote metavar var z end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var y end metavar zermelo is metavar var z end metavar imply metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var z end metavar end quote state proof state cache var c end expand end define