Logiweb aspects of lemma =transitivity in pyk

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The predefined "pyk" aspect

define pyk of lemma =transitivity 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma =transitivity as text unicode start of text 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 =transitivity as system zf infer 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 x end metavar zermelo is metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma =transitivity as lambda var c dot lambda var x dot proof expand quote system zf infer 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 lemma =transitivity0 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 probans quote object var var s end var end quote avoid zero quote metavar var z end metavar end quote conclude 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 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar cut prop lemma mp2 modus ponens 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 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar modus ponens metavar var x end metavar zermelo is metavar var y end metavar modus ponens metavar var y end metavar zermelo is metavar var z end metavar conclude object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar 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 lemma =symmetry 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 conclude metavar var z end metavar zermelo is metavar var y end metavar cut lemma =transitivity0 modus probans quote object var var s end var end quote avoid zero quote metavar var z 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 probans quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote conclude metavar var z end metavar zermelo is metavar var y end metavar imply metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar imply object var var s end var zermelo in metavar var x end metavar cut prop lemma mp2 modus ponens metavar var z end metavar zermelo is metavar var y end metavar imply metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar imply object var var s end var zermelo in metavar var x end metavar modus ponens metavar var z end metavar zermelo is metavar var y end metavar modus ponens metavar var y end metavar zermelo is metavar var x end metavar conclude object var var s end var zermelo in metavar var z end metavar imply object var var s end var zermelo in metavar var x end metavar cut lemma set equality suff condition modus ponens object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var z end metavar modus ponens object var var s end var zermelo in metavar var z end metavar imply object var var s end var zermelo in metavar var x end metavar conclude metavar var x end metavar zermelo is metavar var z end metavar end quote state proof state cache var c end expand end define