Logiweb aspects of lemma er is symmetric in pyk

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The predefined "pyk" aspect

define pyk of lemma er is symmetric 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 e unicode small r unicode space unicode small i unicode small s unicode space unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small i unicode small c unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma er is symmetric as text unicode start of text unicode capital e unicode capital r unicode small i unicode small s unicode capital s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small i unicode small c unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma er is symmetric as system zf infer all metavar var r end metavar indeed not0 not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar imply not0 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 infer for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma er is symmetric as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var r end metavar indeed not0 not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar imply not0 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 infer 1rule repetition modus ponens not0 not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar imply not0 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 conclude not0 not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar imply not0 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 cut prop lemma first conjunct modus ponens not0 not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar imply not0 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 conclude not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar cut prop lemma second conjunct modus ponens not0 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 not0 for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar conclude for all objects object var var s end var indeed for all objects object var var t 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 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 s end var end pair end pair zermelo in metavar var r end metavar end quote state proof state cache var c end expand end define