Logiweb aspects of lemma inSeries helper in pyk

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The predefined "pyk" aspect

define pyk of lemma inSeries helper 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 i unicode small n unicode capital s unicode small e unicode small r unicode small i unicode small e unicode small s unicode space unicode small h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma inSeries helper as text unicode start of text unicode capital i unicode small n unicode capital s unicode small e unicode small r unicode small i unicode small e unicode small s unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma inSeries helper as system Q infer all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sy end metavar in0 metavar var fx end metavar imply not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar imply not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects metavar var m end metavar indeed not0 metavar var sy end metavar = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end define

The user defined "the proof aspect" aspect

define proof of lemma inSeries helper as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sy end metavar in0 metavar var fx end metavar infer not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar infer not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair infer prop lemma first conjunct modus ponens not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair conclude not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar cut prop lemma first conjunct modus ponens not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar conclude object var var op1 end var in0 N cut prop lemma second conjunct modus ponens not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair conclude metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair cut lemma sameMember modus ponens metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair modus ponens metavar var sy end metavar in0 metavar var fx end metavar conclude zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair in0 metavar var fx end metavar cut lemma memberOfSeries modus ponens object var var op1 end var in0 N modus ponens not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar conclude zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair in0 metavar var fx end metavar cut lemma eqReflexivity conclude object var var op1 end var = object var var op1 end var cut lemma uniqueMember modus ponens not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar modus ponens zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair in0 metavar var fx end metavar modus ponens zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair in0 metavar var fx end metavar modus ponens object var var op1 end var = object var var op1 end var conclude object var var op2 end var = [ metavar var fx end metavar ; object var var op1 end var ] cut lemma sameOrderedPair modus ponens object var var op1 end var = object var var op1 end var modus ponens object var var op2 end var = [ metavar var fx end metavar ; object var var op1 end var ] conclude zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair cut lemma eqTransitivity modus ponens metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair modus ponens zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair conclude metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair cut pred lemma intro exist at object var var op1 end var modus ponens metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma [ metavar var fx end metavar ; object var var op1 end var ] end pair end pair conclude not0 for all objects metavar var m end metavar indeed not0 metavar var sy end metavar = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair cut all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sy end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sy end metavar in0 metavar var fx end metavar infer not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar infer not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair infer not0 for all objects metavar var m end metavar indeed not0 metavar var sy end metavar = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair conclude metavar var sy end metavar in0 metavar var fx end metavar imply not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var fx end metavar imply not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 object var var r1 end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects object var var f1 end var indeed for all objects object var var f2 end var indeed for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair object var var f1 end var comma object var var f1 end var end pair comma zermelo pair object var var f1 end var comma object var var f2 end var end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair object var var f3 end var comma object var var f3 end var end pair comma zermelo pair object var var f3 end var comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply object var var f1 end var = object var var f3 end var imply object var var f2 end var = object var var f4 end var imply not0 for all objects object var var s1 end var indeed object var var s1 end var in0 N imply not0 for all objects object var var s2 end var indeed not0 zermelo pair zermelo pair object var var s1 end var comma object var var s1 end var end pair comma zermelo pair object var var s1 end var comma object var var s2 end var end pair end pair in0 metavar var fx end metavar imply not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 metavar var sx end metavar imply not0 metavar var sy end metavar = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair imply not0 for all objects metavar var m end metavar indeed not0 metavar var sy end metavar = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair end quote state proof state cache var c end expand end define