Logiweb aspects of lemma subsetIsRelation in pyk

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The predefined "pyk" aspect

define pyk of lemma subsetIsRelation 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 s unicode small u unicode small b unicode small s unicode small e unicode small t unicode capital i unicode small s unicode capital r unicode small e unicode small l unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma subsetIsRelation as text unicode start of text unicode capital s unicode small u unicode small b unicode small s unicode small e unicode small t unicode capital i unicode small s unicode capital r unicode small e unicode small l unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma subsetIsRelation as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 infer for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar infer for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 end define

The user defined "the proof aspect" aspect

define proof of lemma subsetIsRelation as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 infer for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar infer object var var r1 end var in0 metavar var sy end metavar infer 1rule repetition modus ponens for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 conclude for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut lemma a4 at object var var r1 end var modus ponens for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 conclude object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut lemma fromSubset modus ponens for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar modus ponens object var var r1 end var in0 metavar var sy end metavar conclude object var var r1 end var in0 metavar var sx end metavar cut 1rule mp modus ponens object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 modus ponens object var var r1 end var in0 metavar var sx end metavar conclude 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed 1rule deduction modus ponens all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 infer for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar infer object var var r1 end var in0 metavar var sy end metavar infer 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 conclude for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar imply object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 infer for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar infer prop lemma mp2 modus ponens for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar imply object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 modus ponens for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sx 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 modus ponens for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var sy end metavar imply object var var s1 end var in0 metavar var sx end metavar conclude object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut 1rule gen modus ponens object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 conclude for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 cut 1rule repetition modus ponens for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 conclude for all objects object var var r1 end var indeed object var var r1 end var in0 metavar var sy 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 metavar var sz end metavar imply not0 object var var op2 end var in0 metavar var su 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 end quote state proof state cache var c end expand end define