Logiweb aspects of lemma uniqueMember in pyk

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The predefined "pyk" aspect

define pyk of lemma uniqueMember 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 u unicode small n unicode small i unicode small q unicode small u unicode small e unicode capital m unicode small e unicode small m unicode small b 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 uniqueMember as text unicode start of text unicode capital u unicode small n unicode small i unicode small q unicode small u unicode small e unicode capital m unicode small e unicode small m unicode small b 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 uniqueMember as system Q infer all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed all metavar var sz end metavar indeed 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 sz 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 zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar infer zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair in0 metavar var fx end metavar infer metavar var sx end metavar = metavar var sy end metavar infer metavar var sx1 end metavar = metavar var sy1 end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma uniqueMember as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed all metavar var sz end metavar indeed 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 sz 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 zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar infer zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair in0 metavar var fx end metavar infer metavar var sx end metavar = metavar var sy end metavar infer 1rule repetition 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 sz 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 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 sz 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 cut prop lemma first conjunct 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 sz 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 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 sz 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 cut 1rule repetition modus ponens 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 sz 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 conclude 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 sz 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 cut prop lemma second conjunct modus ponens 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 sz 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 conclude 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 cut lemma a4 at metavar var sx end metavar modus ponens 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 conclude 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 metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar 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 metavar var sx end metavar = object var var f3 end var imply object var var f2 end var = object var var f4 end var cut lemma a4 at metavar var sx1 end metavar modus ponens 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 metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar 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 metavar var sx end metavar = object var var f3 end var imply object var var f2 end var = object var var f4 end var conclude for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar 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 metavar var sx end metavar = object var var f3 end var imply metavar var sx1 end metavar = object var var f4 end var cut lemma a4 at metavar var sy end metavar modus ponens for all objects object var var f3 end var indeed for all objects object var var f4 end var indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar 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 metavar var sx end metavar = object var var f3 end var imply metavar var sx1 end metavar = object var var f4 end var conclude for all objects object var var f4 end var indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply metavar var sx end metavar = metavar var sy end metavar imply metavar var sx1 end metavar = object var var f4 end var cut lemma a4 at metavar var sy1 end metavar modus ponens for all objects object var var f4 end var indeed zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma object var var f4 end var end pair end pair in0 metavar var fx end metavar imply metavar var sx end metavar = metavar var sy end metavar imply metavar var sx1 end metavar = object var var f4 end var conclude zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair in0 metavar var fx end metavar imply metavar var sx end metavar = metavar var sy end metavar imply metavar var sx1 end metavar = metavar var sy1 end metavar cut prop lemma mp3 modus ponens zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar imply zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair in0 metavar var fx end metavar imply metavar var sx end metavar = metavar var sy end metavar imply metavar var sx1 end metavar = metavar var sy1 end metavar modus ponens zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sx1 end metavar end pair end pair in0 metavar var fx end metavar modus ponens zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair in0 metavar var fx end metavar modus ponens metavar var sx end metavar = metavar var sy end metavar conclude metavar var sx1 end metavar = metavar var sy1 end metavar end quote state proof state cache var c end expand end define