Logiweb aspects of lemma subLessRight(R) in pyk

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The predefined "pyk" aspect

define pyk of lemma subLessRight(R) 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 capital l unicode small e unicode small s unicode small s unicode capital r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma subLessRight(R) as text unicode start of text unicode capital s unicode small u unicode small b unicode capital l unicode small e unicode small s unicode small s unicode capital r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma subLessRight(R) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var infer not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var end define

The user defined "the proof aspect" aspect

define proof of lemma subLessRight(R) 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 fy end metavar indeed all metavar var fz end metavar indeed the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set infer not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var infer 1rule from== modus ponens the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set = the set of ph in power the set of ph in power the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that 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 Q imply not0 placeholder-var var a 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 set end power such that not0 not0 for all objects object var var r1 end var indeed object var var r1 end var in0 placeholder-var var f end var 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 Q 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 placeholder-var var f end var 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 placeholder-var var f end var 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 placeholder-var var f end var end set end power such that for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fy end metavar ; object var var m end var ] + - [ placeholder-var var d end var ; object var var m end var ] | = object var var ep end var end set conclude for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var cut 1rule repetition modus ponens not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var conclude not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var cut lemma subLessRight(F) modus ponens for all objects object var var ep end var indeed not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply object var var n end var <= object var var m end var imply not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | <= object var var ep end var imply not0 not0 | [ metavar var fx end metavar ; object var var m end var ] + - [ metavar var fy end metavar ; object var var m end var ] | = object var var ep end var modus ponens not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fx end metavar ; object var var m end var ] + - object var var ep end var conclude not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var cut 1rule repetition modus ponens not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var conclude not0 for all objects object var var ep end var indeed not0 not0 for all objects object var var n end var indeed not0 for all objects object var var m end var indeed not0 not0 0 <= object var var ep end var imply not0 not0 0 = object var var ep end var imply not0 object var var n end var <= object var var m end var imply [ metavar var fz end metavar ; object var var m end var ] <= [ metavar var fy end metavar ; object var var m end var ] + - object var var ep end var end quote state proof state cache var c end expand end define