Logiweb aspects of lemma prime three two g rev in pyk

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The predefined "pyk" aspect

define pyk of lemma prime three two g rev 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 p unicode small r unicode small i unicode small m unicode small e unicode space unicode small t unicode small h unicode small r unicode small e unicode small e unicode space unicode small t unicode small w unicode small o unicode space unicode small g unicode space unicode small r unicode small e unicode small v unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma prime three two g rev as text unicode start of text unicode capital l unicode three unicode period unicode two unicode space unicode left parenthesis unicode small g unicode right parenthesis unicode apostrophe unicode space unicode capital i unicode capital i unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma prime three two g rev as system prime s infer ( peano sub quote peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) end quote is quote peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) end quote where quote var t peano var end quote is quote var s peano var end quote end sub endorse ( peano sub quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) end quote where quote var r peano var end quote is quote var t peano var end quote end sub endorse ( peano sub quote ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote where quote var s peano var end quote is quote var r peano var end quote end sub endorse ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma prime three two g rev as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( lemma prime three two g conclude peano all var t peano var indeed peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) cut ( peano sub quote peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) end quote is quote peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) end quote where quote var t peano var end quote is quote var s peano var end quote end sub endorse ( ( ( axiom prime a four modus probans peano sub quote peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) end quote is quote peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) end quote where quote var t peano var end quote is quote var s peano var end quote end sub ) conclude ( ( peano all var t peano var indeed peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) peano imply peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( peano all var t peano var indeed peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) peano imply peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) ) modus ponens peano all var t peano var indeed peano all var r peano var indeed ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) conclude peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) cut ( peano sub quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) end quote where quote var r peano var end quote is quote var t peano var end quote end sub endorse ( ( ( axiom prime a four modus probans peano sub quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) end quote where quote var r peano var end quote is quote var t peano var end quote end sub ) conclude ( ( peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) peano imply ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) peano imply ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) modus ponens peano all var r peano var indeed ( ( var s peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var s peano var peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) cut ( ( ( rule prime gen modus ponens ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) conclude peano all var s peano var indeed ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) cut ( peano sub quote ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote where quote var s peano var end quote is quote var r peano var end quote end sub endorse ( ( ( axiom prime a four modus probans peano sub quote ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) end quote is quote ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) end quote where quote var s peano var end quote is quote var r peano var end quote end sub ) conclude ( ( peano all var s peano var indeed ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( ( rule prime mp modus ponens ( ( peano all var s peano var indeed ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) modus ponens peano all var s peano var indeed ( ( var s peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var s peano var peano plus ( var t peano var ) ) peano succ ) ) ) conclude ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define