Logiweb aspects of lemma prime three two g in pyk

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The predefined "pyk" aspect

define pyk of lemma prime three two g 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma prime three two g 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 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 as system prime s infer 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 ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma prime three two g as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s five conclude ( ( var t peano var peano succ peano plus peano zero ) peano is ( var t peano var peano succ ) ) ) cut ( ( axiom prime s five conclude ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) ) cut ( ( axiom prime s two conclude ( ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) peano imply ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) peano imply ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) ) ) modus ponens ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) ) conclude ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) ) cut ( ( lemma prime three two d conclude ( ( ( var t peano var peano succ peano plus peano zero ) peano is ( var t peano var peano succ ) ) peano imply ( ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) peano imply ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) ) ) ) cut ( ( ( ( ( lemma mp twice modus ponens ( ( ( var t peano var peano succ peano plus peano zero ) peano is ( var t peano var peano succ ) ) peano imply ( ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) peano imply ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) ) ) ) modus ponens ( ( var t peano var peano succ peano plus peano zero ) peano is ( var t peano var peano succ ) ) ) modus ponens ( ( var t peano var peano plus peano zero ) peano succ peano is ( var t peano var peano succ ) ) ) conclude ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) ) cut ( ( axiom prime s six conclude ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) cut ( ( ( lemma weaken modus ponens ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) ) cut ( ( axiom prime s two conclude ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( lemma prime three two c conclude ( ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) ) modus ponens ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( ( ( lemma tautology two modus ponens ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) conclude ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( axiom prime s six conclude ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) cut ( ( axiom prime s two conclude ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) cut ( ( lemma prime three two d conclude ( ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( ( lemma tautology two modus ponens ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) conclude ( ( ( 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 ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( lemma tautology one modus ponens ( ( ( 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 ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) peano imply ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) modus ponens ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) conclude ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) cut ( ( ( rule prime gen modus ponens ( ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) conclude 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) cut ( ( axiom prime s nine conclude ( ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) peano imply ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) peano imply 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 ( ( ( ( ( lemma mp twice modus ponens ( ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) peano imply ( ( 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) peano imply 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 ) ) ) ) ) modus ponens ( ( var t peano var peano succ peano plus peano zero ) peano is ( ( var t peano var peano plus peano zero ) peano succ ) ) ) modus ponens 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 ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) conclude 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 ( ( rule prime gen modus ponens 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 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define