Logiweb aspects of lemma prime l three two h in pyk

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The predefined "pyk" aspect

define pyk of lemma prime l three two h as text unicode start of text unicode space 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 l 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 h unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma prime l three two h as text unicode start of text unicode capital m unicode three unicode period unicode two unicode left parenthesis unicode small h 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 prime l three two h as system prime s infer peano all var x peano var indeed peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma prime l three two h as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s nine conclude ( ( ( var x peano var peano plus peano zero ) peano is ( peano zero peano plus ( var x peano var ) ) ) peano imply ( ( peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) peano imply peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) ) ) cut ( ( lemma prime l three two h one conclude ( ( var x peano var peano plus peano zero ) peano is ( peano zero peano plus ( var x peano var ) ) ) ) cut ( ( lemma prime l three two h two conclude ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) cut ( ( ( rule prime gen modus ponens ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) conclude peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var x peano var peano plus peano zero ) peano is ( peano zero peano plus ( var x peano var ) ) ) peano imply ( ( peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) peano imply peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) ) ) modus ponens ( ( var x peano var peano plus peano zero ) peano is ( peano zero peano plus ( var x peano var ) ) ) ) conclude ( ( peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) peano imply peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) peano imply peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) ) modus ponens peano all var y peano var indeed ( ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( var y peano var peano succ peano plus ( var x peano var ) ) ) ) ) conclude peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) cut ( ( rule prime gen modus ponens peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) conclude peano all var x peano var indeed peano all var y peano var indeed ( ( var x peano var peano plus ( var y peano var ) ) peano is ( var y peano var peano plus ( var x peano var ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define