define pyk of lemma prime l three two f hyp 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 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 f unicode space unicode small h unicode small y unicode small p unicode end of text end unicode text end text end define
define tex of lemma prime l three two f hyp as text unicode start of text unicode left brace unicode capital l unicode three unicode period unicode two unicode left parenthesis unicode small f unicode right parenthesis unicode apostrophe unicode right brace unicode underscore unicode left brace unicode capital h unicode capital y unicode capital p unicode right brace unicode end of text end unicode text end text end define
define statement of lemma prime l three two f hyp as system prime s infer peano all var t peano var indeed ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) end define
define proof of lemma prime l three two f hyp as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( lemma one point eight conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) ) cut ( ( axiom prime s six conclude ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) cut ( ( axiom prime a one conclude ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) modus ponens ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( axiom prime s two conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( axiom prime a one conclude ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) ) modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) cut ( ( ( lemma prime a two star modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) conclude ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) ) modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( lemma prime l three two d conclude ( ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) cut ( ( ( hypothesize modus ponens ( ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) ) cut ( ( ( lemma prime a two star modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) ) conclude ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) ) modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) cut ( ( ( lemma prime a two star modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) conclude ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) peano imply ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( ( peano zero peano plus ( var t peano var peano succ ) ) peano is ( ( peano zero peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) cut ( ( rule prime gen modus ponens ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) conclude peano all var t peano var indeed ( ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) peano imply ( var t peano var peano succ peano is ( peano zero peano plus ( var t peano var peano succ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,