Logiweb aspects of mendelson proposition three two g ii in pyk

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The predefined "pyk" aspect

define pyk of mendelson proposition three two g ii as text unicode start of text unicode small m unicode small e unicode small n unicode small d unicode small e unicode small l unicode small s unicode small o unicode small n unicode space unicode small p unicode small r unicode small o unicode small p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small o unicode small n 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 i unicode small i unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson proposition three two g ii as text unicode start of text unicode capital m unicode backslash unicode space unicode capital p unicode small r unicode small o unicode small p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small o unicode small n unicode backslash unicode space unicode three unicode period unicode two unicode left parenthesis unicode small g unicode right parenthesis unicode backslash unicode space unicode left parenthesis unicode small i unicode small i unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of mendelson proposition three two g ii as system prime s infer peano all var y peano var indeed ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) end define

The user defined "the proof aspect" aspect

define proof of mendelson proposition three two g ii as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s six conclude ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) ) cut ( ( axiom prime s two conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) cut ( ( mendelson proposition three two c conclude ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) cut ( ( ( mendelson tautology a modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) cut ( ( ( ( mendelson tautology b modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) cut ( ( ( mendelson tautology a modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) ) modus ponens ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano succ ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) cut ( ( axiom prime s six conclude ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) ) cut ( ( axiom prime s two conclude ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) cut ( ( mendelson proposition three two d conclude ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( ( mendelson tautology b modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( mendelson tautology a modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) conclude ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) ) conclude ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) peano imply ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) modus ponens ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ peano succ ) ) ) conclude ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) cut ( ( rule prime gen modus ponens ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) conclude peano all var y peano var indeed ( ( ( var x peano var peano succ peano plus ( var y peano var ) ) peano is ( ( var x peano var peano plus ( var y peano var ) ) peano succ ) ) peano imply ( ( var x peano var peano succ peano plus ( var y peano var peano succ ) ) peano is ( ( var x peano var peano plus ( var y peano var peano succ ) ) peano succ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define