Logiweb aspects of mendelson proposition three two h g ii in pyk

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The predefined "pyk" aspect

define pyk of mendelson proposition three two h 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 h 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 h 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 h unicode right parenthesis unicode underscore unicode left brace unicode left parenthesis unicode small g unicode right parenthesis unicode left parenthesis unicode small i unicode small i unicode right parenthesis unicode right brace 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 h 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 ) ) ) infer ( ( var y peano var peano succ peano plus ( var x peano var ) ) peano is ( ( var y peano var peano plus ( var x peano var ) ) peano succ ) ) ) end define

The user defined "the proof aspect" aspect

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