Logiweb aspects of prop three two h ind in pyk

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The predefined "pyk" aspect

define pyk of prop three two h ind as text unicode start of text unicode small p unicode small r unicode small o unicode small p 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 i unicode small n unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three two h ind as text unicode start of text unicode backslash unicode small m unicode small a unicode small t unicode small h unicode small i unicode small t unicode left brace unicode capital 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 backslash unicode semicolon unicode three unicode period unicode two unicode left parenthesis unicode small h unicode right parenthesis unicode underscore unicode small n unicode right brace unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop three two h ind as system prime s infer peano all var r peano var indeed ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of prop three two h ind as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s six hyp conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( 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 ( ( prop three two g rt hyp conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( axiom prime s two conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( ( ( prop three two c hyp rule modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( 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 ) ) ) ) modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( ( ( prop three two d hyp rule modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) ) cut ( ( rule prime gen modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) ) conclude peano all var r peano var indeed ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define