Logiweb aspects of prop three two h in pyk

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The predefined "pyk" aspect

define pyk of prop three two h 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three two h 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 space unicode backslash unicode semicolon unicode space unicode three unicode period unicode two unicode left parenthesis unicode small h 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 prop three two h as system prime s infer peano all var t peano var indeed 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 ) ) ) end define

The user defined "the proof aspect" aspect

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