Logiweb aspects of mendelson proposition three two a in pyk

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The predefined "pyk" aspect

define pyk of mendelson proposition three two a 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 a unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson proposition three two a 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 a 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 a as system prime s infer all metavar var t end metavar indeed ( metavar var t end metavar peano is metavar var t end metavar ) end define

The user defined "the proof aspect" aspect

define proof of mendelson proposition three two a as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var t end metavar indeed ( ( axiom prime s five conclude ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) ) cut ( ( axiom prime s one conclude ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( metavar var t end metavar peano is metavar var t end metavar ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( metavar var t end metavar peano is metavar var t end metavar ) ) ) ) modus ponens ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) ) conclude ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( metavar var t end metavar peano is metavar var t end metavar ) ) ) cut ( ( ( rule prime mp modus ponens ( ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) peano imply ( metavar var t end metavar peano is metavar var t end metavar ) ) ) modus ponens ( ( metavar var t end metavar peano plus peano zero ) peano is metavar var t end metavar ) ) conclude ( metavar var t end metavar peano is metavar var t end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define