Logiweb aspects of mendelson three two d in pyk

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The predefined "pyk" aspect

define pyk of mendelson three two d 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 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 d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson three two d as text unicode start of text 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 three unicode period unicode two unicode left parenthesis unicode small d 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 three two d as system prime s infer all metavar var t end metavar indeed all metavar var u end metavar indeed all metavar var s end metavar indeed ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of mendelson three two d as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var t end metavar indeed all metavar var u end metavar indeed all metavar var s end metavar indeed ( ( equal transitivity conclude ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var u end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( ( permute antecedents modus ponens ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var u end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) conclude ( ( metavar var u end metavar peano is metavar var s end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( equal symmetry conclude ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( metavar var u end metavar peano is metavar var s end metavar ) ) ) cut ( ( ( ( imply transitivity modus ponens ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( metavar var u end metavar peano is metavar var s end metavar ) ) ) modus ponens ( ( metavar var u end metavar peano is metavar var s end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) conclude ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( permute antecedents modus ponens ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) conclude ( ( metavar var t end metavar peano is metavar var u end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var u end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define