Logiweb aspects of mendelson lemma three two c in pyk

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The predefined "pyk" aspect

define pyk of mendelson lemma three two c 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 l unicode small e unicode small m unicode small m unicode small a 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 c unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson lemma three two c as text unicode start of text unicode capital l unicode capital e unicode capital m unicode capital m unicode capital a unicode space unicode three unicode period unicode two unicode left parenthesis unicode small c 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 lemma three two c as system prime s infer all metavar var t end metavar indeed all metavar var r end metavar indeed all metavar var s end metavar indeed ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s 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 lemma three two c 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 r end metavar indeed all metavar var s end metavar indeed ( ( axiom prime s one conclude ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( mendelson lemma three two b conclude ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) cut ( ( ( transitive imply modus ponens ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) modus ponens ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var r 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 t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s 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