define pyk of lemma prime l three two a as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small p unicode small r unicode small i unicode small m unicode small e unicode space unicode small l 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
define tex of lemma prime l three two a as text unicode start of text unicode newline unicode capital l unicode three unicode period unicode two unicode left parenthesis unicode small a unicode right parenthesis unicode apostrophe unicode end of text end unicode text end text end define
define statement of lemma prime l three two a as system prime s infer all metavar var a end metavar indeed ( metavar var a end metavar peano is metavar var a end metavar ) end define
define proof of lemma prime l three two a as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var a end metavar indeed ( ( axiom prime s five conclude ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) ) cut ( ( axiom prime s one conclude ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( metavar var a end metavar peano is metavar var a end metavar ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( metavar var a end metavar peano is metavar var a end metavar ) ) ) ) modus ponens ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) ) conclude ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( metavar var a end metavar peano is metavar var a end metavar ) ) ) cut ( ( ( rule prime mp modus ponens ( ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) peano imply ( metavar var a end metavar peano is metavar var a end metavar ) ) ) modus ponens ( ( metavar var a end metavar peano plus peano zero ) peano is metavar var a end metavar ) ) conclude ( metavar var a end metavar peano is metavar var a end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,