define pyk of lemma tautology two 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 t unicode small a unicode small u unicode small t unicode small o unicode small l unicode small o unicode small g unicode small y unicode space unicode small t unicode small w unicode small o unicode end of text end unicode text end text end define
define tex of lemma tautology two as text unicode start of text unicode capital t unicode small a unicode small u unicode small t unicode space unicode two unicode end of text end unicode text end text end define
define statement of lemma tautology two as system prime s infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed ( ( metavar var d end metavar peano imply metavar var e end metavar ) infer ( ( metavar var e end metavar peano imply metavar var f end metavar ) infer ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) end define
define proof of lemma tautology two as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed ( ( metavar var d end metavar peano imply metavar var e end metavar ) infer ( ( metavar var e end metavar peano imply metavar var f end metavar ) infer ( ( axiom prime a one conclude ( ( metavar var e end metavar peano imply metavar var f end metavar ) peano imply ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( metavar var e end metavar peano imply metavar var f end metavar ) peano imply ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) ) modus ponens ( metavar var e end metavar peano imply metavar var f end metavar ) ) conclude ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) cut ( ( axiom prime a two conclude ( ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) peano imply ( ( metavar var d end metavar peano imply metavar var e end metavar ) peano imply ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) ) cut ( ( ( ( lemma mp twice modus ponens ( ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) peano imply ( ( metavar var d end metavar peano imply metavar var e end metavar ) peano imply ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) ) modus ponens ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) modus ponens ( metavar var d end metavar peano imply metavar var e end metavar ) ) conclude ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,