define pyk of lemma prime a two star 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 a unicode space unicode small t unicode small w unicode small o unicode space unicode small s unicode small t unicode small a unicode small r unicode end of text end unicode text end text end define
define tex of lemma prime a two star as text unicode start of text unicode left brace unicode capital a unicode two unicode apostrophe unicode right brace unicode circumflex unicode asterisk unicode end of text end unicode text end text end define
define statement of lemma prime a two star as system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) infer ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) end define
define proof of lemma prime a two star as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) infer ( ( axiom prime a two conclude ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) ) cut ( ( ( rule prime mp modus ponens ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) conclude ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,