define pyk of prop three two g as text unicode start of text unicode small p unicode small r unicode small o unicode small p 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 g unicode end of text end unicode text end text end define
define tex of prop three two g as text unicode start of text unicode newline unicode capital p unicode small r unicode small o unicode small p unicode backslash unicode space unicode three unicode period unicode two unicode small g unicode end of text end unicode text end text end define
define statement of prop three two g as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( metavar var a end metavar suc plus metavar var b end metavar ) equal ( ( metavar var a end metavar plus metavar var b end metavar ) suc ) ) end define
define proof of prop three two g as lambda var c dot lambda var x dot proof expand quote system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( ( prop three two g one conclude ( ( object var var x end var suc plus zero ) equal ( ( object var var x end var plus zero ) suc ) ) ) cut ( ( prop three two g two conclude ( ( ( object var var x end var suc plus object var var y end var ) equal ( ( object var var x end var plus object var var y end var ) suc ) ) imply ( ( object var var x end var suc plus ( object var var y end var suc ) ) equal ( ( object var var x end var plus ( object var var y end var suc ) ) suc ) ) ) ) cut ( ( ( ( axiom s nine at object var var y end var ) modus ponens ( ( object var var x end var suc plus zero ) equal ( ( object var var x end var plus zero ) suc ) ) ) modus ponens ( ( ( object var var x end var suc plus object var var y end var ) equal ( ( object var var x end var plus object var var y end var ) suc ) ) imply ( ( object var var x end var suc plus ( object var var y end var suc ) ) equal ( ( object var var x end var plus ( object var var y end var suc ) ) suc ) ) ) ) conclude ( ( object var var x end var suc plus object var var y end var ) equal ( ( object var var x end var plus object var var y end var ) suc ) ) ) ) ) cut ( ( deduction modus ponens ( ( object var var x end var suc plus object var var y end var ) equal ( ( object var var x end var plus object var var y end var ) suc ) ) ) conclude ( ( metavar var a end metavar suc plus metavar var b end metavar ) equal ( ( metavar var a end metavar plus metavar var b end metavar ) suc ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417 by Klaus Grue,