define pyk of axiom s nine as text unicode start of text unicode small a unicode small x unicode small i unicode small o unicode small m unicode space unicode small s unicode space unicode small n unicode small i unicode small n unicode small e unicode end of text end unicode text end text end define
define tex of axiom s nine as text unicode start of text unicode newline unicode capital s unicode nine unicode end of text end unicode text end text end define
define statement of axiom s nine as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var x end metavar indeed ( peano sub metavar var b end metavar is metavar var a end metavar where metavar var x end metavar is peano zero end sub endorse ( peano sub metavar var c end metavar is metavar var a end metavar where metavar var x end metavar is metavar var x end metavar peano succ end sub endorse ( metavar var b end metavar peano imply ( ( peano all metavar var x end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply peano all metavar var x end metavar indeed metavar var a end metavar ) ) ) ) end define
define proof of axiom s nine as rule tactic end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,