define pyk of equal symmetry as text unicode start of text unicode small e unicode small q unicode small u unicode small a unicode small l unicode space unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define
define tex of equal symmetry as text unicode start of text unicode capital e unicode small q unicode small u unicode small a unicode small l unicode capital s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define
define statement of equal symmetry as system prime s infer all metavar var t end metavar indeed all metavar var r end metavar indeed ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) end define
define proof of equal symmetry as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var t end metavar indeed all metavar var r end metavar indeed ( ( axiom prime s one conclude ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) cut ( ( ( permute antecedents modus ponens ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) conclude ( ( metavar var t end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) cut ( ( equal reflexivity conclude ( metavar var t end metavar peano is metavar var t end metavar ) ) cut ( ( ( rule prime mp modus ponens ( ( metavar var t end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) modus ponens ( metavar var t end metavar peano is metavar var t end metavar ) ) conclude ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,