Logiweb aspects of equal symmetry rule in pyk

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The predefined "pyk" aspect

define pyk of equal symmetry rule 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 space unicode small r unicode small u unicode small l unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of equal symmetry rule 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 capital r unicode small u unicode small l unicode small e unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of equal symmetry rule 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 ) infer ( metavar var r end metavar peano is metavar var t end metavar ) ) end define

The user defined "the proof aspect" aspect

define proof of equal symmetry rule 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 ( ( metavar var t end metavar peano is metavar var r end metavar ) infer ( ( equal symmetry 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 ) ) ) cut ( ( ( rule prime mp modus ponens ( ( 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 r end metavar ) ) conclude ( metavar var r end metavar peano is metavar var t end metavar ) ) ) ) end quote state proof state cache var c end expand end define