Logiweb aspects of substitution macro in pyk

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The predefined "pyk" aspect

define pyk of substitution macro as text unicode start of text unicode small s unicode small u unicode small b unicode small s unicode small t unicode small i unicode small t unicode small u unicode small t unicode small i unicode small o unicode small n unicode space unicode small m unicode small a unicode small c unicode small r unicode small o unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of substitution macro as text unicode start of text unicode capital s unicode small u unicode small b unicode small s unicode small t unicode small i unicode small t unicode small u unicode small t unicode small i unicode small o unicode small n unicode capital m unicode small a unicode small c unicode small r unicode small o unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of substitution macro as system prime s infer all metavar var z end metavar indeed all metavar var c end metavar indeed all metavar var a end metavar indeed all metavar var d end metavar indeed ( peano sub quote metavar var a end metavar end quote is quote metavar var d end metavar end quote where quote metavar var z end metavar end quote is quote metavar var c end metavar end quote end sub endorse ( metavar var d end metavar infer metavar var a end metavar ) ) end define

The user defined "the proof aspect" aspect

define proof of substitution macro as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var z end metavar indeed all metavar var c end metavar indeed all metavar var a end metavar indeed all metavar var d end metavar indeed ( peano sub quote metavar var a end metavar end quote is quote metavar var d end metavar end quote where quote metavar var z end metavar end quote is quote metavar var c end metavar end quote end sub endorse ( metavar var d end metavar infer ( ( ( rule prime gen modus ponens metavar var d end metavar ) conclude peano all metavar var z end metavar indeed metavar var d end metavar ) cut ( ( ( axiom prime a four modus probans peano sub quote metavar var a end metavar end quote is quote metavar var d end metavar end quote where quote metavar var z end metavar end quote is quote metavar var c end metavar end quote end sub ) conclude ( ( peano all metavar var z end metavar indeed metavar var d end metavar ) peano imply metavar var a end metavar ) ) cut ( ( ( rule prime mp modus ponens ( ( peano all metavar var z end metavar indeed metavar var d end metavar ) peano imply metavar var a end metavar ) ) modus ponens peano all metavar var z end metavar indeed metavar var d end metavar ) conclude metavar var a end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define