Logiweb aspects of lemma sameExp base in pyk

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The predefined "pyk" aspect

define pyk of lemma sameExp base as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small s unicode small a unicode small m unicode small e unicode capital e unicode small x unicode small p unicode space unicode small b unicode small a unicode small s unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameExp base as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital e unicode small x unicode small p unicode left parenthesis unicode capital b unicode small a unicode small s unicode small e unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameExp base as system Q infer all metavar var n end metavar indeed all metavar var x end metavar indeed for all objects metavar var n end metavar indeed 0 = metavar var n end metavar imply metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma sameExp base as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var n end metavar indeed all metavar var x end metavar indeed 0 = metavar var n end metavar infer lemma expZero exact conclude metavar var x end metavar ^ 0 = 1 cut lemma eqSymmetry modus ponens 0 = metavar var n end metavar conclude metavar var n end metavar = 0 cut 1rule expZero modus ponens metavar var n end metavar = 0 conclude metavar var x end metavar ^ metavar var n end metavar = 1 cut lemma eqSymmetry modus ponens metavar var x end metavar ^ metavar var n end metavar = 1 conclude 1 = metavar var x end metavar ^ metavar var n end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar ^ 0 = 1 modus ponens 1 = metavar var x end metavar ^ metavar var n end metavar conclude metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar cut all metavar var n end metavar indeed all metavar var x end metavar indeed 1rule deduction modus ponens all metavar var n end metavar indeed all metavar var x end metavar indeed 0 = metavar var n end metavar infer metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar conclude 0 = metavar var n end metavar imply metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar cut 1rule gen modus ponens 0 = metavar var n end metavar imply metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar conclude for all objects metavar var n end metavar indeed 0 = metavar var n end metavar imply metavar var x end metavar ^ 0 = metavar var x end metavar ^ metavar var n end metavar end quote state proof state cache var c end expand end define