Logiweb aspects of lemma sameExp in pyk

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The predefined "pyk" aspect

define pyk of lemma sameExp 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameExp 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameExp as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var x end metavar indeed metavar var m end metavar = metavar var n end metavar infer metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma sameExp as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var x end metavar indeed metavar var m end metavar = metavar var n end metavar infer lemma sameExp base 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 cut lemma sameExp indu conclude for all objects metavar var n end metavar indeed metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar imply for all objects metavar var n end metavar indeed metavar var m end metavar + 1 = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar + 1 = metavar var x end metavar ^ metavar var n end metavar cut lemma induction modus ponens 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 modus ponens for all objects metavar var n end metavar indeed metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar imply for all objects metavar var n end metavar indeed metavar var m end metavar + 1 = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar + 1 = metavar var x end metavar ^ metavar var n end metavar conclude for all objects metavar var n end metavar indeed metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar cut lemma a4 at metavar var n end metavar modus ponens for all objects metavar var n end metavar indeed metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar conclude metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar cut 1rule mp modus ponens metavar var m end metavar = metavar var n end metavar imply metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar modus ponens metavar var m end metavar = metavar var n end metavar conclude metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var n end metavar end quote state proof state cache var c end expand end define