Logiweb aspects of lemma to=f in pyk

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The predefined "pyk" aspect

define pyk of lemma to=f 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 t unicode small o unicode equal sign unicode small f unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma to=f as text unicode start of text unicode capital t unicode small o unicode equal sign unicode small f unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma to=f as system Q infer all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote Q end quote ) endorse lambda var c dot typeSeries0( quote metavar var fy end metavar end quote , quote Q end quote ) endorse for all objects metavar var m end metavar indeed [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] infer metavar var fx end metavar = metavar var fy end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma to=f 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 fx end metavar indeed all metavar var fy end metavar indeed lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote Q end quote ) endorse lambda var c dot typeSeries0( quote metavar var fy end metavar end quote , quote Q end quote ) endorse for all objects metavar var m end metavar indeed [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] infer lemma a4 at metavar var m end metavar modus ponens for all objects metavar var m end metavar indeed [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] conclude [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] cut lemma eqSymmetry modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] conclude [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] cut 1rule gen modus ponens [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] conclude for all objects metavar var m end metavar indeed [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] cut lemma to=f subset modus probans lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote Q end quote ) modus probans lambda var c dot typeSeries0( quote metavar var fy end metavar end quote , quote Q end quote ) modus ponens for all objects metavar var m end metavar indeed [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] conclude for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fx end metavar imply object var var s1 end var in0 metavar var fy end metavar cut lemma to=f subset modus probans lambda var c dot typeSeries0( quote metavar var fy end metavar end quote , quote Q end quote ) modus probans lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote Q end quote ) modus ponens for all objects metavar var m end metavar indeed [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] conclude for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fy end metavar imply object var var s1 end var in0 metavar var fx end metavar cut lemma set equality suff condition modus ponens for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fx end metavar imply object var var s1 end var in0 metavar var fy end metavar modus ponens for all objects object var var s1 end var indeed object var var s1 end var in0 metavar var fy end metavar imply object var var s1 end var in0 metavar var fx end metavar conclude metavar var fx end metavar = metavar var fy end metavar end quote state proof state cache var c end expand end define