Logiweb aspects of lemma sameSeries(NumDiff) in pyk

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The predefined "pyk" aspect

define pyk of lemma sameSeries(NumDiff) 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 s unicode small e unicode small r unicode small i unicode small e unicode small s unicode left parenthesis unicode capital n unicode small u unicode small m unicode capital d unicode small i unicode small f unicode small f unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameSeries(NumDiff) as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital s unicode small e unicode small r unicode small i unicode small e unicode small s unicode left parenthesis unicode capital n unicode small u unicode small m unicode capital d unicode small i unicode small f unicode small f 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 sameSeries(NumDiff) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var o end metavar indeed all metavar var p end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed metavar var o end metavar = metavar var p end metavar infer metavar var n1 end metavar = metavar var n2 end metavar infer | [ metavar var fx end metavar ; metavar var o end metavar ] + - [ metavar var fy end metavar ; metavar var n1 end metavar ] | = | [ metavar var fx end metavar ; metavar var p end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | end define

The user defined "the proof aspect" aspect

define proof of lemma sameSeries(NumDiff) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var o end metavar indeed all metavar var p end metavar indeed all metavar var n1 end metavar indeed all metavar var n2 end metavar indeed metavar var o end metavar = metavar var p end metavar infer metavar var n1 end metavar = metavar var n2 end metavar infer lemma sameSeries modus ponens metavar var o end metavar = metavar var p end metavar conclude [ metavar var fx end metavar ; metavar var o end metavar ] = [ metavar var fx end metavar ; metavar var p end metavar ] cut lemma sameSeries modus ponens metavar var n1 end metavar = metavar var n2 end metavar conclude [ metavar var fy end metavar ; metavar var n1 end metavar ] = [ metavar var fy end metavar ; metavar var n2 end metavar ] cut lemma eqNegated modus ponens [ metavar var fy end metavar ; metavar var n1 end metavar ] = [ metavar var fy end metavar ; metavar var n2 end metavar ] conclude - [ metavar var fy end metavar ; metavar var n1 end metavar ] = - [ metavar var fy end metavar ; metavar var n2 end metavar ] cut lemma addEquations modus ponens [ metavar var fx end metavar ; metavar var o end metavar ] = [ metavar var fx end metavar ; metavar var p end metavar ] modus ponens - [ metavar var fy end metavar ; metavar var n1 end metavar ] = - [ metavar var fy end metavar ; metavar var n2 end metavar ] conclude [ metavar var fx end metavar ; metavar var o end metavar ] + - [ metavar var fy end metavar ; metavar var n1 end metavar ] = [ metavar var fx end metavar ; metavar var p end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] cut lemma sameNumerical modus ponens [ metavar var fx end metavar ; metavar var o end metavar ] + - [ metavar var fy end metavar ; metavar var n1 end metavar ] = [ metavar var fx end metavar ; metavar var p end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] conclude | [ metavar var fx end metavar ; metavar var o end metavar ] + - [ metavar var fy end metavar ; metavar var n1 end metavar ] | = | [ metavar var fx end metavar ; metavar var p end metavar ] + - [ metavar var fy end metavar ; metavar var n2 end metavar ] | end quote state proof state cache var c end expand end define