Logiweb aspects of lemma sameSeries in pyk

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The predefined "pyk" aspect

define pyk of lemma sameSeries 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameSeries 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameSeries as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed all metavar var fx end metavar indeed all metavar var sy end metavar indeed lambda var c dot typeNat0( quote metavar var m end metavar end quote ) endorse lambda var c dot typeNat0( quote metavar var n end metavar end quote ) endorse lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) endorse metavar var m end metavar = metavar var n end metavar infer [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var n end metavar ] end define

The user defined "the proof aspect" aspect

define proof of lemma sameSeries 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 fx end metavar indeed all metavar var sy end metavar indeed lambda var c dot typeNat0( quote metavar var m end metavar end quote ) endorse lambda var c dot typeNat0( quote metavar var n end metavar end quote ) endorse lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) endorse metavar var m end metavar = metavar var n end metavar infer lemma memberOfSeries(Type) modus probans lambda var c dot typeNat0( quote metavar var m end metavar end quote ) modus probans lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) conclude zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair in0 metavar var fx end metavar cut lemma memberOfSeries(Type) modus probans lambda var c dot typeNat0( quote metavar var n end metavar end quote ) modus probans lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) conclude zermelo pair zermelo pair metavar var n end metavar comma metavar var n end metavar end pair comma zermelo pair metavar var n end metavar comma [ metavar var fx end metavar ; metavar var n end metavar ] end pair end pair in0 metavar var fx end metavar cut lemma uniqueMember(Type) modus probans lambda var c dot typeSeries0( quote metavar var fx end metavar end quote , quote metavar var sy end metavar end quote ) modus ponens zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma [ metavar var fx end metavar ; metavar var m end metavar ] end pair end pair in0 metavar var fx end metavar modus ponens zermelo pair zermelo pair metavar var n end metavar comma metavar var n end metavar end pair comma zermelo pair metavar var n end metavar comma [ metavar var fx end metavar ; metavar var n end metavar ] end pair end pair in0 metavar var fx end metavar modus ponens metavar var m end metavar = metavar var n end metavar conclude [ metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var n end metavar ] end quote state proof state cache var c end expand end define