Logiweb aspects of lemma distribution(F) in pyk

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The predefined "pyk" aspect

define pyk of lemma distribution(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 d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode left parenthesis unicode capital f unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma distribution(F) as text unicode start of text unicode capital d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode left parenthesis unicode capital 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 distribution(F) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar =f metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma distribution(F) 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 fz end metavar indeed axiom timesF conclude [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] cut axiom plusF conclude [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] cut lemma eqMultiplicationLeft modus ponens [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] conclude [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] cut axiom distribution conclude [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] cut lemma timesF(Sym) conclude [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] cut lemma timesF(Sym) conclude [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] cut lemma addEquations modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fz 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 ] + [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] cut lemma plusF(Sym) conclude [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] cut lemma eqTransitivity6 modus ponens [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar *f metavar var fy end metavar ; metavar var m end metavar ] + [ metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] conclude [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] cut 1rule to=f modus ponens [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar ; metavar var m end metavar ] conclude metavar var fx end metavar *f metavar var fy end metavar +f metavar var fz end metavar =f metavar var fx end metavar *f metavar var fy end metavar +f metavar var fx end metavar *f metavar var fz end metavar end quote state proof state cache var c end expand end define