define pyk of lemma timesAssociativity(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 i unicode small m unicode small e unicode small s unicode capital a unicode small s unicode small s unicode small o unicode small c unicode small i unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode left parenthesis unicode capital f unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma timesAssociativity(F) as text unicode start of text unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital a unicode small s unicode small s unicode small o unicode small c unicode small i unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode left parenthesis unicode capital f unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma timesAssociativity(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 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 fz end metavar end define
define proof of lemma timesAssociativity(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 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 *f metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] cut axiom timesF conclude [ metavar var fx end metavar *f metavar var fy 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 ] cut lemma eqMultiplication modus ponens [ metavar var fx end metavar *f metavar var fy 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 ] conclude [ metavar var fx end metavar *f 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 fz end metavar ; metavar var m end metavar ] cut axiom timesAssociativity 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 fz end metavar ; metavar var m end metavar ] cut lemma timesF(Sym) conclude [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fy end metavar *f metavar var fz end metavar ; metavar var m end metavar ] cut lemma eqMultiplicationLeft modus ponens [ metavar var fy end metavar ; metavar var m end metavar ] * [ metavar var fz end metavar ; metavar var m end metavar ] = [ metavar var fy 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 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 lemma timesF(Sym) 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 *f metavar var fy 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 *f 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 *f 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 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 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 *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 *f metavar var fy 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 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 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 fz end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,