define pyk of lemma plusAssociativity(R) 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 p unicode small l unicode small u 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 r unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma plusAssociativity(R) as text unicode start of text unicode capital p unicode small l unicode small u 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 r unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma plusAssociativity(R) 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 R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) end define
define proof of lemma plusAssociativity(R) 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 lemma plusAssociativity(F) 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 cut lemma =f to sameF modus ponens 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 conclude metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar sameF metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar cut lemma f2R(Plus) modus ponens metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar sameF metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar conclude R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) cut lemma plusR(Sym) conclude R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( var fx +f var fy ) cut lemma ==Transitivity modus ponens R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( var fx +f var fy ) modus ponens R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) conclude R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( 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,