define pyk of lemma f2R(Times) 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 f unicode two unicode capital r unicode left parenthesis unicode capital t unicode small i unicode small m unicode small e unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma f2R(Times) as text unicode start of text unicode small f unicode two unicode capital r unicode left parenthesis unicode capital t unicode small i unicode small m unicode small e unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma f2R(Times) 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 sameF metavar var fz end metavar infer R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) == R( metavar var fz end metavar ) end define
define proof of lemma f2R(Times) 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 metavar var fx end metavar *f metavar var fy end metavar sameF metavar var fz end metavar infer 1rule to== modus ponens metavar var fx end metavar *f metavar var fy end metavar sameF metavar var fz end metavar conclude R( metavar var fx end metavar *f metavar var fy end metavar ) == R( metavar var fz end metavar ) cut axiom timesR conclude R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) == R( metavar var fx end metavar *f metavar var fy end metavar ) cut lemma ==Transitivity modus ponens R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) == R( metavar var fx end metavar *f metavar var fy end metavar ) modus ponens R( metavar var fx end metavar *f metavar var fy end metavar ) == R( metavar var fz end metavar ) conclude R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) == R( 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,