define pyk of lemma timesR(Sym) 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 r unicode left parenthesis unicode capital s unicode small y unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma timesR(Sym) as text unicode start of text unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital r unicode left parenthesis unicode capital s unicode small y unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma timesR(Sym) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed R( metavar var fx end metavar *f metavar var fy end metavar ) == R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) end define
define proof of lemma timesR(Sym) 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 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 ==Symmetry 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 ) conclude R( metavar var fx end metavar *f metavar var fy end metavar ) == R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,