define pyk of lemma positiveToLeft(Eq)(1 term) 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 o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital e unicode small q unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma positiveToLeft(Eq)(1 term) as text unicode start of text unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital e unicode small q unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma positiveToLeft(Eq)(1 term) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar = metavar var y end metavar infer metavar var x end metavar + - metavar var y end metavar = 0 end define
define proof of lemma positiveToLeft(Eq)(1 term) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar = metavar var y end metavar infer lemma eqAddition modus ponens metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar + - metavar var y end metavar = metavar var y end metavar + - metavar var y end metavar cut axiom negative conclude metavar var y end metavar + - metavar var y end metavar = 0 cut lemma eqTransitivity modus ponens metavar var x end metavar + - metavar var y end metavar = metavar var y end metavar + - metavar var y end metavar modus ponens metavar var y end metavar + - metavar var y end metavar = 0 conclude metavar var x end metavar + - metavar var y end metavar = 0 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,