define pyk of lemma positiveToRight(Leq)(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 r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital l unicode small 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 positiveToRight(Leq)(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 r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital l unicode small 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 positiveToRight(Leq)(1 term) as system Q infer all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var y end metavar <= metavar var z end metavar infer 0 <= metavar var z end metavar + - metavar var y end metavar end define
define proof of lemma positiveToRight(Leq)(1 term) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var y end metavar <= metavar var z end metavar infer lemma plus0Left conclude 0 + metavar var y end metavar = metavar var y end metavar cut lemma eqSymmetry modus ponens 0 + metavar var y end metavar = metavar var y end metavar conclude metavar var y end metavar = 0 + metavar var y end metavar cut lemma subLeqLeft modus ponens metavar var y end metavar = 0 + metavar var y end metavar modus ponens metavar var y end metavar <= metavar var z end metavar conclude 0 + metavar var y end metavar <= metavar var z end metavar cut lemma positiveToRight(Leq) modus ponens 0 + metavar var y end metavar <= metavar var z end metavar conclude 0 <= metavar var z end metavar + - metavar var y end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,