define pyk of lemma negativeToRight(Neq)(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 n unicode small e unicode small g unicode small a 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 n 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 negativeToRight(Neq)(1 term) as text unicode start of text unicode capital n unicode small e unicode small g unicode small a 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 n 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 negativeToRight(Neq)(1 term) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar + - metavar var y end metavar = 0 infer not0 metavar var x end metavar = metavar var y end metavar end define
define proof of lemma negativeToRight(Neq)(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 positiveToLeft(Eq)(1 term) modus ponens metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar + - metavar var y end metavar = 0 cut all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens 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 conclude metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar + - metavar var y end metavar = 0 cut not0 metavar var x end metavar + - metavar var y end metavar = 0 infer prop lemma mt modus ponens metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar + - metavar var y end metavar = 0 modus ponens not0 metavar var x end metavar + - metavar var y end metavar = 0 conclude not0 metavar var x 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,