define pyk of lemma signNumerical(+) 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 s unicode small i unicode small g unicode small n unicode capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode left parenthesis unicode plus sign unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma signNumerical(+) as text unicode start of text unicode capital s unicode small i unicode small g unicode small n unicode capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode left parenthesis unicode plus sign unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma signNumerical(+) as system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer | metavar var x end metavar | = | - metavar var x end metavar | end define
define proof of lemma signNumerical(+) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer lemma positiveNumerical modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude | metavar var x end metavar | = metavar var x end metavar cut lemma positiveNegated modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 - metavar var x end metavar <= 0 imply not0 not0 - metavar var x end metavar = 0 cut lemma negativeNumerical modus ponens not0 - metavar var x end metavar <= 0 imply not0 not0 - metavar var x end metavar = 0 conclude | - metavar var x end metavar | = - - metavar var x end metavar cut lemma doubleMinus conclude - - metavar var x end metavar = metavar var x end metavar cut lemma eqTransitivity modus ponens | - metavar var x end metavar | = - - metavar var x end metavar modus ponens - - metavar var x end metavar = metavar var x end metavar conclude | - metavar var x end metavar | = metavar var x end metavar cut lemma eqSymmetry modus ponens | - metavar var x end metavar | = metavar var x end metavar conclude metavar var x end metavar = | - metavar var x end metavar | cut lemma eqTransitivity modus ponens | metavar var x end metavar | = metavar var x end metavar modus ponens metavar var x end metavar = | - metavar var x end metavar | conclude | metavar var x end metavar | = | - metavar var x end metavar | end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,