Logiweb aspects of lemma signNumerical(+) in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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