Logiweb aspects of lemma fromPositiveNumerical in pyk

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The predefined "pyk" aspect

define pyk of lemma fromPositiveNumerical 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 f unicode small r unicode small o unicode small m 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 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromPositiveNumerical as text unicode start of text unicode capital f unicode small r unicode small o unicode small m 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 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromPositiveNumerical 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 not0 metavar var x end metavar = 0 end define

The user defined "the proof aspect" aspect

define proof of lemma fromPositiveNumerical as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed 0 <= metavar var x end metavar infer not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | infer lemma nonnegativeNumerical modus ponens 0 <= metavar var x end metavar conclude | metavar var x end metavar | = metavar var x end metavar cut lemma subLessRight modus ponens | metavar var x end metavar | = metavar var x end metavar modus ponens not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | conclude not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar cut lemma lessNeq modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 0 = metavar var x end metavar cut lemma neqSymmetry modus ponens not0 0 = metavar var x end metavar conclude not0 metavar var x end metavar = 0 cut all metavar var x end metavar indeed metavar var x end metavar <= 0 infer not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | infer lemma nonpositiveNumerical modus ponens metavar var x end metavar <= 0 conclude | metavar var x end metavar | = - metavar var x end metavar cut lemma subLessRight modus ponens | metavar var x end metavar | = - metavar var x end metavar modus ponens not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | conclude not0 0 <= - metavar var x end metavar imply not0 not0 0 = - 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 doubleMinus conclude - - metavar var x end metavar = metavar var x end metavar cut lemma subLessLeft modus ponens - - metavar var x end metavar = metavar var x end metavar modus ponens not0 - - metavar var x end metavar <= 0 imply not0 not0 - - metavar var x end metavar = 0 conclude not0 metavar var x end metavar <= 0 imply not0 not0 metavar var x end metavar = 0 cut lemma lessNeq modus ponens not0 metavar var x end metavar <= 0 imply not0 not0 metavar var x end metavar = 0 conclude not0 metavar var x end metavar = 0 cut all metavar var x end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed 0 <= metavar var x end metavar infer not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | infer not0 metavar var x end metavar = 0 conclude 0 <= metavar var x end metavar imply not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 cut 1rule deduction modus ponens all metavar var x end metavar indeed metavar var x end metavar <= 0 infer not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | infer not0 metavar var x end metavar = 0 conclude metavar var x end metavar <= 0 imply not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 cut not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | infer lemma from leqGeq modus ponens 0 <= metavar var x end metavar imply not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 modus ponens metavar var x end metavar <= 0 imply not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 conclude not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 cut 1rule mp modus ponens not0 0 <= | metavar var x end metavar | imply not0 not0 0 = | metavar var x end metavar | imply not0 metavar var x end metavar = 0 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 end quote state proof state cache var c end expand end define