Logiweb aspects of lemma fromNumericalGreater in pyk

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The predefined "pyk" aspect

define pyk of lemma fromNumericalGreater 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 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 capital g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromNumericalGreater as text unicode start of text unicode capital f unicode small r unicode small o unicode small m 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 capital g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromNumericalGreater 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 | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromNumericalGreater 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 not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer 0 <= metavar var y end metavar infer lemma nonnegativeNumerical modus ponens 0 <= metavar var y end metavar conclude | metavar var y end metavar | = metavar var y end metavar cut lemma subLessRight modus ponens | metavar var y end metavar | = metavar var y end metavar modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | conclude not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut prop lemma weaken or first modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut 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 | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer metavar var y end metavar <= 0 infer lemma nonpositiveNumerical modus ponens metavar var y end metavar <= 0 conclude | metavar var y end metavar | = - metavar var y end metavar cut lemma subLessRight modus ponens | metavar var y end metavar | = - metavar var y end metavar modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | conclude not0 metavar var x end metavar <= - metavar var y end metavar imply not0 not0 metavar var x end metavar = - metavar var y end metavar cut lemma lessNegated modus ponens not0 metavar var x end metavar <= - metavar var y end metavar imply not0 not0 metavar var x end metavar = - metavar var y end metavar conclude not0 - - metavar var y end metavar <= - metavar var x end metavar imply not0 not0 - - metavar var y end metavar = - metavar var x end metavar cut lemma doubleMinus conclude - - metavar var y end metavar = metavar var y end metavar cut lemma subLessLeft modus ponens - - metavar var y end metavar = metavar var y end metavar modus ponens not0 - - metavar var y end metavar <= - metavar var x end metavar imply not0 not0 - - metavar var y end metavar = - metavar var x end metavar conclude not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar cut prop lemma weaken or second modus ponens not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar conclude not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar 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 not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer 0 <= metavar var y end metavar infer not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | imply 0 <= metavar var y end metavar imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut 1rule deduction modus ponens 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 | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer metavar var y end metavar <= 0 infer not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | imply metavar var y end metavar <= 0 imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | infer 1rule mp modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | imply 0 <= metavar var y end metavar imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | conclude 0 <= metavar var y end metavar imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut 1rule mp modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | imply metavar var y end metavar <= 0 imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar modus ponens not0 metavar var x end metavar <= | metavar var y end metavar | imply not0 not0 metavar var x end metavar = | metavar var y end metavar | conclude metavar var y end metavar <= 0 imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar cut lemma from leqGeq modus ponens 0 <= metavar var y end metavar imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar modus ponens metavar var y end metavar <= 0 imply not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 not0 metavar var y end metavar <= - metavar var x end metavar imply not0 not0 metavar var y end metavar = - metavar var x end metavar imply not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar end quote state proof state cache var c end expand end define