Logiweb aspects of lemma f-Bounded helper in pyk

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The predefined "pyk" aspect

define pyk of lemma f-Bounded helper 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 hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e unicode small d unicode space unicode small h unicode small e unicode small l unicode small p 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 f-Bounded helper as text unicode start of text unicode capital f unicode hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e unicode small d unicode left parenthesis unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r 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 f-Bounded helper as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 | metavar var x end metavar + - metavar var y end metavar | <= metavar var z end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = metavar var z end metavar infer not0 | metavar var y end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) imply not0 not0 | metavar var y end metavar | = if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) end define

The user defined "the proof aspect" aspect

define proof of lemma f-Bounded helper 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 all metavar var z end metavar indeed not0 | metavar var x end metavar + - metavar var y end metavar | <= metavar var z end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = metavar var z end metavar infer lemma numericalDifferenceLess modus ponens not0 | metavar var x end metavar + - metavar var y end metavar | <= metavar var z end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = metavar var z end metavar conclude not0 not0 metavar var y end metavar + - metavar var z end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar + - metavar var z end metavar = metavar var x end metavar imply not0 not0 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar + metavar var z end metavar cut prop lemma first conjunct modus ponens not0 not0 metavar var y end metavar + - metavar var z end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar + - metavar var z end metavar = metavar var x end metavar imply not0 not0 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar + metavar var z end metavar conclude not0 metavar var y end metavar + - metavar var z end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar + - metavar var z end metavar = metavar var x end metavar cut lemma negativeToRight(Less) modus ponens not0 metavar var y end metavar + - metavar var z end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar + - metavar var z end metavar = metavar var x end metavar conclude not0 metavar var y end metavar <= metavar var x end metavar + metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar + metavar var z end metavar cut lemma x<=|x| conclude metavar var x end metavar + metavar var z end metavar <= | metavar var x end metavar + metavar var z end metavar | cut lemma lessLeqTransitivity modus ponens not0 metavar var y end metavar <= metavar var x end metavar + metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar + metavar var z end metavar modus ponens metavar var x end metavar + metavar var z end metavar <= | metavar var x end metavar + metavar var z end metavar | conclude not0 metavar var y end metavar <= | metavar var x end metavar + metavar var z end metavar | imply not0 not0 metavar var y end metavar = | metavar var x end metavar + metavar var z end metavar | cut lemma leqMax1 conclude | metavar var x end metavar + metavar var z end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) cut lemma lessLeqTransitivity modus ponens not0 metavar var y end metavar <= | metavar var x end metavar + metavar var z end metavar | imply not0 not0 metavar var y end metavar = | metavar var x end metavar + metavar var z end metavar | modus ponens | metavar var x end metavar + metavar var z end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) conclude not0 metavar var y end metavar <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) imply not0 not0 metavar var y end metavar = if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) cut prop lemma second conjunct modus ponens not0 not0 metavar var y end metavar + - metavar var z end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar + - metavar var z end metavar = metavar var x end metavar imply not0 not0 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar + metavar var z end metavar conclude not0 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar + metavar var z end metavar cut lemma positiveToLeft(Less) modus ponens not0 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar + metavar var z end metavar conclude not0 metavar var x end metavar + - metavar var z end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar + - metavar var z end metavar = metavar var y end metavar cut lemma x<=|x| conclude metavar var z end metavar + - metavar var x end metavar <= | metavar var z end metavar + - metavar var x end metavar | cut lemma numericalDifference conclude | metavar var z end metavar + - metavar var x end metavar | = | metavar var x end metavar + - metavar var z end metavar | cut lemma subLeqRight modus ponens | metavar var z end metavar + - metavar var x end metavar | = | metavar var x end metavar + - metavar var z end metavar | modus ponens metavar var z end metavar + - metavar var x end metavar <= | metavar var z end metavar + - metavar var x end metavar | conclude metavar var z end metavar + - metavar var x end metavar <= | metavar var x end metavar + - metavar var z end metavar | cut lemma leqNegated modus ponens metavar var z end metavar + - metavar var x end metavar <= | metavar var x end metavar + - metavar var z end metavar | conclude - | metavar var x end metavar + - metavar var z end metavar | <= - metavar var z end metavar + - metavar var x end metavar cut lemma minusNegated conclude - metavar var z end metavar + - metavar var x end metavar = metavar var x end metavar + - metavar var z end metavar cut lemma subLeqRight modus ponens - metavar var z end metavar + - metavar var x end metavar = metavar var x end metavar + - metavar var z end metavar modus ponens - | metavar var x end metavar + - metavar var z end metavar | <= - metavar var z end metavar + - metavar var x end metavar conclude - | metavar var x end metavar + - metavar var z end metavar | <= metavar var x end metavar + - metavar var z end metavar cut lemma leqLessTransitivity modus ponens - | metavar var x end metavar + - metavar var z end metavar | <= metavar var x end metavar + - metavar var z end metavar modus ponens not0 metavar var x end metavar + - metavar var z end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar + - metavar var z end metavar = metavar var y end metavar conclude not0 - | metavar var x end metavar + - metavar var z end metavar | <= metavar var y end metavar imply not0 not0 - | metavar var x end metavar + - metavar var z end metavar | = metavar var y end metavar cut lemma leqMax2 conclude | metavar var x end metavar + - metavar var z end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) cut lemma leqNegated modus ponens | metavar var x end metavar + - metavar var z end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) conclude - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) <= - | metavar var x end metavar + - metavar var z end metavar | cut lemma leqLessTransitivity modus ponens - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) <= - | metavar var x end metavar + - metavar var z end metavar | modus ponens not0 - | metavar var x end metavar + - metavar var z end metavar | <= metavar var y end metavar imply not0 not0 - | metavar var x end metavar + - metavar var z end metavar | = metavar var y end metavar conclude not0 - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) <= metavar var y end metavar imply not0 not0 - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) = metavar var y end metavar cut lemma toNumericalLess modus ponens not0 - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) <= metavar var y end metavar imply not0 not0 - if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) = metavar var y end metavar modus ponens not0 metavar var y end metavar <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) imply not0 not0 metavar var y end metavar = if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) conclude not0 | metavar var y end metavar | <= if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) imply not0 not0 | metavar var y end metavar | = if( | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + metavar var z end metavar | , | metavar var x end metavar + - metavar var z end metavar | ) end quote state proof state cache var c end expand end define