Logiweb aspects of lemma fromNotSameF(Strong) helper2 in pyk

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The predefined "pyk" aspect

define pyk of lemma fromNotSameF(Strong) helper2 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 o unicode small t unicode capital s unicode small a unicode small m unicode small e unicode capital f unicode left parenthesis unicode capital s unicode small t unicode small r unicode small o unicode small n unicode small g unicode right parenthesis unicode space unicode small h unicode small e unicode small l unicode small p unicode small e unicode small r unicode two unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromNotSameF(Strong) helper2 as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital n unicode small o unicode small t unicode capital s unicode small a unicode small m unicode small e unicode capital f unicode left parenthesis unicode capital s unicode small t unicode small r unicode small o unicode small n unicode small g unicode right parenthesis unicode left parenthesis unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode two 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 fromNotSameF(Strong) helper2 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 all metavar var u end metavar indeed all metavar var v end metavar indeed metavar var v end metavar <= | metavar var x end metavar + - metavar var z end metavar | infer not0 | metavar var x end metavar + - metavar var y end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = 1/ 1 + 1 * metavar var v end metavar infer not0 | metavar var z end metavar + - metavar var u end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var z end metavar + - metavar var u end metavar | = 1/ 1 + 1 * metavar var v end metavar infer not0 metavar var y end metavar = metavar var u end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromNotSameF(Strong) helper2 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 all metavar var u end metavar indeed all metavar var v end metavar indeed metavar var v end metavar <= | metavar var x end metavar + - metavar var z end metavar | infer not0 | metavar var x end metavar + - metavar var y end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = 1/ 1 + 1 * metavar var v end metavar infer not0 | metavar var z end metavar + - metavar var u end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var z end metavar + - metavar var u end metavar | = 1/ 1 + 1 * metavar var v end metavar infer lemma lessNegated modus ponens not0 | metavar var x end metavar + - metavar var y end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var x end metavar + - metavar var y end metavar | = 1/ 1 + 1 * metavar var v end metavar conclude not0 - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | cut lemma numericalDifference conclude | metavar var z end metavar + - metavar var u end metavar | = | metavar var u end metavar + - metavar var z end metavar | cut lemma subLessLeft modus ponens | metavar var z end metavar + - metavar var u end metavar | = | metavar var u end metavar + - metavar var z end metavar | modus ponens not0 | metavar var z end metavar + - metavar var u end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var z end metavar + - metavar var u end metavar | = 1/ 1 + 1 * metavar var v end metavar conclude not0 | metavar var u end metavar + - metavar var z end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var u end metavar + - metavar var z end metavar | = 1/ 1 + 1 * metavar var v end metavar cut lemma lessNegated modus ponens not0 | metavar var u end metavar + - metavar var z end metavar | <= 1/ 1 + 1 * metavar var v end metavar imply not0 not0 | metavar var u end metavar + - metavar var z end metavar | = 1/ 1 + 1 * metavar var v end metavar conclude not0 - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar = - | metavar var u end metavar + - metavar var z end metavar | cut lemma addEquations(Less) modus ponens not0 - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | modus ponens not0 - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar = - | metavar var u end metavar + - metavar var z end metavar | conclude not0 - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | cut lemma (1/2)x+(1/2)x=x conclude 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar = metavar var v end metavar cut lemma eqNegated modus ponens 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar = metavar var v end metavar conclude - 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar = - metavar var v end metavar cut lemma -x-y=-(x+y) conclude - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar cut lemma eqTransitivity modus ponens - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar modus ponens - 1/ 1 + 1 * metavar var v end metavar + 1/ 1 + 1 * metavar var v end metavar = - metavar var v end metavar conclude - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - metavar var v end metavar cut lemma subLessLeft modus ponens - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - metavar var v end metavar modus ponens not0 - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - 1/ 1 + 1 * metavar var v end metavar + - 1/ 1 + 1 * metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | conclude not0 - metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | cut axiom plusCommutativity conclude - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | = - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut lemma subLessRight modus ponens - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | = - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | modus ponens not0 - metavar var v end metavar <= - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | imply not0 not0 - metavar var v end metavar = - | metavar var x end metavar + - metavar var y end metavar | + - | metavar var u end metavar + - metavar var z end metavar | conclude not0 - metavar var v end metavar <= - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 - metavar var v end metavar = - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut lemma addEquations(LeqLess) modus ponens metavar var v end metavar <= | metavar var x end metavar + - metavar var z end metavar | modus ponens not0 - metavar var v end metavar <= - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 - metavar var v end metavar = - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | conclude not0 metavar var v end metavar + - metavar var v end metavar <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 metavar var v end metavar + - metavar var v end metavar = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut axiom negative conclude metavar var v end metavar + - metavar var v end metavar = 0 cut lemma subLessLeft modus ponens metavar var v end metavar + - metavar var v end metavar = 0 modus ponens not0 metavar var v end metavar + - metavar var v end metavar <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 metavar var v end metavar + - metavar var v end metavar = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | conclude not0 0 <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 0 = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut axiom plusAssociativity conclude | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut lemma eqSymmetry modus ponens | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | conclude | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut lemma subLessRight modus ponens | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | modus ponens not0 0 <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 0 = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | conclude not0 0 <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 0 = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | cut lemma insertTwoMiddleTerms(Numerical) conclude | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | + | metavar var u end metavar + - metavar var z end metavar | cut lemma positiveToLeft(Leq) modus ponens | metavar var x end metavar + - metavar var z end metavar | <= | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | + | metavar var u end metavar + - metavar var z end metavar | conclude | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | <= | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | cut axiom plusCommutativity conclude | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | = | metavar var y end metavar + - metavar var u end metavar | + | metavar var x end metavar + - metavar var y end metavar | cut lemma subLeqRight modus ponens | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | = | metavar var y end metavar + - metavar var u end metavar | + | metavar var x end metavar + - metavar var y end metavar | modus ponens | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | <= | metavar var x end metavar + - metavar var y end metavar | + | metavar var y end metavar + - metavar var u end metavar | conclude | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | <= | metavar var y end metavar + - metavar var u end metavar | + | metavar var x end metavar + - metavar var y end metavar | cut lemma positiveToLeft(Leq) modus ponens | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | <= | metavar var y end metavar + - metavar var u end metavar | + | metavar var x end metavar + - metavar var y end metavar | conclude | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | <= | metavar var y end metavar + - metavar var u end metavar | cut lemma lessLeqTransitivity modus ponens not0 0 <= | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | imply not0 not0 0 = | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | modus ponens | metavar var x end metavar + - metavar var z end metavar | + - | metavar var u end metavar + - metavar var z end metavar | + - | metavar var x end metavar + - metavar var y end metavar | <= | metavar var y end metavar + - metavar var u end metavar | conclude not0 0 <= | metavar var y end metavar + - metavar var u end metavar | imply not0 not0 0 = | metavar var y end metavar + - metavar var u end metavar | cut lemma fromPositiveNumerical modus ponens not0 0 <= | metavar var y end metavar + - metavar var u end metavar | imply not0 not0 0 = | metavar var y end metavar + - metavar var u end metavar | conclude not0 metavar var y end metavar + - metavar var u end metavar = 0 cut lemma negativeToRight(Neq)(1 term) modus ponens not0 metavar var y end metavar + - metavar var u end metavar = 0 conclude not0 metavar var y end metavar = metavar var u end metavar end quote state proof state cache var c end expand end define