Logiweb aspects of lemma toNumericalLess in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma toNumericalLess 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 t unicode small o 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 l unicode small e unicode small s unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma toNumericalLess as text unicode start of text unicode capital t unicode small o 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 l unicode small e unicode small s unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma toNumericalLess as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 - metavar var y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar infer 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 | 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 toNumericalLess 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 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 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 subLessLeft modus ponens metavar var x end metavar = | metavar var x 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 all metavar var x end metavar indeed all metavar var y end metavar indeed not0 - metavar var y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar infer metavar var x end metavar <= 0 infer lemma lessNegated 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 x end metavar <= - - metavar var y end metavar imply not0 not0 - metavar var x end metavar = - - metavar var y end metavar cut lemma nonpositiveNumerical modus ponens metavar var x end metavar <= 0 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 subLessLeft modus ponens - metavar var x end metavar = | metavar var x 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 doubleMinus 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 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 x end metavar infer 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 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 y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar infer metavar var x end metavar <= 0 infer 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 imply metavar var x end metavar <= 0 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 y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar infer 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 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 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 y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar imply metavar var x end metavar <= 0 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 y end metavar <= metavar var x end metavar imply not0 not0 - metavar var y end metavar = metavar var x end metavar conclude metavar var x end metavar <= 0 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 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 x end metavar <= 0 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 end quote state proof state cache var c end expand end define