define pyk of lemma negativeToLeft(Less) 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 n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma negativeToLeft(Less) as text unicode start of text unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma negativeToLeft(Less) 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 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 end define
define proof of lemma negativeToLeft(Less) 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 lessAddition 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 + - metavar var z end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma three2threeTerms conclude metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma x=x+y-y conclude metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar conclude metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar cut lemma eqTransitivity modus ponens metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar modus ponens metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar conclude metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar cut lemma subLessRight modus ponens metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar = metavar var y end metavar modus ponens not0 metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + - metavar var z end metavar + metavar var z end metavar imply not0 not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + - metavar var z 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,