define pyk of lemma positiveToRight(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 p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital r unicode small i unicode small g unicode small h 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 positiveToRight(Less) as text unicode start of text unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital r unicode small i unicode small g unicode small h 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 positiveToRight(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 positiveToRight(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 y end metavar + - metavar var y end metavar <= metavar var z end metavar + - metavar var y end metavar imply not0 not0 metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var z end metavar + - metavar var y end metavar cut lemma x=x+y-y conclude metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar cut lemma subLessLeft modus ponens metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar modus ponens not0 metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar <= metavar var z end metavar + - metavar var y end metavar imply not0 not0 metavar var x end metavar + metavar var y end metavar + - metavar var y 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,