define pyk of lemma positiveToLeft(Leq) 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 l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma positiveToLeft(Leq) 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 l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma positiveToLeft(Leq) 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 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar infer metavar var x end metavar + - metavar var z end metavar <= metavar var y end metavar end define
define proof of lemma positiveToLeft(Leq) 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 metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar infer lemma leqAddition modus ponens metavar var x end metavar <= metavar var y end metavar + metavar var z end metavar conclude 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 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 subLeqRight modus ponens metavar var y end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var y end metavar modus ponens 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 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,