define pyk of lemma splitNumericalSum(--) 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 s unicode small p unicode small l unicode small i unicode small t 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 s unicode small u unicode small m unicode left parenthesis unicode hyphen unicode hyphen unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma splitNumericalSum(--) as text unicode start of text unicode small s unicode small p unicode small l unicode small i unicode small t 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 s unicode small u unicode small m unicode left parenthesis unicode hyphen unicode hyphen unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma splitNumericalSum(--) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= 0 infer metavar var y end metavar <= 0 infer | metavar var x end metavar + metavar var y end metavar | <= | metavar var x end metavar | + | metavar var y end metavar | end define
define proof of lemma splitNumericalSum(--) 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 metavar var x end metavar <= 0 infer metavar var y end metavar <= 0 infer lemma nonpositiveNegated modus ponens metavar var x end metavar <= 0 conclude 0 <= - metavar var x end metavar cut lemma nonpositiveNegated modus ponens metavar var y end metavar <= 0 conclude 0 <= - metavar var y end metavar cut lemma splitNumericalSum(++) modus ponens 0 <= - metavar var x end metavar modus ponens 0 <= - metavar var y end metavar conclude | - metavar var x end metavar + - metavar var y end metavar | <= | - metavar var x end metavar | + | - metavar var y end metavar | cut lemma splitNumericalSumHelper modus ponens | - metavar var x end metavar + - metavar var y end metavar | <= | - metavar var x end metavar | + | - metavar var y end metavar | conclude | metavar var x end metavar + metavar var y end metavar | <= | metavar var x 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,