Logiweb aspects of lemma splitNumericalSum(--) in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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