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 plus sign 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 plus sign 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 0 <= metavar var y end metavar infer if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) + if( 0 <= metavar var y end metavar , metavar var y 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 0 <= metavar var y end metavar infer lemma nonpositiveNegated modus ponens metavar var x end metavar <= 0 conclude 0 <= - metavar var x end metavar cut lemma nonnegativeNegated modus ponens 0 <= metavar var y end metavar conclude - metavar var y end metavar <= 0 cut lemma splitNumericalSum(+-) modus ponens 0 <= - metavar var x end metavar modus ponens - metavar var y end metavar <= 0 conclude if( 0 <= - metavar var x end metavar + - metavar var y end metavar , - metavar var x end metavar + - metavar var y end metavar , - - metavar var x end metavar + - metavar var y end metavar ) <= if( 0 <= - metavar var x end metavar , - metavar var x end metavar , - - metavar var x end metavar ) + if( 0 <= - metavar var y end metavar , - metavar var y end metavar , - - metavar var y end metavar ) cut lemma splitNumericalSumHelper modus ponens if( 0 <= - metavar var x end metavar + - metavar var y end metavar , - metavar var x end metavar + - metavar var y end metavar , - - metavar var x end metavar + - metavar var y end metavar ) <= if( 0 <= - metavar var x end metavar , - metavar var x end metavar , - - metavar var x end metavar ) + if( 0 <= - metavar var y end metavar , - metavar var y end metavar , - - metavar var y end metavar ) conclude if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) + if( 0 <= metavar var y end metavar , metavar var y 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,