Logiweb aspects of lemma splitNumericalSumHelper in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma splitNumericalSumHelper 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 capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma splitNumericalSumHelper as text unicode start of text unicode capital 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 capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma splitNumericalSumHelper as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed 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 ) 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

The user defined "the proof aspect" aspect

define proof of lemma splitNumericalSumHelper 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 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 ) infer lemma signNumerical conclude if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = if( 0 <= - metavar var x end metavar , - metavar var x end metavar , - - metavar var x end metavar ) cut lemma signNumerical conclude if( 0 <= metavar var y end metavar , metavar var y end metavar , - metavar var y end metavar ) = if( 0 <= - metavar var y end metavar , - metavar var y end metavar , - - metavar var y end metavar ) cut lemma addEquations modus ponens if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = if( 0 <= - metavar var x end metavar , - metavar var x end metavar , - - metavar var x end metavar ) modus ponens if( 0 <= metavar var y end metavar , metavar var y end metavar , - metavar var y 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 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 ) = 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 eqSymmetry modus ponens 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 ) = 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 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 ) = 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 -x-y=-(x+y) conclude - metavar var x end metavar + - metavar var y end metavar = - metavar var x end metavar + metavar var y end metavar cut lemma sameNumerical modus ponens - metavar var x end metavar + - metavar var y end metavar = - metavar var x 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 y end metavar , - metavar var x end metavar + metavar var y end metavar , - - metavar var x end metavar + metavar var y end metavar ) cut lemma signNumerical 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 y end metavar , - metavar var x end metavar + metavar var y end metavar , - - metavar var x end metavar + metavar var y end metavar ) cut lemma eqSymmetry 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 y end metavar , - metavar var x end metavar + metavar var y end metavar , - - metavar var x 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 y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) cut lemma eqTransitivity 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 y end metavar , - metavar var x end metavar + metavar var y end metavar , - - metavar var x end metavar + metavar var y end metavar ) 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 y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x 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 y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) cut lemma subLeqRight modus ponens 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 ) = 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 ) 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 ) cut lemma subLeqLeft 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 y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) 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