define pyk of lemma nonnegativeNumerical 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 n unicode small o unicode small n unicode small n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e 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 end of text end unicode text end text end define
define tex of lemma nonnegativeNumerical as text unicode start of text unicode capital n unicode small o unicode small n unicode small n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e 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 end of text end unicode text end text end define
define statement of lemma nonnegativeNumerical as system Q infer all metavar var x end metavar indeed 0 <= metavar var x end metavar infer if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = metavar var x end metavar end define
define proof of lemma nonnegativeNumerical as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed 0 <= metavar var x end metavar infer 1rule ifThenElse true modus ponens 0 <= metavar var x end metavar conclude if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = metavar var x end metavar cut 1rule repetition modus ponens if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = metavar var x end metavar conclude if( 0 <= metavar var x end metavar , metavar var x end metavar , - metavar var x end metavar ) = metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,