Logiweb aspects of lemma nonnegativeFactors in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma nonnegativeFactors 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 f unicode small a unicode small c unicode small t unicode small o unicode small r unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma nonnegativeFactors 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 f unicode small a unicode small c unicode small t unicode small o unicode small r unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma nonnegativeFactors as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed 0 <= metavar var x end metavar infer 0 <= metavar var y end metavar infer 0 <= metavar var x end metavar * metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma nonnegativeFactors 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 0 <= metavar var x end metavar infer 0 <= metavar var y end metavar infer lemma leqMultiplication modus ponens 0 <= metavar var y end metavar modus ponens 0 <= metavar var x end metavar conclude 0 * metavar var y end metavar <= metavar var x end metavar * metavar var y end metavar cut axiom timesCommutativity conclude 0 * metavar var y end metavar = metavar var y end metavar * 0 cut lemma x*0=0 conclude metavar var y end metavar * 0 = 0 cut lemma eqTransitivity modus ponens 0 * metavar var y end metavar = metavar var y end metavar * 0 modus ponens metavar var y end metavar * 0 = 0 conclude 0 * metavar var y end metavar = 0 cut lemma subLeqLeft modus ponens 0 * metavar var y end metavar = 0 modus ponens 0 * metavar var y end metavar <= metavar var x end metavar * metavar var y end metavar conclude 0 <= metavar var x end metavar * metavar var y end metavar end quote state proof state cache var c end expand end define