Logiweb aspects of lemma positiveFactors in pyk

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The predefined "pyk" aspect

define pyk of lemma positiveFactors 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 p unicode small o unicode small s unicode small i 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 positiveFactors as text unicode start of text unicode capital p unicode small o unicode small s unicode small i 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 positiveFactors as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar infer not0 0 <= metavar var x end metavar * metavar var y end metavar imply not0 not0 0 = metavar var x end metavar * metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma positiveFactors 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 not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar infer 1rule repetition modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar cut prop lemma first conjunct modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude 0 <= metavar var x end metavar cut prop lemma second conjunct modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 0 = metavar var x end metavar cut lemma neqSymmetry modus ponens not0 0 = metavar var x end metavar conclude not0 metavar var x end metavar = 0 cut 1rule repetition modus ponens not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar conclude not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar cut prop lemma first conjunct modus ponens not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar conclude 0 <= metavar var y end metavar cut prop lemma second conjunct modus ponens not0 0 <= metavar var y end metavar imply not0 not0 0 = metavar var y end metavar conclude not0 0 = metavar var y end metavar cut lemma neqSymmetry modus ponens not0 0 = metavar var y end metavar conclude not0 metavar var y end metavar = 0 cut lemma nonnegativeFactors modus ponens 0 <= metavar var x end metavar modus ponens 0 <= metavar var y end metavar conclude 0 <= metavar var x end metavar * metavar var y end metavar cut lemma nonzeroFactors modus ponens not0 metavar var x end metavar = 0 modus ponens not0 metavar var y end metavar = 0 conclude not0 metavar var x end metavar * metavar var y end metavar = 0 cut lemma neqSymmetry modus ponens not0 metavar var x end metavar * metavar var y end metavar = 0 conclude not0 0 = metavar var x end metavar * metavar var y end metavar cut prop lemma join conjuncts modus ponens 0 <= metavar var x end metavar * metavar var y end metavar modus ponens not0 0 = metavar var x end metavar * metavar var y end metavar conclude not0 0 <= metavar var x end metavar * metavar var y end metavar imply not0 not0 0 = metavar var x end metavar * metavar var y end metavar cut 1rule repetition modus ponens not0 0 <= metavar var x end metavar * metavar var y end metavar imply not0 not0 0 = metavar var x end metavar * metavar var y end metavar conclude not0 0 <= metavar var x end metavar * metavar var y end metavar imply not0 not0 0 = metavar var x end metavar * metavar var y end metavar end quote state proof state cache var c end expand end define