Logiweb aspects of lemma lessMultiplication in pyk

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The predefined "pyk" aspect

define pyk of lemma lessMultiplication 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 l unicode small e unicode small s unicode small s unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma lessMultiplication as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma lessMultiplication as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar infer not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer not0 metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar imply not0 not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma lessMultiplication 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 all metavar var z end metavar indeed not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar infer not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer lemma lessLeq modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar <= metavar var y end metavar cut lemma lessLeq modus ponens not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar conclude 0 <= metavar var z end metavar cut lemma leqMultiplication modus ponens 0 <= metavar var z end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar cut lemma lessNeq modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar = metavar var y end metavar cut lemma lessNeq modus ponens not0 0 <= metavar var z end metavar imply not0 not0 0 = metavar var z end metavar conclude not0 0 = metavar var z end metavar cut lemma neqSymmetry modus ponens not0 0 = metavar var z end metavar conclude not0 metavar var z end metavar = 0 cut lemma neqMultiplication modus ponens not0 metavar var z end metavar = 0 modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar cut lemma leqNeqLess modus ponens metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar modus ponens not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar conclude not0 metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar imply not0 not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar end quote state proof state cache var c end expand end define