Logiweb aspects of lemma lessDivision in pyk

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The predefined "pyk" aspect

define pyk of lemma lessDivision 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 d unicode small i unicode small v unicode small i unicode small s 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 lessDivision as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital d unicode small i unicode small v unicode small i unicode small s 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 lessDivision 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 0 <= metavar var z 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 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 end define

The user defined "the proof aspect" aspect

define proof of lemma lessDivision 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 0 <= metavar var z 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 infer lemma fromLess modus ponens 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 conclude not0 metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar cut axiom leqMultiplication conclude 0 <= metavar var z end metavar imply metavar var y end metavar <= metavar var x end metavar imply metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar cut 1rule mp modus ponens 0 <= metavar var z end metavar imply metavar var y end metavar <= metavar var x end metavar imply metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar modus ponens 0 <= metavar var z end metavar conclude metavar var y end metavar <= metavar var x end metavar imply metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar cut prop lemma contrapositive modus ponens metavar var y end metavar <= metavar var x end metavar imply metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar conclude not0 metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar imply not0 metavar var y end metavar <= metavar var x end metavar cut 1rule mp modus ponens not0 metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar imply not0 metavar var y end metavar <= metavar var x end metavar modus ponens not0 metavar var y end metavar * metavar var z end metavar <= metavar var x end metavar * metavar var z end metavar conclude not0 metavar var y end metavar <= metavar var x end metavar cut lemma toLess modus ponens not0 metavar var y end metavar <= metavar var x end metavar conclude not0 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar end quote state proof state cache var c end expand end define