Logiweb aspects of lemma toNotLess in pyk

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The predefined "pyk" aspect

define pyk of lemma toNotLess 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 t unicode small o unicode capital n unicode small o unicode small t unicode capital l unicode small e unicode small s unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma toNotLess as text unicode start of text unicode small t unicode small o unicode capital n unicode small o unicode small t unicode capital l unicode small e unicode small s 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 toNotLess as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma toNotLess 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 metavar var x end metavar <= metavar var y end metavar infer metavar var y end metavar <= metavar var x end metavar infer lemma leqAntisymmetry modus ponens metavar var y end metavar <= metavar var x end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude metavar var y end metavar = metavar var x end metavar cut prop lemma add double neg modus ponens metavar var y end metavar = metavar var x end metavar conclude not0 not0 metavar var y end metavar = metavar var x end metavar cut all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar infer metavar var y end metavar <= metavar var x end metavar infer not0 not0 metavar var y end metavar = metavar var x end metavar conclude metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar cut metavar var x end metavar <= metavar var y end metavar infer 1rule mp modus ponens metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar cut prop lemma add double neg modus ponens metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar conclude not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar cut 1rule repetition modus ponens not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar conclude not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar cut 1rule repetition modus ponens not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar conclude not0 not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define