Logiweb aspects of lemma lessNeq in pyk

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The predefined "pyk" aspect

define pyk of lemma lessNeq 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 n unicode small e unicode small q unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma lessNeq as text unicode start of text unicode capital l unicode small e unicode small s unicode small s unicode capital n unicode small e unicode small q unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma lessNeq as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed 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 y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma lessNeq 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 metavar var x end metavar <= metavar var y end metavar imply not0 not0 metavar var x end metavar = metavar var y end metavar infer 1rule repetition 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 imply not0 not0 metavar var x end metavar = metavar var y end metavar cut prop lemma second conjunct 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 end quote state proof state cache var c end expand end define