Logiweb aspects of lemma neqNegated in pyk

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The predefined "pyk" aspect

define pyk of lemma neqNegated 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 n unicode small e unicode small q unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma neqNegated as text unicode start of text unicode capital n unicode small e unicode small q unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma neqNegated 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 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 neqNegated 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 infer - metavar var x end metavar = - metavar var y end metavar infer lemma eqNegated modus ponens - metavar var x end metavar = - metavar var y end metavar conclude - - metavar var x end metavar = - - metavar var y end metavar cut lemma doubleMinus conclude - - metavar var x end metavar = metavar var x end metavar cut lemma eqSymmetry modus ponens - - metavar var x end metavar = metavar var x end metavar conclude metavar var x end metavar = - - metavar var x end metavar cut lemma doubleMinus conclude - - metavar var y end metavar = metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar = - - metavar var x end metavar modus ponens - - metavar var x end metavar = - - metavar var y end metavar modus ponens - - metavar var y end metavar = metavar var y end metavar conclude metavar var x end metavar = metavar var y end metavar cut prop lemma from contradiction modus ponens metavar var x end metavar = metavar var y end metavar modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude not0 - metavar var x end metavar = - metavar var y 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 not0 metavar var x end metavar = metavar var y end metavar infer - metavar var x end metavar = - metavar var y end metavar infer not0 - metavar var x end metavar = - metavar var y end metavar conclude not0 metavar var x end metavar = metavar var y end metavar imply - metavar var x end metavar = - metavar var y end metavar imply not0 - metavar var x end metavar = - metavar var y end metavar cut not0 metavar var x end metavar = metavar var y end metavar infer 1rule mp modus ponens not0 metavar var x end metavar = metavar var y end metavar imply - metavar var x end metavar = - metavar var y end metavar imply not0 - metavar var x end metavar = - metavar var y end metavar modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude - metavar var x end metavar = - metavar var y end metavar imply not0 - metavar var x end metavar = - metavar var y end metavar cut prop lemma imply negation modus ponens - metavar var x end metavar = - metavar var y end metavar imply 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