Logiweb aspects of lemma neqAddition in pyk

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The predefined "pyk" aspect

define pyk of lemma neqAddition 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 a unicode small d unicode small d unicode small i 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 neqAddition as text unicode start of text unicode capital n unicode small e unicode small q unicode capital a unicode small d unicode small d unicode small i 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 neqAddition 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 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 end define

The user defined "the proof aspect" aspect

define proof of lemma neqAddition 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 metavar var x end metavar = metavar var y end metavar infer metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar infer lemma eqReflexivity conclude metavar var z end metavar = metavar var z end metavar cut lemma subtractEquations modus ponens metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar modus ponens metavar var z end metavar = metavar var z 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 z end metavar = metavar var y end metavar + metavar var z end metavar cut all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var x end metavar = metavar var y end metavar infer 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 z end metavar = metavar var y end metavar + metavar var z end metavar conclude not0 metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar imply not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z 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 z end metavar = metavar var y end metavar + metavar var z end metavar imply not0 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 y end metavar conclude metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar imply not0 metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar cut prop lemma imply negation modus ponens metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar imply 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 end quote state proof state cache var c end expand end define