Logiweb aspects of lemma three2threeTerms in pyk

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The predefined "pyk" aspect

define pyk of lemma three2threeTerms 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 h unicode small r unicode small e unicode small e unicode two unicode small t unicode small h unicode small r unicode small e unicode small e unicode capital t unicode small e unicode small r unicode small m unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma three2threeTerms as text unicode start of text unicode capital t unicode small h unicode small r unicode small e unicode small e unicode two unicode small t unicode small h unicode small r unicode small e unicode small e unicode capital t unicode small e unicode small r unicode small m 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 three2threeTerms 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 metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma three2threeTerms 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 axiom plusCommutativity conclude metavar var y end metavar + metavar var z end metavar = metavar var z end metavar + metavar var y end metavar cut lemma three2twoTerms modus ponens metavar var y end metavar + metavar var z end metavar = metavar var z end metavar + metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar cut axiom plusAssociativity conclude metavar var x end metavar + metavar var z end metavar + metavar var y end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar + metavar var z end metavar + metavar var y end metavar = metavar var x end metavar + metavar var z 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 x end metavar + metavar var z end metavar + metavar var y end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar modus ponens metavar var x end metavar + metavar var z end metavar + metavar var y end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var z end metavar + metavar var y end metavar end quote state proof state cache var c end expand end define