Logiweb aspects of lemma insertTwoMiddleTerms(Sum) in pyk

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The predefined "pyk" aspect

define pyk of lemma insertTwoMiddleTerms(Sum) 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 i unicode small n unicode small s unicode small e unicode small r unicode small t unicode capital t unicode small w unicode small o unicode capital m unicode small i unicode small d unicode small d unicode small l unicode small e unicode capital t unicode small e unicode small r unicode small m unicode small s unicode left parenthesis unicode capital s unicode small u unicode small m unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma insertTwoMiddleTerms(Sum) as text unicode start of text unicode small i unicode small n unicode small s unicode small e unicode small r unicode small t unicode capital t unicode small w unicode small o unicode capital m unicode small i unicode small d unicode small d unicode small l unicode small e unicode capital t unicode small e unicode small r unicode small m unicode small s unicode left parenthesis unicode capital s unicode small u unicode small m unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma insertTwoMiddleTerms(Sum) 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 all metavar var u end metavar indeed metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma insertTwoMiddleTerms(Sum) 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 all metavar var u end metavar indeed lemma insertMiddleTerm(Sum) conclude metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar cut lemma insertMiddleTerm(Sum) conclude metavar var z end metavar + metavar var y end metavar = metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar cut lemma eqAdditionLeft modus ponens metavar var z end metavar + metavar var y end metavar = metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar conclude metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar cut axiom plusAssociativity conclude metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar conclude metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z 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 z end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar modus ponens metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + - metavar var u end metavar + metavar var u end metavar + metavar var y end metavar end quote state proof state cache var c end expand end define