Logiweb aspects of lemma insertMiddleTerm(Sum) in pyk

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The predefined "pyk" aspect

define pyk of lemma insertMiddleTerm(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 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 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 insertMiddleTerm(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 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 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 insertMiddleTerm(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 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 end define

The user defined "the proof aspect" aspect

define proof of lemma insertMiddleTerm(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 lemma x=x+y-y conclude metavar var x end metavar = metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar cut lemma three2threeTerms conclude metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar = metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar modus ponens metavar var x end metavar + metavar var z end metavar + - metavar var z end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar conclude metavar var x end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar cut lemma eqAddition modus ponens metavar var x end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z 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 y end metavar cut axiom plusAssociativity 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 y end metavar cut lemma eqTransitivity 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 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 y end metavar end quote state proof state cache var c end expand end define