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
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
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
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
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,