define pyk of lemma insertMiddleTerm(Difference) 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 d unicode small i unicode small f unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma insertMiddleTerm(Difference) 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 d unicode small i unicode small f unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma insertMiddleTerm(Difference) 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 y end metavar + metavar var z end metavar end define
define proof of lemma insertMiddleTerm(Difference) 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 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 doubleMinus conclude - - metavar var z end metavar = metavar var z end metavar cut lemma eqAdditionLeft modus ponens - - metavar var z end metavar = metavar var z end metavar conclude metavar var x end metavar + - - metavar var z end metavar = metavar var x end metavar + metavar var z end metavar cut axiom plusCommutativity conclude - metavar var z end metavar + - metavar var y end metavar = - metavar var y end metavar + - metavar var z end metavar cut lemma -x-y=-(x+y) conclude - metavar var y end metavar + - metavar var z end metavar = - metavar var y end metavar + metavar var z end metavar cut lemma eqTransitivity modus ponens - metavar var z end metavar + - metavar var y end metavar = - metavar var y end metavar + - metavar var z end metavar modus ponens - metavar var y end metavar + - metavar var z end metavar = - metavar var y end metavar + metavar var z end metavar conclude - metavar var z end metavar + - metavar var y end metavar = - metavar var y end metavar + metavar var z end metavar cut lemma addEquations modus ponens metavar var x end metavar + - - metavar var z end metavar = metavar var x end metavar + metavar var z end metavar modus ponens - metavar var z end metavar + - metavar var y end metavar = - metavar var y end metavar + metavar var z 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 y end metavar + metavar var z 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 y 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 y end metavar + metavar var z end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,