(**Thoughapencil-and-paperproofmightclockoutatthispoint,writing"by a routine induction on [e],"itturnsoutnottomakesensetoattackthisproofdirectly.Weneedtousethestandardtrickof%\index{strengtheningtheinductionhypothesis}%_strengtheningtheinductionhypothesis_.Wedothatbyprovinganauxiliarylemma,usingthecommand[Lemma]thatisasynonymfor[Theorem],conventionallyusedforlessimportanttheoremsthatappearintheproofsofprimarytheorems.%\index{Vernacularcommands!Lemma}%*)
(**Thoughapencil-and-paperproofmightclockoutatthispoint,writing"by a routine induction on [e],"itturnsoutnottomakesensetoattackthisproofdirectly.Weneedtousethestandardtrickof%\index{strengtheningtheinductionhypothesis}%_strengtheningtheinductionhypothesis_.Wedothatbyprovinganauxiliarylemma,usingthecommand[Lemma]thatisasynonymfor[Theorem],conventionallyusedforlessimportanttheoremsthatappearintheproofsofprimarytheorems.%\index{Vernacularcommands!Lemma}%*)