nested local scopes in latex, what up

\local{
  \newcommand\recel{\nonterm{recaccess}}
}{
  Let
  \[
  \ntHash\ntPosInt (\ntSExp) := \recel
  \]
  in the definitions that follow.

  \local{
    \newcommand\recty{\indexedTerms}
    \newcommand\posval{l}
    \newcommand\resty{\term_{\posval}}
  }{
    \[
    \typeRule{
      \curr \says \ntSExp \is \recty
    }{
      \curr \says \ntHash\posval (\ntSExp) \is \resty
    }
    \]
  }

  \local{
    \newcommand\elty{\term}
    \newcommand\inputty{\elty}
    \newcommand\returnty{()}
  }{
    \[
    \typeRule{
      \curr \says \recel \is \elty \andAlso
      \curr \says \ntSExp \is \inputty
    }{
      \curr \says \recel := \ntSExp \is \returnty
    }
    \]
  }
}