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Daniel Hillerström
2021-05-27 00:50:09 +01:00
parent e84b4605c2
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thesis.tex
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@@ -14545,7 +14545,7 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
% %
\begin{derivation} \begin{derivation}
& \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}\\ & \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}\\
=\reducesto^\ast& \reason{\semlab{Op} ($\ell \notin \BL(\sdtrans{\EC})$), $2\times$\semlab{Let},\semlab{Split},\semlab{App}, Lemma~\ref{lem:sdtrans-subst}}\\ =\reducesto^+& \reason{\semlab{Op} ($\ell \notin \BL(\sdtrans{\EC})$), $2\times$\semlab{Let},\semlab{Split},\semlab{App}, Lemma~\ref{lem:sdtrans-subst}}\\
&\sdtrans{N_\ell[\lambda x. &\sdtrans{N_\ell[\lambda x.
\bl \bl
\Let\;z \revto (\lambda y.\Handle\;\EC[\Return\;y]\;\With\;H)~x\;\In\\ \Let\;z \revto (\lambda y.\Handle\;\EC[\Return\;y]\;\With\;H)~x\;\In\\
@@ -14588,9 +14588,16 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
\sdtrans{\EC}[\Return\;W]$. \sdtrans{\EC}[\Return\;W]$.
\item Inductive step: Assume $M' \reducesto M''$ and \item Inductive step: Assume $M' \reducesto M''$ and
$M'' \approxa \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}$. Take $N' = M''$ then by the induction hypothesis $M' \reducesto N'$ $M'' \approxa \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}$. Using a similar argument to above we get that
\[
\item Inductive step: Assume $admin(\EC)$ and \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}
\reducesto^+ \sdtrans{N_\ell[V/p,\lambda y.\EC[\Return\;y]/r]}.
\]
Take $N' = M''$ then by the first induction hypothesis
$M' \reducesto N'$ and by the second induction hypothesis
$N' \approxa \sdtrans{N_\ell[V/p,\lambda y.\EC[\Return\;y]/r]}$ as
desired.
\item Inductive step: Assume $admin(\EC')$ and
$M'' \approxa \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}$. $M'' \approxa \sdtrans{\ShallowHandle\;\EC[\Do\;\ell~V]\;\With\;H}$.
\end{enumerate} \end{enumerate}
\end{proof} \end{proof}