Add theorem's definition to have more context

This commit is contained in:
Dionisio E Alonso 2019-07-17 19:45:11 -03:00
parent ca90fb565e
commit 54ad0a7726
1 changed files with 11 additions and 6 deletions

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@ -6,17 +6,22 @@
\renewcommand{\familydefault}{\sfdefault}
\pagestyle{empty}
\begin{document}
\[
e = \lambda v.e_0
\]
\paragraph{Teo Sustitución (cálculo-\(\lambda\) eager):} Si \(\llbracket\delta
w\rrbracket\eta = \eta'w\) para todo \(w \in \textit{FV}(e)\), entonces
\(\llbracket e/_\delta\rrbracket\eta = \llbracket e\rrbracket \eta'\)
\underline{Caso \(e = \lambda v.\, e_0\)}:
\begin{align*}
\llbracket(\lambda v.e_0)_{/\delta}\rrbracket\eta &= \llbracket\lambda v_{new} {e_0}_{/[\delta | v:v_{new}]}\rrbracket\eta \label{eq:1}\tag{1}\\
&= (\iota_\bot \circ \Psi)(\lambda d. \llbracket{e_0}_{/[\delta | v: v_{new}]}\rrbracket [\eta | v_{new}: d])
\end{align*}
\eqref{eq:1} donde \(v_{new} \notin \bigcup_{w\in FV(e_0)-\{v\}}FV(\delta w)\)
\noindent\rule{2cm}{0.4pt}
\rule{2cm}{0.4pt}
\[\llbracket\lambda v. e_0\rrbracket\eta' = (\iota_\bot \circ \Psi)(\lambda d. \llbracket e_0\rrbracket[\eta' | v: d])\]
debemos ver que:
@ -30,7 +35,7 @@ p/usar \(H.I.\)
&= \iota_\bot d
\end{align*}
\noindent\rule{2cm}{0.4pt}
\rule{2cm}{0.4pt}
\[\iota_\bot \eta'_0 w = \iota_\bot[\eta' | v: d]w \underset{\mathclap{\overbrace{\text{si}\, v=w}{}}}{=} \iota_\bot d\]
@ -39,4 +44,4 @@ p/usar \(H.I.\)
\[\iota_\bot[\eta'| v: d]w \underset{\mathclap{\overbrace{v\neq w}{}}}{=} \boxed{\iota_\bot\eta'w}\]
\end{document}
\end{document}