mirror of https://gitlab.com/baco/l-c2019.git
Add theorem's definition to have more context
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@ -6,17 +6,22 @@
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\renewcommand{\familydefault}{\sfdefault}
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\pagestyle{empty}
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\begin{document}
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\[
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e = \lambda v.e_0
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\]
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\paragraph{Teo Sustitución (cálculo-\(\lambda\) eager):} Si \(\llbracket\delta
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w\rrbracket\eta = \eta'w\) para todo \(w \in \textit{FV}(e)\), entonces
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\(\llbracket e/_\delta\rrbracket\eta = \llbracket e\rrbracket \eta'\)
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\underline{Caso \(e = \lambda v.\, e_0\)}:
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\begin{align*}
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\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}\\
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&= (\iota_\bot \circ \Psi)(\lambda d. \llbracket{e_0}_{/[\delta | v: v_{new}]}\rrbracket [\eta | v_{new}: d])
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\end{align*}
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\eqref{eq:1} donde \(v_{new} \notin \bigcup_{w\in FV(e_0)-\{v\}}FV(\delta w)\)
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\noindent\rule{2cm}{0.4pt}
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\rule{2cm}{0.4pt}
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\[\llbracket\lambda v. e_0\rrbracket\eta' = (\iota_\bot \circ \Psi)(\lambda d. \llbracket e_0\rrbracket[\eta' | v: d])\]
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debemos ver que:
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@ -30,7 +35,7 @@ p/usar \(H.I.\)
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&= \iota_\bot d
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\end{align*}
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\noindent\rule{2cm}{0.4pt}
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\rule{2cm}{0.4pt}
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\[\iota_\bot \eta'_0 w = \iota_\bot[\eta' | v: d]w \underset{\mathclap{\overbrace{\text{si}\, v=w}{}}}{=} \iota_\bot d\]
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@ -39,4 +44,4 @@ p/usar \(H.I.\)
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\[\iota_\bot[\eta'| v: d]w \underset{\mathclap{\overbrace{v\neq w}{}}}{=} \boxed{\iota_\bot\eta'w}\]
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\end{document}
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\end{document}
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