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clean up latex junk
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digama0 committed Mar 17, 2018
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2 changes: 1 addition & 1 deletion Wtypes.tex
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Expand Up @@ -53,7 +53,7 @@ \section{Reduction of inductive types to $\W$-types}
1\le\ell\quad \Gamma\vdash C:\alpha\to\U_\ell\\
\Gamma\vdash e:\forall x:\alpha.\; (\forall y:\alpha.\;r\;y\;x\to\acc_r\;y)\to (\forall y:\alpha.\;r\;y\;x\to C\;y)\to C\;x
\end{matrix}}{\Gamma\vdash \rec_\acc\;e:\forall x:\alpha.\;\acc_r\;x\to C\;x}$$
All of these could have been defined as inductive types in the sense of section \ref{inductive}:
All of these could have been defined as inductive types in the sense of section \ref{sec:inductive}:
\begin{align*}
\bot&:=\mu t:\P.\;0\\
\Sigma x:\alpha.\;\beta&:=\mu t:\U_{\max(\ell,\ell',1)}.\;(\mathsf{pair}:\forall x:\alpha.\;\beta\to t)\\
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88 changes: 0 additions & 88 deletions aliascnt.sty

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132 changes: 0 additions & 132 deletions history.txt

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2 changes: 1 addition & 1 deletion intro.tex
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@@ -1,2 +1,2 @@
\section{Introduction}
UNFINISHED
In this paper, we develop the foundational theory used in the Lean theorem prover.
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