### Merge branch 'master' of gitlab.math.univ-paris-diderot.fr:beppe/occurrence-typing

parents 49beef11 06d91497
 ... ... @@ -217,7 +217,7 @@ \end{definition} \begin{definition}[(Pre)order on environments] Let $\Gamma$ and $\Gamma'$ two environments. We say that $\Gamma' \leq \Gamma$ iff: Let $\Gamma$ and $\Gamma'$ two environments. We write $\Gamma' \leq \Gamma$ iff: \begin{align*} &\Gamma'=\bot \text{ or } (\Gamma\neq\bot \text{ and } \forall e \in \dom \Gamma.\ \Gamma' \vdash e : \Gamma(e)) \end{align*} ... ... @@ -984,7 +984,7 @@ If $\Gamma = \bot$, we trivially have $\Gamma \vdash e:t$ with the rule \Rule{Efq}. Let's assume $\Gamma \neq \bot$. If $e=x$ a variable, then the last rule used is \Rule{Var\Aa}. If $e=x$ is a variable, then the last rule used is \Rule{Var\Aa}. We can derive $\Gamma \vdash x:t$ by using the rule \Rule{Env} and \Rule{Subs}. So let's assume that $e$ is not a variable. ... ... @@ -1002,7 +1002,7 @@ \item[$e=x$] Already treated. \item[$e=\lambda^{\bigwedge_{i\in I} \arrow {t_i}{s_i}}x.e'$] The last rule is \Rule{Abs\Aa}. We have $\arrow {t_i}{s_i} \leq t$. We have $\bigwedge_{i\in I} \arrow {t_i}{s_i} \leq t$. Using the definition of type schemes, let $t'=\bigwedge_{i\in I} \arrow {t_i}{s_i} \land \bigwedge_{j\in J} \neg \arrow {t'_j}{s'_j}$ such that $\Empty \neq t' \leq t$. The induction hypothesis gives, for all $i\in I$, $\Gamma,x:s_i\vdash e':t_i$. ... ...
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