Laboratoire de l'Informatique et du Parallélisme » Linear Arithmetic

\section{Completeness}

The main result of this section is the following:

\begin{theorem}

	\label{thm:completeness}

	For every $\mubci{i-1}$ program $f(\vec u ; \vec x)$ (which is in $\fphi i$), there is a $\Sigma_i$ formula $A_f(\vec u, \vec x)$ such that $\arith^i$ proves $\forall \vec u \in \normal . \forall \vec x \in \safe. \exists ! y \in \safe . A_f(\vec u , \vec x , y )$ and $\Nat \models \forall \vec u , \vec x. A(\vec u , \vec x , f(\vec u ; \vec x))$.

\end{theorem}