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\subsection{Simple proofs by induction}
%CP Pourquoi ne pas commencer par des preuves d'egalite entre termes
% convertibles.
+\begin{coq_eval}
+Reset Initial.
+\end{coq_eval}
Let us now show how to do proofs by structural induction. We start with easy
properties of the \verb:plus: function we just defined. Let us first