$<\mathbb{N}$,+$>$ $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$<\mathbb{N}$, $\lambda$$x$,$y$. ($x$ =$_{0}$ $y$), $\lambda$$x$,$y$. $x$ $\leq$z $y$, $\lambda$$x$,$y$. $x$+$y$, 0, $\lambda$$x$.$x$$>$