EDB — 27Y

\[ ∀ n,m,k∈ℕ\quad ,\quad (n+m)+h=n+(m+h)\quad ; \]

\[ P(n)≐ ∀ m,k∈ℕ\quad ,\quad (n+m)+h=n+(m+h)\quad ; \]

\[ P(S(n))≐ ∀ m,k∈ℕ\quad ,\quad (S(n)+m)+h\stackrel?=S(n)+(m+h)\quad ; \]

\begin{equation*} S(h) + n = S(h+n)= h + S(n) \end{equation*}

\begin{eqnarray*} (S(n)+m)+h \stackrel{\text{\scriptsize per \href{@URLPLACEHOLDER91HDLP@27P}{{\texttt{\scriptsize [({4.15})]}}}}}{=} S\Big((n+m)+h\Big) \stackrel{P(n)}{=} S\Big(n+(m+h)\Big) \stackrel{\text{\scriptsize per \href{@URLPLACEHOLDER91HDLP@27P}{{\texttt{\scriptsize [({4.15})]}}}}}{=} S(n)+(m+h) \end{eqnarray*}