Proposition
16
[27Q]Addition is associative.
Proof
Consider
\[ P(h)β β n,mβ β, (n+m)+h = n+ (m+h)\quad ; \]
Obviously \(P(0)\) is true, moreover \(P(Sh)\) is proven (omitting β\(β n,mβ β\)β) like this
\begin{align*} (n+m)+Sh = S(n+m)+h = (Sn + m) + h \stackrel{P(n)}{=}\\ = Sn + (m + h) = n+ S (m+h)= n+ (m+Sh)\quad \qedhere \end{align*}