Proving equality between foldl recursive and iterative fold
The two definitions are not equal. Consider $h$ defined by
\begin{align*}
h(c, a) = 10 \cdot c + a
\end{align*}
and $c = 0$. Then
$$\mathsf{foldl} \, (c,h) \, [1,2,3] = 321$$
but
$$\mathsf{fold}_{itr} \, (c,h) \, [1,2,3] = 123.$$