Prove function composition is associative $f \circ h \circ g = (f \circ h) \circ g$
\[ \begin{align*} \mbox{let } g:a \rightarrow b, \quad f:b \rightarrow c, \quad h:c \rightarrow d \\ h \circ f \circ g &= h(f(g(a))):a \rightarrow d \\ (h \circ f )\circ g &= (h(f(b)):b \rightarrow d) \circ (g:a \rightarrow b) \\ &= h(f(g(a))):a \rightarrow d \\ \mbox{Thereforce, } h \circ f \circ g &= (h \circ f \circ) \circ g \end{align*} \]