associativity of function composition
1. Proposition
Let \(A,B,C,D\) be sets and \(f: A \rightarrow B, g: B \rightarrow C, h: C \rightarrow D\) be maps. Then
\begin{align*} (f \circ g) \circ h =& f \circ (g \circ h) \end{align*}i.e. composition of maps is associative.