Mapping/Composition/Associativity/Fact/Proof/Exercise

Let ${}L,M,N$ and ${}P$ be sets and let

$F\colon L\longrightarrow M,x\longmapsto F(x),$

$G\colon M\longrightarrow N,y\longmapsto G(y),$

and

$H\colon N\longrightarrow P,z\longmapsto H(z),$

be functions. Show that

${}H\circ (G\circ F)=(H\circ G)\circ F\,.$

To solution