Mapping/Composition/Associativity/Fact

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 mappings.

Then

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

holds.

Proof, Write another proof