Proposition 1.5.12.  Let W, X, Y, Z be sets, f : W → X, g : X → Y, h : Y → Z be functions. Then:
(h ∘ g) ∘ f = h ∘ (g ∘ f)
Proof.  Let w ∈ W. Then (h ∘ g)(f(w)) = h(g(f(w))) = h((g ∘ f)(w)).
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