We will write Δ(m,n) for the set of order preserving functionswith source m and target n.
Let f ∈ ∆(k, n), g ∈ ∆(m, n), and h ∈ ∆(n, p). Suppose im f = img. Prove that im(h ◦ f) = im(h ◦ g).
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