One can check that every tree which is finite is also finite-order. The following propositions are true: (1) For every decorated tree t holds t ε = t. (2) For every tree t and for all finite sequences p, q of elements of such that p q ∈ t holds t (p q) = t p q. (3) Let t be a decorated tree and let p, q be finite sequences of elements of . If p q ∈ dom t, then t (p q) = t p q. A decorated tree ...