The structure of this theme sentence is what is significant to the theme of The Robber Bridegroom. In the first clause, "Jamie Lockhart is the bandit of the woods" notice that the subject is Jamie Lockhart and "the bandit of the woods" is the predicate nominative - that is, it is something in the predicate of the sentence that refers back to the subject (the verb is "is" - state of being verb). In the second clause, "The bandit of the woods is Jamie Lockhart" the subject is "The bandit of the woods" and the predicate nominative is "Jamie Lockhart." A bunch of grammar gobbeldygook, you say? Ah, but no!
A major theme in this work is the duality of human nature. Jamie is a handsome, well-respected gentlemen in society, but when he is "in the woods" he becomes someone else entirely - the robber bridegroom, painting his face to hide who he really is. So the structure of the theme sentence you identify reflects this concept. Jamie is the same person, but he appears on the stage of life in two different forms. Your theme sentence says the same thing, but in two different ways.
Very clever question!
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