Usually proved by minimal bad sequence arguments. Besides Cartesian product Higman (a), There is Higman (b) re injective order-preserving finite subsequences, and Higman (c) which says that if Q is a wqo then the finite subsets of Q are wqo by injective order-preserving maps. There could be further Higman (d) and beyond.
Higman's Lemma is basic to WQO theory, but has many specific forms, for example: the Cartesian product of two wqos is a wqo. Any new extensions?
michael fellows
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