Well Quasi Orders

Well-Quasi-Orders. Based on Isabelle/HOL’s type class for preorders, we introduce a type class for well-quasi-orders (wqo) which is characterized by the absence of ”bad” sequences (our proofs are along the lines of the proof of Nash-Williams, from which we also borrow terminology). Our main results are instantiations for the product type, the list type, and a type of finite trees, which (almost) directly follow from our proofs of (1) Dickson’s Lemma, (2) Higman’s Lemma, and (3) Kruskal’s Tree Theorem. More concretely: If the sets A and B are wqo then their Cartesian product is wqo. If the set A is wqo then the set of finite lists over A is wqo. If the set A is wqo then the set of finite trees over A is wqo.

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