- 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.
[2012-06-11] Added Kruskal's Tree Theorem.
[2012-12-19] New variant of Kruskal's tree theorem for terms (as opposed to variadic terms, i.e., trees), plus finite version of the tree theorem as corollary.
[2013-05-16] Simplified construction of minimal bad sequences.
[2014-07-09] Simplified proofs of Higman's lemma and Kruskal's tree theorem, based on homogeneous sequences.
[2016-01-03] An alternative proof of Higman's lemma by open induction.
[2017-06-08] Proved (classical) equivalence to inductive definition of almost-full relations according to the ITP 2012 paper "Stop When You Are Almost-Full" by Vytiniotis, Coquand, and Wahlstedt.