Input decomposition theorem for parse-*-in-either-range.
Theorem:
(defthm input-decomposition-of-parse-*-in-either-range (b* (((mv & trees rest-input) (parse-*-in-either-range min1 max1 min2 max2 input))) (equal (append (tree-list->string trees) rest-input) (nat-list-fix input))))