Input decomposition theorem for parse-in-either-range.
Theorem:
(defthm input-decomposition-of-parse-in-either-range (b* (((mv error? tree? rest-input) (parse-in-either-range min1 max1 min2 max2 input))) (implies (not error?) (equal (append (tree->string tree?) rest-input) (nat-list-fix input)))))