Completeness theorem for parse-rule.
Theorem:
(defthm parse-rule-when-tree-match (implies (and (tree-match-element-p tree (element-rulename *rule*) *grammar*) (tree-terminatedp tree) (mv-nth 0 (parse-wsp rest-input))) (equal (parse-rule (append (tree->string tree) rest-input)) (mv nil (tree-fix tree) (nat-list-fix rest-input)))))