Completeness theorem for parse-*digit-star-*digit.
Theorem:
(defthm parse-*digit-star-*digit-when-tree-match (implies (and (tree-match-element-p tree (!_ (/_ (*_ *digit*) "*" (*_ *digit*))) *grammar*) (tree-terminatedp tree) (mv-nth 0 (parse-digit rest-input))) (equal (parse-*digit-star-*digit (append (tree->string tree) rest-input)) (mv nil (tree-fix tree) (nat-list-fix rest-input)))))