Completeness property for parse-group.
Theorem:
(defthm pred-group-necc (implies (pred-group input) (implies (and (tree-match-element-p tree (element-rulename *group*) *grammar*) (tree-terminatedp tree) (nat-listp rest-input) (equal input (append (tree->string tree) rest-input))) (equal (parse-group (append (tree->string tree) rest-input)) (mv nil (tree-fix tree) rest-input)))))
Theorem:
(defthm booleanp-of-pred-group (b* ((bool (pred-group input))) (booleanp bool)) :rule-classes :type-prescription)