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