Basic theorems about namelist-p, generated by std::deflist.
Theorem:
(defthm namelist-p-of-cons (equal (namelist-p (cons acl2::a x)) (and (name-p acl2::a) (namelist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-cdr-when-namelist-p (implies (namelist-p (double-rewrite x)) (namelist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-when-not-consp (implies (not (consp x)) (equal (namelist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm name-p-of-car-when-namelist-p (implies (namelist-p x) (iff (name-p (car x)) (or (consp x) (name-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-namelist-p-compound-recognizer (implies (namelist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm namelist-p-of-list-fix (implies (namelist-p x) (namelist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-rev (equal (namelist-p (rev x)) (namelist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-repeat (iff (namelist-p (repeat acl2::n x)) (or (name-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-append (equal (namelist-p (append acl2::a acl2::b)) (and (namelist-p (list-fix acl2::a)) (namelist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-take (implies (namelist-p (double-rewrite x)) (iff (namelist-p (take acl2::n x)) (or (name-p nil) (<= (nfix acl2::n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm namelist-p-of-butlast (implies (namelist-p (double-rewrite x)) (namelist-p (butlast x acl2::n))) :rule-classes ((:rewrite)))