Basic theorems about branch-listp, generated by std::deflist.
Theorem:
(defthm branch-listp-of-cons (equal (branch-listp (cons acl2::a acl2::x)) (and (branchp acl2::a) (branch-listp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm branch-listp-of-cdr-when-branch-listp (implies (branch-listp (double-rewrite acl2::x)) (branch-listp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm branch-listp-when-not-consp (implies (not (consp acl2::x)) (equal (branch-listp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm branchp-of-car-when-branch-listp (implies (branch-listp acl2::x) (iff (branchp (car acl2::x)) (consp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-branch-listp-compound-recognizer (implies (branch-listp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm branch-listp-of-list-fix (implies (branch-listp acl2::x) (branch-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm branch-listp-of-rev (equal (branch-listp (rev acl2::x)) (branch-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm branch-listp-of-append (equal (branch-listp (append acl2::a acl2::b)) (and (branch-listp (list-fix acl2::a)) (branch-listp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm branchp-of-nth-when-branch-listp (implies (branch-listp acl2::x) (iff (branchp (nth acl2::n acl2::x)) (< (nfix acl2::n) (len acl2::x)))) :rule-classes ((:rewrite)))