Basic theorems about perm4-list-p, generated by deflist.
Theorem:
(defthm perm4-list-p-of-cons (equal (perm4-list-p (cons acl2::a acl2::x)) (and (perm4p acl2::a) (perm4-list-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm perm4-list-p-of-cdr-when-perm4-list-p (implies (perm4-list-p (double-rewrite acl2::x)) (perm4-list-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm perm4-list-p-when-not-consp (implies (not (consp acl2::x)) (perm4-list-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm perm4p-of-car-when-perm4-list-p (implies (perm4-list-p acl2::x) (iff (perm4p (car acl2::x)) (or (consp acl2::x) (perm4p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm perm4-list-p-of-append (equal (perm4-list-p (append acl2::a acl2::b)) (and (perm4-list-p acl2::a) (perm4-list-p acl2::b))) :rule-classes ((:rewrite)))