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