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