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