Basic theorems about equiv-contextslist-p, generated by std::deflist.
Theorem:
(defthm equiv-contextslist-p-of-cons (equal (equiv-contextslist-p (cons a x)) (and (equiv-contextsp a) (equiv-contextslist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextslist-p-of-cdr-when-equiv-contextslist-p (implies (equiv-contextslist-p (double-rewrite x)) (equiv-contextslist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextslist-p-when-not-consp (implies (not (consp x)) (equal (equiv-contextslist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextsp-of-car-when-equiv-contextslist-p (implies (equiv-contextslist-p x) (iff (equiv-contextsp (car x)) (or (consp x) (equiv-contextsp nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-equiv-contextslist-p-compound-recognizer (implies (equiv-contextslist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm equiv-contextslist-p-of-list-fix (implies (equiv-contextslist-p x) (equiv-contextslist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextslist-p-of-append (equal (equiv-contextslist-p (append a b)) (and (equiv-contextslist-p (list-fix a)) (equiv-contextslist-p b))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextslist-p-of-take (implies (equiv-contextslist-p (double-rewrite x)) (iff (equiv-contextslist-p (take n x)) (or (equiv-contextsp nil) (<= (nfix n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm equiv-contextslist-p-of-nthcdr (implies (equiv-contextslist-p (double-rewrite x)) (equiv-contextslist-p (nthcdr n x))) :rule-classes ((:rewrite)))