Basic theorems about pseudo-command-landmark-listp, generated by std::deflist.

**Theorem: **

(defthm pseudo-command-landmark-listp-of-cons (equal (pseudo-command-landmark-listp (cons a x)) (and (pseudo-command-landmarkp a) (pseudo-command-landmark-listp x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-cdr-when-pseudo-command-landmark-listp (implies (pseudo-command-landmark-listp (double-rewrite x)) (pseudo-command-landmark-listp (cdr x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-when-not-consp (implies (not (consp x)) (equal (pseudo-command-landmark-listp x) (not x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmarkp-of-car-when-pseudo-command-landmark-listp (implies (pseudo-command-landmark-listp x) (iff (pseudo-command-landmarkp (car x)) (consp x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm true-listp-when-pseudo-command-landmark-listp-compound-recognizer (implies (pseudo-command-landmark-listp x) (true-listp x)) :rule-classes :compound-recognizer)

**Theorem: **

(defthm pseudo-command-landmark-listp-of-list-fix (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (list-fix x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-sfix (iff (pseudo-command-landmark-listp (set::sfix x)) (or (pseudo-command-landmark-listp x) (not (set::setp x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-insert (iff (pseudo-command-landmark-listp (set::insert a x)) (and (pseudo-command-landmark-listp (set::sfix x)) (pseudo-command-landmarkp a))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-delete (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (set::delete k x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-mergesort (iff (pseudo-command-landmark-listp (set::mergesort x)) (pseudo-command-landmark-listp (list-fix x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-union (iff (pseudo-command-landmark-listp (set::union x y)) (and (pseudo-command-landmark-listp (set::sfix x)) (pseudo-command-landmark-listp (set::sfix y)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-intersect-1 (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (set::intersect x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-intersect-2 (implies (pseudo-command-landmark-listp y) (pseudo-command-landmark-listp (set::intersect x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-difference (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (set::difference x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-duplicated-members (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (duplicated-members x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-rev (equal (pseudo-command-landmark-listp (rev x)) (pseudo-command-landmark-listp (list-fix x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-append (equal (pseudo-command-landmark-listp (append a b)) (and (pseudo-command-landmark-listp (list-fix a)) (pseudo-command-landmark-listp b))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-rcons (iff (pseudo-command-landmark-listp (rcons a x)) (and (pseudo-command-landmarkp a) (pseudo-command-landmark-listp (list-fix x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmarkp-when-member-equal-of-pseudo-command-landmark-listp (and (implies (and (member-equal a x) (pseudo-command-landmark-listp x)) (pseudo-command-landmarkp a)) (implies (and (pseudo-command-landmark-listp x) (member-equal a x)) (pseudo-command-landmarkp a))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-when-subsetp-equal (and (implies (and (subsetp-equal x y) (pseudo-command-landmark-listp y)) (equal (pseudo-command-landmark-listp x) (true-listp x))) (implies (and (pseudo-command-landmark-listp y) (subsetp-equal x y)) (equal (pseudo-command-landmark-listp x) (true-listp x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-set-difference-equal (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (set-difference-equal x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-intersection-equal-1 (implies (pseudo-command-landmark-listp (double-rewrite x)) (pseudo-command-landmark-listp (intersection-equal x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-intersection-equal-2 (implies (pseudo-command-landmark-listp (double-rewrite y)) (pseudo-command-landmark-listp (intersection-equal x y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-union-equal (equal (pseudo-command-landmark-listp (union-equal x y)) (and (pseudo-command-landmark-listp (list-fix x)) (pseudo-command-landmark-listp (double-rewrite y)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-take (implies (pseudo-command-landmark-listp (double-rewrite x)) (iff (pseudo-command-landmark-listp (take n x)) (or (pseudo-command-landmarkp nil) (<= (nfix n) (len x))))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-repeat (iff (pseudo-command-landmark-listp (repeat n x)) (or (pseudo-command-landmarkp x) (zp n))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmarkp-of-nth-when-pseudo-command-landmark-listp (implies (pseudo-command-landmark-listp x) (iff (pseudo-command-landmarkp (nth n x)) (< (nfix n) (len x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-update-nth (implies (pseudo-command-landmark-listp (double-rewrite x)) (iff (pseudo-command-landmark-listp (update-nth n y x)) (and (pseudo-command-landmarkp y) (or (<= (nfix n) (len x)) (pseudo-command-landmarkp nil))))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-butlast (implies (pseudo-command-landmark-listp (double-rewrite x)) (pseudo-command-landmark-listp (butlast x n))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-nthcdr (implies (pseudo-command-landmark-listp (double-rewrite x)) (pseudo-command-landmark-listp (nthcdr n x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-last (implies (pseudo-command-landmark-listp (double-rewrite x)) (pseudo-command-landmark-listp (last x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-remove (implies (pseudo-command-landmark-listp x) (pseudo-command-landmark-listp (remove a x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm pseudo-command-landmark-listp-of-revappend (equal (pseudo-command-landmark-listp (revappend x y)) (and (pseudo-command-landmark-listp (list-fix x)) (pseudo-command-landmark-listp y))) :rule-classes ((:rewrite)))