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• Modnamelist-p

Modnamelist-p-basics

Basic theorems about modnamelist-p, generated by std::deflist.

Definitions and Theorems

Theorem: modnamelist-p-of-cons

(defthm modnamelist-p-of-cons
  (equal (modnamelist-p (cons acl2::a x))
         (and (modname-p acl2::a)
              (modnamelist-p x)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-cdr-when-modnamelist-p

(defthm modnamelist-p-of-cdr-when-modnamelist-p
  (implies (modnamelist-p (double-rewrite x))
           (modnamelist-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-when-not-consp

(defthm modnamelist-p-when-not-consp
  (implies (not (consp x))
           (equal (modnamelist-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: modname-p-of-car-when-modnamelist-p

(defthm modname-p-of-car-when-modnamelist-p
  (implies (modnamelist-p x)
           (iff (modname-p (car x)) (consp x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-modnamelist-p-compound-recognizer

(defthm true-listp-when-modnamelist-p-compound-recognizer
  (implies (modnamelist-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: modnamelist-p-of-list-fix

(defthm modnamelist-p-of-list-fix
  (implies (modnamelist-p x)
           (modnamelist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-rev

(defthm modnamelist-p-of-rev
  (equal (modnamelist-p (rev x))
         (modnamelist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-repeat

(defthm modnamelist-p-of-repeat
  (iff (modnamelist-p (repeat acl2::n x))
       (or (modname-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-append

(defthm modnamelist-p-of-append
  (equal (modnamelist-p (append acl2::a acl2::b))
         (and (modnamelist-p (list-fix acl2::a))
              (modnamelist-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-take

(defthm modnamelist-p-of-take
  (implies (modnamelist-p (double-rewrite x))
           (iff (modnamelist-p (take acl2::n x))
                (or (modname-p nil)
                    (<= (nfix acl2::n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: modnamelist-p-of-butlast

(defthm modnamelist-p-of-butlast
  (implies (modnamelist-p (double-rewrite x))
           (modnamelist-p (butlast x acl2::n)))
  :rule-classes ((:rewrite)))