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• Svstmt-writelist-p

Svstmt-writelist-p-basics

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

Definitions and Theorems

Theorem: svstmt-writelist-p-of-cons

(defthm svstmt-writelist-p-of-cons
  (equal (svstmt-writelist-p (cons acl2::a x))
         (and (svstmt-write-p acl2::a)
              (svstmt-writelist-p x)))
  :rule-classes ((:rewrite)))

Theorem: svstmt-writelist-p-of-cdr-when-svstmt-writelist-p

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

Theorem: svstmt-writelist-p-when-not-consp

(defthm svstmt-writelist-p-when-not-consp
  (implies (not (consp x))
           (svstmt-writelist-p x))
  :rule-classes ((:rewrite)))

Theorem: svstmt-write-p-of-car-when-svstmt-writelist-p

(defthm svstmt-write-p-of-car-when-svstmt-writelist-p
  (implies (svstmt-writelist-p x)
           (iff (svstmt-write-p (car x))
                (or (consp x) (svstmt-write-p nil))))
  :rule-classes ((:rewrite)))

Theorem: svstmt-writelist-p-of-append

(defthm svstmt-writelist-p-of-append
  (equal (svstmt-writelist-p (append acl2::a acl2::b))
         (and (svstmt-writelist-p acl2::a)
              (svstmt-writelist-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: svstmt-writelist-p-of-list-fix

(defthm svstmt-writelist-p-of-list-fix
  (equal (svstmt-writelist-p (list-fix x))
         (svstmt-writelist-p x))
  :rule-classes ((:rewrite)))

Theorem: svstmt-writelist-p-of-rev

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

Theorem: svstmt-writelist-p-of-repeat

(defthm svstmt-writelist-p-of-repeat
  (iff (svstmt-writelist-p (repeat acl2::n x))
       (or (svstmt-write-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: svstmt-writelist-p-of-butlast

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