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Symbolic-arithmetic

Aabf-logtail-ns

Signature
(aabf-logtail-ns place x) → xx
Arguments: place — Guard (natp place).; x — Guard (true-listp x).

Definitions and Theorems

Function: aabf-logtail-ns

(defun aabf-logtail-ns (place x)
  (declare (xargs :guard (and (natp place) (true-listp x))))
  (declare (xargs :guard (and)))
  (let ((__function__ 'aabf-logtail-ns))
    (declare (ignorable __function__))
    (if (or (zp place) (s-endp x))
        (llist-fix x)
      (aabf-logtail-ns (1- place) (scdr x)))))

Theorem: trivial-theorem-about-aabf-logtail-ns

(defthm trivial-theorem-about-aabf-logtail-ns
  (b* nil
    (b* ((?ignore (aabf-logtail-ns place x)))
      t))
  :rule-classes nil)

Theorem: true-listp-of-aabf-logtail-ns.xx

(defthm true-listp-of-aabf-logtail-ns.xx
  (b* ((?xx (aabf-logtail-ns place x)))
    (true-listp xx))
  :rule-classes :type-prescription)

Theorem: aabf-p-of-aabf-logtail-ns

(defthm aabf-p-of-aabf-logtail-ns
  (b* ((xx (aabf-logtail-ns place x)))
    (implies (and (aabflist-p x man))
             (and (aabflist-p xx man)))))

Theorem: aabf-eval-of-aabf-logtail-ns

(defthm aabf-eval-of-aabf-logtail-ns
 (b* ((xx (aabf-logtail-ns place x)))
  (implies
   (and (aabflist-p x man))
   (and (equal (bools->int (aabflist-eval xx env man))
               (logtail (nfix place)
                        (bools->int (aabflist-eval x env man))))))))

Theorem: aabf-pred-of-aabf-logtail-ns

(defthm aabf-pred-of-aabf-logtail-ns
  (b* ((xx (aabf-logtail-ns place x)))
    (implies (and (aabflist-p x man)
                  (aabflist-pred x man))
             (and (aabflist-pred xx man)))))