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Symbolic-arithmetic

Aabf-loghead-ns

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

Definitions and Theorems

Function: aabf-loghead-ns

(defun aabf-loghead-ns (n x)
  (declare (xargs :guard (and (natp n) (true-listp x))))
  (declare (xargs :guard (and)))
  (let ((__function__ 'aabf-loghead-ns))
    (declare (ignorable __function__))
    (b* (((when (zp n)) (list (aabf-false)))
         ((mv head tail ?end)
          (aabf-first/rest/end x)))
      (aabf-scons head (aabf-loghead-ns (1- n) tail)))))

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

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

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

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

Theorem: aabf-p-of-aabf-loghead-ns

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

Theorem: aabf-eval-of-aabf-loghead-ns

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

Theorem: aabf-pred-of-aabf-loghead-ns

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