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Bit-blasting

Svexlist-nth

Signature
(svexlist-nth n x) → elt
Arguments: n — Guard (natp n).; x — Guard (svexlist-p x).
Returns: elt — Type (svex-p elt).

Definitions and Theorems

Function: svexlist-nth

(defun svexlist-nth (n x)
  (declare (xargs :guard (and (natp n) (svexlist-p x))))
  (let ((__function__ 'svexlist-nth))
    (declare (ignorable __function__))
    (mbe :logic
         (if (< (nfix n) (len x))
             (svex-fix (nth n x))
           (svex-x))
         :exec (or (nth n x) (svex-x)))))

Theorem: svex-p-of-svexlist-nth

(defthm svex-p-of-svexlist-nth
  (b* ((elt (svexlist-nth n x)))
    (svex-p elt))
  :rule-classes :rewrite)

Theorem: svexlist-nth-out-of-bounds

(defthm svexlist-nth-out-of-bounds
  (implies (<= (len x) (nfix n))
           (equal (svexlist-nth n x) (svex-x))))

Theorem: svexlist-nth-in-of-bounds

(defthm svexlist-nth-in-of-bounds
  (implies (< (nfix n) (len x))
           (equal (svexlist-nth n x)
                  (svex-fix (nth n x)))))

Theorem: svexlist-nth-of-nfix-n

(defthm svexlist-nth-of-nfix-n
  (equal (svexlist-nth (nfix n) x)
         (svexlist-nth n x)))

Theorem: svexlist-nth-nat-equiv-congruence-on-n

(defthm svexlist-nth-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (svexlist-nth n x)
                  (svexlist-nth n-equiv x)))
  :rule-classes :congruence)

Theorem: svexlist-nth-of-svexlist-fix-x

(defthm svexlist-nth-of-svexlist-fix-x
  (equal (svexlist-nth n (svexlist-fix x))
         (svexlist-nth n x)))

Theorem: svexlist-nth-svexlist-equiv-congruence-on-x

(defthm svexlist-nth-svexlist-equiv-congruence-on-x
  (implies (svexlist-equiv x x-equiv)
           (equal (svexlist-nth n x)
                  (svexlist-nth n x-equiv)))
  :rule-classes :congruence)