		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integers

Integer-from-ulong

Accessor for values of type unsigned long.

Signature
(integer-from-ulong x) → y
Arguments: x — Guard (ulongp x).
Returns: y — Type (ulong-integerp y).

Definitions and Theorems

Function: integer-from-ulong

(defun integer-from-ulong (x)
  (declare (xargs :guard (ulongp x)))
  (let ((__function__ 'integer-from-ulong))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (ulong-integer-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: ulong-integerp-of-integer-from-ulong

(defthm ulong-integerp-of-integer-from-ulong
  (b* ((y (integer-from-ulong x)))
    (ulong-integerp y))
  :rule-classes :rewrite)

Theorem: ulong-from-integer-of-integer-from-ulong

(defthm ulong-from-integer-of-integer-from-ulong
  (equal (ulong-from-integer (integer-from-ulong x))
         (ulong-fix x)))

Theorem: integer-from-ulong-of-ulong-from-integer

(defthm integer-from-ulong-of-ulong-from-integer
  (equal (integer-from-ulong (ulong-from-integer get))
         (ulong-integer-fix get)))

Theorem: integer-from-ulong-upper-bound

(defthm integer-from-ulong-upper-bound
  (<= (integer-from-ulong x) (ulong-max))
  :rule-classes :linear)

Theorem: integer-from-ulong-of-ulong-fix-x

(defthm integer-from-ulong-of-ulong-fix-x
  (equal (integer-from-ulong (ulong-fix x))
         (integer-from-ulong x)))

Theorem: integer-from-ulong-ulong-equiv-congruence-on-x

(defthm integer-from-ulong-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (integer-from-ulong x)
                  (integer-from-ulong x-equiv)))
  :rule-classes :congruence)