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Representation-of-integers

Integer-from-slong

Accessor for values of type signed long.

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

Definitions and Theorems

Function: integer-from-slong

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

Theorem: slong-integerp-of-integer-from-slong

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

Theorem: slong-from-integer-of-integer-from-slong

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

Theorem: integer-from-slong-of-slong-from-integer

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

Theorem: integer-from-slong-upper-bound

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

Theorem: integer-from-slong-lower-bound

(defthm integer-from-slong-lower-bound
  (>= (integer-from-slong x) (slong-min))
  :rule-classes :linear)

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

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

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

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