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Representation-of-integers

Integer-from-ullong

Accessor for values of type unsigned long long.

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

Definitions and Theorems

Function: integer-from-ullong

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

Theorem: ullong-integerp-of-integer-from-ullong

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

Theorem: ullong-from-integer-of-integer-from-ullong

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

Theorem: integer-from-ullong-of-ullong-from-integer

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

Theorem: integer-from-ullong-upper-bound

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

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

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

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

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