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Representation-of-integers

Integer-from-ushort

Accessor for values of type unsigned short.

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

Definitions and Theorems

Function: integer-from-ushort

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

Theorem: ushort-integerp-of-integer-from-ushort

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

Theorem: ushort-from-integer-of-integer-from-ushort

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

Theorem: integer-from-ushort-of-ushort-from-integer

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

Theorem: integer-from-ushort-upper-bound

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

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

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

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

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