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Representation-of-integer-conversions

Ushort-from-ulong

Convert from type unsigned long to type unsigned short.

Signature
(ushort-from-ulong x) → result
Arguments: x — Guard (ulongp x).
Returns: result — Type (ushortp result).

Definitions and Theorems

Function: ushort-from-ulong

(defun ushort-from-ulong (x)
  (declare (xargs :guard (ulongp x)))
  (let ((__function__ 'ushort-from-ulong))
    (declare (ignorable __function__))
    (ushort-from-integer-mod (integer-from-ulong x))))

Theorem: ushortp-of-ushort-from-ulong

(defthm ushortp-of-ushort-from-ulong
  (b* ((result (ushort-from-ulong x)))
    (ushortp result))
  :rule-classes :rewrite)

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

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

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

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