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Representation-of-integer-conversions

Sshort-from-ullong

Convert from type unsigned long long to type signed short.

Signature
(sshort-from-ullong x) → result
Arguments: x — Guard (ullongp x).
Returns: result — Type (sshortp result).

Definitions and Theorems

Function: sshort-from-ullong

(defun sshort-from-ullong (x)
  (declare (xargs :guard (ullongp x)))
  (declare (xargs :guard (sshort-from-ullong-okp x)))
  (let ((__function__ 'sshort-from-ullong))
    (declare (ignorable __function__))
    (sshort-from-integer (integer-from-ullong x))))

Theorem: sshortp-of-sshort-from-ullong

(defthm sshortp-of-sshort-from-ullong
  (b* ((result (sshort-from-ullong x)))
    (sshortp result))
  :rule-classes :rewrite)

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

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

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

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