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Representation-of-integer-conversions

Sshort-from-ushort

Convert from type unsigned short to type signed short.

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

Definitions and Theorems

Function: sshort-from-ushort

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

Theorem: sshortp-of-sshort-from-ushort

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

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

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

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

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