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Representation-of-integers

Sshort-from-integer

Constructor for values of type signed short.

Signature
(sshort-from-integer get) → y
Arguments: get — Guard (sshort-integerp get).
Returns: y — Type (sshortp y).

Definitions and Theorems

Function: sshort-from-integer

(defun sshort-from-integer (get)
  (declare (xargs :guard (sshort-integerp get)))
  (let ((__function__ 'sshort-from-integer))
    (declare (ignorable __function__))
    (b* ((get (mbe :logic (sshort-integer-fix get)
                   :exec get)))
      (cons :sshort (list get)))))

Theorem: sshortp-of-sshort-from-integer

(defthm sshortp-of-sshort-from-integer
  (b* ((y (sshort-from-integer get)))
    (sshortp y))
  :rule-classes :rewrite)

Theorem: sshort-from-integer-of-sshort-integer-fix-get

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

Theorem: sshort-from-integer-sshort-integer-equiv-congruence-on-get

(defthm sshort-from-integer-sshort-integer-equiv-congruence-on-get
  (implies (sshort-integer-equiv get get-equiv)
           (equal (sshort-from-integer get)
                  (sshort-from-integer get-equiv)))
  :rule-classes :congruence)