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Sshort-integer

Sshort-integerp

Recognizer for sshort-integer.

Signature
(sshort-integerp x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sshort-integerp

(defun sshort-integerp (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p (short-bits) x)
       :exec (and (integerp x)
                  (<= (- (expt 2 (1- (short-bits)))) x)
                  (< x (expt 2 (1- (short-bits)))))))

Theorem: booleanp-of-sshort-integerp

(defthm booleanp-of-sshort-integerp
  (b* ((yes/no (sshort-integerp x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sshort-integerp-forward-signed-byte-p

(defthm sshort-integerp-forward-signed-byte-p
  (implies (sshort-integerp x)
           (signed-byte-p (short-bits) x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sshort-integerp

(defthm signed-byte-p-rewrite-sshort-integerp
  (equal (signed-byte-p (short-bits) x)
         (sshort-integerp x)))

Theorem: integerp-when-sshort-integerp

(defthm integerp-when-sshort-integerp
  (implies (sshort-integerp x)
           (integerp x))
  :rule-classes :compound-recognizer)