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Sbyte16

Sbyte16p

Recognizer for sbyte16.

Signature
(sbyte16p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sbyte16p

(defun sbyte16p (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p 16 x)
       :exec (and (integerp x)
                  (<= -32768 x)
                  (< x 32768))))

Theorem: booleanp-of-sbyte16p

(defthm booleanp-of-sbyte16p
  (b* ((yes/no (sbyte16p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte16p-forward-signed-byte-p

(defthm sbyte16p-forward-signed-byte-p
  (implies (sbyte16p x)
           (signed-byte-p 16 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte16p

(defthm signed-byte-p-rewrite-sbyte16p
  (equal (signed-byte-p 16 x)
         (sbyte16p x)))

Theorem: integerp-when-sbyte16p

(defthm integerp-when-sbyte16p
  (implies (sbyte16p x) (integerp x))
  :rule-classes :compound-recognizer)