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Ushort-integer

Ushort-integerp

Recognizer for ushort-integer.

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

Definitions and Theorems

Function: ushort-integerp

(defun ushort-integerp (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p (short-bits) x)
       :exec (and (integerp x)
                  (<= 0 x)
                  (< x (expt 2 (short-bits))))))

Theorem: booleanp-of-ushort-integerp

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

Theorem: ushort-integerp-forward-unsigned-byte-p

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

Theorem: unsigned-byte-p-rewrite-ushort-integerp

(defthm unsigned-byte-p-rewrite-ushort-integerp
  (equal (unsigned-byte-p (short-bits) x)
         (ushort-integerp x)))

Theorem: natp-when-ushort-integerp

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