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Sbyte4p

Recognizer for sbyte4.

Function: sbyte4p

(defun sbyte4p (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p 4 x)
       :exec (and (integerp x) (<= -8 x) (< x 8))))

Theorem: booleanp-of-sbyte4p

(defthm booleanp-of-sbyte4p
  (b* ((yes/no (sbyte4p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte4p-forward-signed-byte-p

(defthm sbyte4p-forward-signed-byte-p
  (implies (sbyte4p x)
           (signed-byte-p 4 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte4p

(defthm signed-byte-p-rewrite-sbyte4p
  (equal (signed-byte-p 4 x) (sbyte4p x)))

Theorem: integerp-when-sbyte4p

(defthm integerp-when-sbyte4p
  (implies (sbyte4p x) (integerp x))
  :rule-classes :compound-recognizer)