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Sbyte128

Sbyte128p

Recognizer for sbyte128.

Signature
(sbyte128p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sbyte128p

(defun sbyte128p (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p 128 x)
       :exec (and (integerp x)
                  (<= -170141183460469231731687303715884105728
                      x)
                  (< x
                     170141183460469231731687303715884105728))))

Theorem: booleanp-of-sbyte128p

(defthm booleanp-of-sbyte128p
  (b* ((yes/no (sbyte128p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte128p-forward-signed-byte-p

(defthm sbyte128p-forward-signed-byte-p
  (implies (sbyte128p x)
           (signed-byte-p 128 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte128p

(defthm signed-byte-p-rewrite-sbyte128p
  (equal (signed-byte-p 128 x)
         (sbyte128p x)))

Theorem: integerp-when-sbyte128p

(defthm integerp-when-sbyte128p
  (implies (sbyte128p x) (integerp x))
  :rule-classes :compound-recognizer)