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Sbyte64

Sbyte64p

Recognizer for sbyte64.

Signature
(sbyte64p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sbyte64p

(defun sbyte64p (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p 64 x)
       :exec (and (integerp x)
                  (<= -9223372036854775808 x)
                  (< x 9223372036854775808))))

Theorem: booleanp-of-sbyte64p

(defthm booleanp-of-sbyte64p
  (b* ((yes/no (sbyte64p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte64p-forward-signed-byte-p

(defthm sbyte64p-forward-signed-byte-p
  (implies (sbyte64p x)
           (signed-byte-p 64 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte64p

(defthm signed-byte-p-rewrite-sbyte64p
  (equal (signed-byte-p 64 x)
         (sbyte64p x)))

Theorem: integerp-when-sbyte64p

(defthm integerp-when-sbyte64p
  (implies (sbyte64p x) (integerp x))
  :rule-classes :compound-recognizer)