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Sint-integer

Sint-integerp

Recognizer for sint-integer.

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

Definitions and Theorems

Function: sint-integerp

(defun sint-integerp (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p (int-bits) x)
       :exec (and (integerp x)
                  (<= (- (expt 2 (1- (int-bits)))) x)
                  (< x (expt 2 (1- (int-bits)))))))

Theorem: booleanp-of-sint-integerp

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

Theorem: sint-integerp-forward-signed-byte-p

(defthm sint-integerp-forward-signed-byte-p
  (implies (sint-integerp x)
           (signed-byte-p (int-bits) x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sint-integerp

(defthm signed-byte-p-rewrite-sint-integerp
  (equal (signed-byte-p (int-bits) x)
         (sint-integerp x)))

Theorem: integerp-when-sint-integerp

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