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Sbyte32

Sbyte32p

Recognizer for sbyte32.

Signature
(sbyte32p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sbyte32p

(defun sbyte32p (x)
  (declare (xargs :guard t))
  (mbe :logic (signed-byte-p 32 x)
       :exec (and (integerp x)
                  (<= -2147483648 x)
                  (< x 2147483648))))

Theorem: booleanp-of-sbyte32p

(defthm booleanp-of-sbyte32p
  (b* ((yes/no (sbyte32p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte32p-forward-signed-byte-p

(defthm sbyte32p-forward-signed-byte-p
  (implies (sbyte32p x)
           (signed-byte-p 32 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte32p

(defthm signed-byte-p-rewrite-sbyte32p
  (equal (signed-byte-p 32 x)
         (sbyte32p x)))

Theorem: integerp-when-sbyte32p

(defthm integerp-when-sbyte32p
  (implies (sbyte32p x) (integerp x))
  :rule-classes :compound-recognizer)