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Sbyte256

Sbyte256p

Recognizer for sbyte256.

Signature
(sbyte256p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sbyte256p

(defun sbyte256p (x)
 (declare (xargs :guard t))
 (mbe
  :logic (signed-byte-p 256 x)
  :exec
  (and
   (integerp x)
   (<=
    -57896044618658097711785492504343953926634992332820282019728792003956564819968
    x)
   (<
    x
    57896044618658097711785492504343953926634992332820282019728792003956564819968))))

Theorem: booleanp-of-sbyte256p

(defthm booleanp-of-sbyte256p
  (b* ((yes/no (sbyte256p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sbyte256p-forward-signed-byte-p

(defthm sbyte256p-forward-signed-byte-p
  (implies (sbyte256p x)
           (signed-byte-p 256 x))
  :rule-classes :forward-chaining)

Theorem: signed-byte-p-rewrite-sbyte256p

(defthm signed-byte-p-rewrite-sbyte256p
  (equal (signed-byte-p 256 x)
         (sbyte256p x)))

Theorem: integerp-when-sbyte256p

(defthm integerp-when-sbyte256p
  (implies (sbyte256p x) (integerp x))
  :rule-classes :compound-recognizer)