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Prefixes-p

Recognizer for prefixes bit structures.

Function: prefixes-p$inline

(defun prefixes-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 52 x)
       :exec (and (natp x) (< x 4503599627370496))))

Theorem: prefixes-p-when-unsigned-byte-p

(defthm prefixes-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 52 x)
           (prefixes-p x)))

Theorem: unsigned-byte-p-when-prefixes-p

(defthm unsigned-byte-p-when-prefixes-p
  (implies (prefixes-p x)
           (unsigned-byte-p 52 x)))

Theorem: prefixes-p-compound-recognizer

(defthm prefixes-p-compound-recognizer
  (implies (prefixes-p x) (natp x))
  :rule-classes :compound-recognizer)