		Search-engine friendly clone of the ACL2 documentation.

13bits

13bits-p

Recognizer for 13bits bit structures.

Signature
(13bits-p x) → *

Definitions and Theorems

Function: 13bits-p

(defun 13bits-p (x)
  (declare (xargs :guard t))
  (let ((__function__ '13bits-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 13 x)
         :exec (and (natp x) (< x 8192)))))

Theorem: 13bits-p-when-unsigned-byte-p

(defthm 13bits-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 13 x)
           (13bits-p x)))

Theorem: unsigned-byte-p-when-13bits-p

(defthm unsigned-byte-p-when-13bits-p
  (implies (13bits-p x)
           (unsigned-byte-p 13 x)))

Theorem: 13bits-p-compound-recognizer

(defthm 13bits-p-compound-recognizer
  (implies (13bits-p x) (natp x))
  :rule-classes :compound-recognizer)