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4bits

4bits-p

Recognizer for 4bits bit structures.

Signature
(4bits-p x) → *

Definitions and Theorems

Function: 4bits-p

(defun 4bits-p (x)
  (declare (xargs :guard t))
  (let ((__function__ '4bits-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 4 x)
         :exec (and (natp x) (< x 16)))))

Theorem: 4bits-p-when-unsigned-byte-p

(defthm 4bits-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 4 x)
           (4bits-p x)))

Theorem: unsigned-byte-p-when-4bits-p

(defthm unsigned-byte-p-when-4bits-p
  (implies (4bits-p x)
           (unsigned-byte-p 4 x)))

Theorem: 4bits-p-compound-recognizer

(defthm 4bits-p-compound-recognizer
  (implies (4bits-p x) (natp x))
  :rule-classes :compound-recognizer)