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2bits

2bits-p

Recognizer for 2bits bit structures.

Signature
(2bits-p x) → *

Definitions and Theorems

Function: 2bits-p

(defun 2bits-p (x)
  (declare (xargs :guard t))
  (let ((__function__ '2bits-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 2 x)
         :exec (and (natp x) (< x 4)))))

Theorem: 2bits-p-when-unsigned-byte-p

(defthm 2bits-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 2 x)
           (2bits-p x)))

Theorem: unsigned-byte-p-when-2bits-p

(defthm unsigned-byte-p-when-2bits-p
  (implies (2bits-p x)
           (unsigned-byte-p 2 x)))

Theorem: 2bits-p-compound-recognizer

(defthm 2bits-p-compound-recognizer
  (implies (2bits-p x) (natp x))
  :rule-classes :compound-recognizer)