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7bits

7bits-p

Recognizer for 7bits bit structures.

Signature
(7bits-p x) → *

Definitions and Theorems

Function: 7bits-p

(defun 7bits-p (x)
  (declare (xargs :guard t))
  (let ((__function__ '7bits-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 7 x)
         :exec (and (natp x) (< x 128)))))

Theorem: 7bits-p-when-unsigned-byte-p

(defthm 7bits-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 7 x)
           (7bits-p x)))

Theorem: unsigned-byte-p-when-7bits-p

(defthm unsigned-byte-p-when-7bits-p
  (implies (7bits-p x)
           (unsigned-byte-p 7 x)))

Theorem: 7bits-p-compound-recognizer

(defthm 7bits-p-compound-recognizer
  (implies (7bits-p x) (natp x))
  :rule-classes :compound-recognizer)