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      Nthcdr-bytes

      Skip past some number of bytes in an open file.

      (nthcdr-bytes n channel state) is like nthcdr for an :byte input channel. That is, it just reads n bytes and ignores them, returning the updated state.

      This is notably useful as a way to express the post-state after take-bytes.

      Definitions and Theorems

      Function: nthcdr-bytes

      (defun nthcdr-bytes (n channel state)
        (declare (xargs :guard (and (natp n)
                                    (state-p state)
                                    (symbolp channel)
                                    (open-input-channel-p channel
                                                          :byte state))))
        (b* (((when (zp n)) state)
             ((mv ?byte state)
              (read-byte$ channel state)))
          (nthcdr-bytes (- n 1) channel state)))

      Theorem: state-p1-of-nthcdr-bytes

      (defthm state-p1-of-nthcdr-bytes
        (implies (and (force (state-p1 state))
                      (force (symbolp channel))
                      (force (open-input-channel-p1 channel
                                                    :byte state)))
                 (state-p1 (nthcdr-bytes n channel state))))

      Theorem: open-input-channel-p1-of-nthcdr-bytes

      (defthm open-input-channel-p1-of-nthcdr-bytes
       (implies
            (and (force (state-p1 state))
                 (force (symbolp channel))
                 (force (open-input-channel-p1 channel
                                               :byte state)))
            (open-input-channel-p1 channel
                                   :byte (nthcdr-bytes n channel state))))

      Theorem: read-byte$-all-of-nthcdr-bytes

      (defthm read-byte$-all-of-nthcdr-bytes
       (implies
        (and (force (state-p1 state))
             (force (symbolp channel))
             (force (open-input-channel-p1 channel
                                           :byte state)))
        (equal
          (mv-nth 0
                  (read-byte$-all channel (nthcdr-bytes n channel state)))
          (nthcdr n
                  (mv-nth 0 (read-byte$-all channel state))))))

      Theorem: nthcdr-bytes-1

      (defthm nthcdr-bytes-1
        (equal (nthcdr-bytes 1 channel state)
               (mv-nth 1 (read-byte$ channel state))))

      Theorem: nthcdr-bytes-2

      (defthm nthcdr-bytes-2
        (equal
             (nthcdr-bytes 2 channel state)
             (mv-nth 1
                     (read-byte$ channel
                                 (mv-nth 1 (read-byte$ channel state))))))

      Theorem: nthcdr-bytes-3

      (defthm nthcdr-bytes-3
       (equal
        (nthcdr-bytes 3 channel state)
        (mv-nth
         1
         (read-byte$
           channel
           (mv-nth 1
                   (read-byte$ channel
                               (mv-nth 1 (read-byte$ channel state))))))))

      Theorem: nthcdr-bytes-4

      (defthm nthcdr-bytes-4
       (equal
        (nthcdr-bytes 4 channel state)
        (mv-nth
         1
         (read-byte$
          channel
          (mv-nth
           1
           (read-byte$
            channel
            (mv-nth
                 1
                 (read-byte$ channel
                             (mv-nth 1 (read-byte$ channel state))))))))))

      Theorem: nthcdr-bytes-measure-weak

      (defthm nthcdr-bytes-measure-weak
        (implies (and (force (state-p1 state))
                      (force (open-input-channel-p1 channel
                                                    :byte state))
                      (force (symbolp channel)))
                 (<= (file-measure channel (nthcdr-bytes n channel state))
                     (file-measure channel state)))
        :rule-classes (:rewrite :linear))

      Theorem: nthcdr-bytes-measure-strong

      (defthm nthcdr-bytes-measure-strong
        (implies (and (mv-nth 0 (read-byte$ channel state))
                      (not (zp n))
                      (force (state-p1 state))
                      (force (open-input-channel-p1 channel
                                                    :byte state))
                      (force (symbolp channel)))
                 (< (file-measure channel (nthcdr-bytes n channel state))
                    (file-measure channel state)))
        :rule-classes (:rewrite :linear))