		Search-engine friendly clone of the ACL2 documentation.

Rflagsbits

!rflagsbits->id

Update the |ACL2|::|ID| field of a rflagsbits bit structure.

Signature
(!rflagsbits->id id x) → new-x
Arguments: id — Guard (bitp id).; x — Guard (rflagsbits-p x).
Returns: new-x — Type (rflagsbits-p new-x).

Definitions and Theorems

Function: !rflagsbits->id$inline

(defun !rflagsbits->id$inline (id x)
 (declare (xargs :guard (and (bitp id) (rflagsbits-p x))))
 (mbe
   :logic
   (b* ((id (mbe :logic (bfix id) :exec id))
        (x (rflagsbits-fix x)))
     (part-install id x :width 1 :low 21))
   :exec (the (unsigned-byte 32)
              (logior (the (unsigned-byte 32)
                           (logand (the (unsigned-byte 32) x)
                                   (the (signed-byte 23) -2097153)))
                      (the (unsigned-byte 22)
                           (ash (the (unsigned-byte 1) id) 21))))))

Theorem: rflagsbits-p-of-!rflagsbits->id

(defthm rflagsbits-p-of-!rflagsbits->id
  (b* ((new-x (!rflagsbits->id$inline id x)))
    (rflagsbits-p new-x))
  :rule-classes :rewrite)

Theorem: !rflagsbits->id$inline-of-bfix-id

(defthm !rflagsbits->id$inline-of-bfix-id
  (equal (!rflagsbits->id$inline (bfix id) x)
         (!rflagsbits->id$inline id x)))

Theorem: !rflagsbits->id$inline-bit-equiv-congruence-on-id

(defthm !rflagsbits->id$inline-bit-equiv-congruence-on-id
  (implies (bit-equiv id id-equiv)
           (equal (!rflagsbits->id$inline id x)
                  (!rflagsbits->id$inline id-equiv x)))
  :rule-classes :congruence)

Theorem: !rflagsbits->id$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->id$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->id$inline id (rflagsbits-fix x))
         (!rflagsbits->id$inline id x)))

Theorem: !rflagsbits->id$inline-rflagsbits-equiv-congruence-on-x

(defthm !rflagsbits->id$inline-rflagsbits-equiv-congruence-on-x
  (implies (rflagsbits-equiv x x-equiv)
           (equal (!rflagsbits->id$inline id x)
                  (!rflagsbits->id$inline id x-equiv)))
  :rule-classes :congruence)

Theorem: !rflagsbits->id-is-rflagsbits

(defthm !rflagsbits->id-is-rflagsbits
  (equal (!rflagsbits->id id x)
         (change-rflagsbits x :id id)))

Theorem: rflagsbits->id-of-!rflagsbits->id

(defthm rflagsbits->id-of-!rflagsbits->id
  (b* ((?new-x (!rflagsbits->id$inline id x)))
    (equal (rflagsbits->id new-x)
           (bfix id))))

Theorem: !rflagsbits->id-equiv-under-mask

(defthm !rflagsbits->id-equiv-under-mask
  (b* ((?new-x (!rflagsbits->id$inline id x)))
    (rflagsbits-equiv-under-mask new-x x -2097153)))