		Search-engine friendly clone of the ACL2 documentation.

Mxcsrbits

!mxcsrbits->ie

Update the |X86ISA|::|IE| field of a mxcsrbits bit structure.

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

Definitions and Theorems

Function: !mxcsrbits->ie$inline

(defun !mxcsrbits->ie$inline (ie x)
  (declare (xargs :guard (and (bitp ie) (mxcsrbits-p x))))
  (mbe :logic
       (b* ((ie (mbe :logic (bfix ie) :exec ie))
            (x (mxcsrbits-fix x)))
         (part-install ie x :width 1 :low 0))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) ie)))))

Theorem: mxcsrbits-p-of-!mxcsrbits->ie

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

Theorem: !mxcsrbits->ie$inline-of-bfix-ie

(defthm !mxcsrbits->ie$inline-of-bfix-ie
  (equal (!mxcsrbits->ie$inline (bfix ie) x)
         (!mxcsrbits->ie$inline ie x)))

Theorem: !mxcsrbits->ie$inline-bit-equiv-congruence-on-ie

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

Theorem: !mxcsrbits->ie$inline-of-mxcsrbits-fix-x

(defthm !mxcsrbits->ie$inline-of-mxcsrbits-fix-x
  (equal (!mxcsrbits->ie$inline ie (mxcsrbits-fix x))
         (!mxcsrbits->ie$inline ie x)))

Theorem: !mxcsrbits->ie$inline-mxcsrbits-equiv-congruence-on-x

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

Theorem: !mxcsrbits->ie-is-mxcsrbits

(defthm !mxcsrbits->ie-is-mxcsrbits
  (equal (!mxcsrbits->ie ie x)
         (change-mxcsrbits x :ie ie)))

Theorem: mxcsrbits->ie-of-!mxcsrbits->ie

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

Theorem: !mxcsrbits->ie-equiv-under-mask

(defthm !mxcsrbits->ie-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->ie$inline ie x)))
    (mxcsrbits-equiv-under-mask new-x x -2)))