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Mxcsrbits

!mxcsrbits->pe

Update the |ACL2|::|PE| field of a mxcsrbits bit structure.

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

Definitions and Theorems

Function: !mxcsrbits->pe$inline

(defun !mxcsrbits->pe$inline (pe x)
 (declare (xargs :guard (and (bitp pe) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((pe (mbe :logic (bfix pe) :exec pe))
          (x (mxcsrbits-fix x)))
       (part-install pe x :width 1 :low 5))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 7) -33)))
                        (the (unsigned-byte 6)
                             (ash (the (unsigned-byte 1) pe) 5))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->pe-is-mxcsrbits

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

Theorem: mxcsrbits->pe-of-!mxcsrbits->pe

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

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

(defthm !mxcsrbits->pe-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->pe$inline pe x)))
    (mxcsrbits-equiv-under-mask new-x x -33)))