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Cr4bits

!cr4bits->smxe

Update the |X86ISA|::|SMXE| field of a cr4bits bit structure.

Signature
(!cr4bits->smxe smxe x) → new-x
Arguments: smxe — Guard (bitp smxe).; x — Guard (cr4bits-p x).
Returns: new-x — Type (cr4bits-p new-x).

Definitions and Theorems

Function: !cr4bits->smxe$inline

(defun !cr4bits->smxe$inline (smxe x)
 (declare (xargs :guard (and (bitp smxe) (cr4bits-p x))))
 (mbe
     :logic
     (b* ((smxe (mbe :logic (bfix smxe) :exec smxe))
          (x (cr4bits-fix x)))
       (part-install smxe x :width 1 :low 14))
     :exec (the (unsigned-byte 26)
                (logior (the (unsigned-byte 26)
                             (logand (the (unsigned-byte 26) x)
                                     (the (signed-byte 16) -16385)))
                        (the (unsigned-byte 15)
                             (ash (the (unsigned-byte 1) smxe)
                                  14))))))

Theorem: cr4bits-p-of-!cr4bits->smxe

(defthm cr4bits-p-of-!cr4bits->smxe
  (b* ((new-x (!cr4bits->smxe$inline smxe x)))
    (cr4bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr4bits->smxe$inline-of-bfix-smxe

(defthm !cr4bits->smxe$inline-of-bfix-smxe
  (equal (!cr4bits->smxe$inline (bfix smxe) x)
         (!cr4bits->smxe$inline smxe x)))

Theorem: !cr4bits->smxe$inline-bit-equiv-congruence-on-smxe

(defthm !cr4bits->smxe$inline-bit-equiv-congruence-on-smxe
  (implies (bit-equiv smxe smxe-equiv)
           (equal (!cr4bits->smxe$inline smxe x)
                  (!cr4bits->smxe$inline smxe-equiv x)))
  :rule-classes :congruence)

Theorem: !cr4bits->smxe$inline-of-cr4bits-fix-x

(defthm !cr4bits->smxe$inline-of-cr4bits-fix-x
  (equal (!cr4bits->smxe$inline smxe (cr4bits-fix x))
         (!cr4bits->smxe$inline smxe x)))

Theorem: !cr4bits->smxe$inline-cr4bits-equiv-congruence-on-x

(defthm !cr4bits->smxe$inline-cr4bits-equiv-congruence-on-x
  (implies (cr4bits-equiv x x-equiv)
           (equal (!cr4bits->smxe$inline smxe x)
                  (!cr4bits->smxe$inline smxe x-equiv)))
  :rule-classes :congruence)

Theorem: !cr4bits->smxe-is-cr4bits

(defthm !cr4bits->smxe-is-cr4bits
  (equal (!cr4bits->smxe smxe x)
         (change-cr4bits x :smxe smxe)))

Theorem: cr4bits->smxe-of-!cr4bits->smxe

(defthm cr4bits->smxe-of-!cr4bits->smxe
  (b* ((?new-x (!cr4bits->smxe$inline smxe x)))
    (equal (cr4bits->smxe new-x)
           (bfix smxe))))

Theorem: !cr4bits->smxe-equiv-under-mask

(defthm !cr4bits->smxe-equiv-under-mask
  (b* ((?new-x (!cr4bits->smxe$inline smxe x)))
    (cr4bits-equiv-under-mask new-x x -16385)))