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Cr4bits

!cr4bits->fsgsbase

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

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

Definitions and Theorems

Function: !cr4bits->fsgsbase$inline

(defun !cr4bits->fsgsbase$inline (fsgsbase x)
 (declare (xargs :guard (and (bitp fsgsbase) (cr4bits-p x))))
 (mbe
     :logic
     (b* ((fsgsbase (mbe :logic (bfix fsgsbase)
                         :exec fsgsbase))
          (x (cr4bits-fix x)))
       (part-install fsgsbase x
                     :width 1
                     :low 16))
     :exec (the (unsigned-byte 26)
                (logior (the (unsigned-byte 26)
                             (logand (the (unsigned-byte 26) x)
                                     (the (signed-byte 18) -65537)))
                        (the (unsigned-byte 17)
                             (ash (the (unsigned-byte 1) fsgsbase)
                                  16))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->fsgsbase-is-cr4bits

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

Theorem: cr4bits->fsgsbase-of-!cr4bits->fsgsbase

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

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

(defthm !cr4bits->fsgsbase-equiv-under-mask
  (b* ((?new-x (!cr4bits->fsgsbase$inline fsgsbase x)))
    (cr4bits-equiv-under-mask new-x x -65537)))