		Search-engine friendly clone of the ACL2 documentation.

Cr4bits

!cr4bits->pge

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

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

Definitions and Theorems

Function: !cr4bits->pge$inline

(defun !cr4bits->pge$inline (pge x)
 (declare (xargs :guard (and (bitp pge) (cr4bits-p x))))
 (mbe
    :logic
    (b* ((pge (mbe :logic (bfix pge) :exec pge))
         (x (cr4bits-fix x)))
      (part-install pge x :width 1 :low 7))
    :exec (the (unsigned-byte 26)
               (logior (the (unsigned-byte 26)
                            (logand (the (unsigned-byte 26) x)
                                    (the (signed-byte 9) -129)))
                       (the (unsigned-byte 8)
                            (ash (the (unsigned-byte 1) pge) 7))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->pge-is-cr4bits

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

Theorem: cr4bits->pge-of-!cr4bits->pge

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

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

(defthm !cr4bits->pge-equiv-under-mask
  (b* ((?new-x (!cr4bits->pge$inline pge x)))
    (cr4bits-equiv-under-mask new-x x -129)))