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Ia32e-page-tablesbits

!ia32e-page-tablesbits->p

Update the |ACL2|::|P| field of a ia32e-page-tablesbits bit structure.

Signature
(!ia32e-page-tablesbits->p p x) → new-x
Arguments: p — Guard (bitp p).; x — Guard (ia32e-page-tablesbits-p x).
Returns: new-x — Type (ia32e-page-tablesbits-p new-x).

Definitions and Theorems

Function: !ia32e-page-tablesbits->p$inline

(defun !ia32e-page-tablesbits->p$inline (p x)
  (declare (xargs :guard (and (bitp p)
                              (ia32e-page-tablesbits-p x))))
  (mbe :logic
       (b* ((p (mbe :logic (bfix p) :exec p))
            (x (ia32e-page-tablesbits-fix x)))
         (part-install p x :width 1 :low 0))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) p)))))

Theorem: ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->p

(defthm ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->p
  (b* ((new-x (!ia32e-page-tablesbits->p$inline p x)))
    (ia32e-page-tablesbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-page-tablesbits->p$inline-of-bfix-p

(defthm !ia32e-page-tablesbits->p$inline-of-bfix-p
  (equal (!ia32e-page-tablesbits->p$inline (bfix p)
                                           x)
         (!ia32e-page-tablesbits->p$inline p x)))

Theorem: !ia32e-page-tablesbits->p$inline-bit-equiv-congruence-on-p

(defthm !ia32e-page-tablesbits->p$inline-bit-equiv-congruence-on-p
  (implies (bit-equiv p p-equiv)
           (equal (!ia32e-page-tablesbits->p$inline p x)
                  (!ia32e-page-tablesbits->p$inline p-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->p$inline-of-ia32e-page-tablesbits-fix-x

(defthm
    !ia32e-page-tablesbits->p$inline-of-ia32e-page-tablesbits-fix-x
 (equal
  (!ia32e-page-tablesbits->p$inline p (ia32e-page-tablesbits-fix x))
  (!ia32e-page-tablesbits->p$inline p x)))

Theorem: !ia32e-page-tablesbits->p$inline-ia32e-page-tablesbits-equiv-congruence-on-x

(defthm
 !ia32e-page-tablesbits->p$inline-ia32e-page-tablesbits-equiv-congruence-on-x
 (implies (ia32e-page-tablesbits-equiv x x-equiv)
          (equal (!ia32e-page-tablesbits->p$inline p x)
                 (!ia32e-page-tablesbits->p$inline p x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->p-is-ia32e-page-tablesbits

(defthm !ia32e-page-tablesbits->p-is-ia32e-page-tablesbits
  (equal (!ia32e-page-tablesbits->p p x)
         (change-ia32e-page-tablesbits x :p p)))

Theorem: ia32e-page-tablesbits->p-of-!ia32e-page-tablesbits->p

(defthm ia32e-page-tablesbits->p-of-!ia32e-page-tablesbits->p
  (b* ((?new-x (!ia32e-page-tablesbits->p$inline p x)))
    (equal (ia32e-page-tablesbits->p new-x)
           (bfix p))))

Theorem: !ia32e-page-tablesbits->p-equiv-under-mask

(defthm !ia32e-page-tablesbits->p-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->p$inline p x)))
    (ia32e-page-tablesbits-equiv-under-mask new-x x -2)))