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Ia32e-pdpte-1gb-pagebits

!ia32e-pdpte-1gb-pagebits->page

Update the |X86ISA|::|PAGE| field of a ia32e-pdpte-1gb-pagebits bit structure.

Signature
(!ia32e-pdpte-1gb-pagebits->page page x) → new-x
Arguments: page — Guard (22bits-p page).; x — Guard (ia32e-pdpte-1gb-pagebits-p x).
Returns: new-x — Type (ia32e-pdpte-1gb-pagebits-p new-x).

Definitions and Theorems

Function: !ia32e-pdpte-1gb-pagebits->page$inline

(defun !ia32e-pdpte-1gb-pagebits->page$inline (page x)
  (declare (xargs :guard (and (22bits-p page)
                              (ia32e-pdpte-1gb-pagebits-p x))))
  (mbe :logic
       (b* ((page (mbe :logic (22bits-fix page)
                       :exec page))
            (x (ia32e-pdpte-1gb-pagebits-fix x)))
         (part-install page x :width 22 :low 30))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 53)
                                            -4503598553628673)))
                          (the (unsigned-byte 52)
                               (ash (the (unsigned-byte 22) page)
                                    30))))))

Theorem: ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->page

(defthm
      ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->page
  (b* ((new-x (!ia32e-pdpte-1gb-pagebits->page$inline page x)))
    (ia32e-pdpte-1gb-pagebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pdpte-1gb-pagebits->page$inline-of-22bits-fix-page

(defthm !ia32e-pdpte-1gb-pagebits->page$inline-of-22bits-fix-page
  (equal (!ia32e-pdpte-1gb-pagebits->page$inline (22bits-fix page)
                                                 x)
         (!ia32e-pdpte-1gb-pagebits->page$inline page x)))

Theorem: !ia32e-pdpte-1gb-pagebits->page$inline-22bits-equiv-congruence-on-page

(defthm
 !ia32e-pdpte-1gb-pagebits->page$inline-22bits-equiv-congruence-on-page
 (implies
      (22bits-equiv page page-equiv)
      (equal (!ia32e-pdpte-1gb-pagebits->page$inline page x)
             (!ia32e-pdpte-1gb-pagebits->page$inline page-equiv x)))
 :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->page$inline-of-ia32e-pdpte-1gb-pagebits-fix-x

(defthm
 !ia32e-pdpte-1gb-pagebits->page$inline-of-ia32e-pdpte-1gb-pagebits-fix-x
 (equal (!ia32e-pdpte-1gb-pagebits->page$inline
             page (ia32e-pdpte-1gb-pagebits-fix x))
        (!ia32e-pdpte-1gb-pagebits->page$inline page x)))

Theorem: !ia32e-pdpte-1gb-pagebits->page$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x

(defthm
 !ia32e-pdpte-1gb-pagebits->page$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x
 (implies
      (ia32e-pdpte-1gb-pagebits-equiv x x-equiv)
      (equal (!ia32e-pdpte-1gb-pagebits->page$inline page x)
             (!ia32e-pdpte-1gb-pagebits->page$inline page x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->page-is-ia32e-pdpte-1gb-pagebits

(defthm !ia32e-pdpte-1gb-pagebits->page-is-ia32e-pdpte-1gb-pagebits
  (equal (!ia32e-pdpte-1gb-pagebits->page page x)
         (change-ia32e-pdpte-1gb-pagebits x
                                          :page page)))

Theorem: ia32e-pdpte-1gb-pagebits->page-of-!ia32e-pdpte-1gb-pagebits->page

(defthm
  ia32e-pdpte-1gb-pagebits->page-of-!ia32e-pdpte-1gb-pagebits->page
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->page$inline page x)))
    (equal (ia32e-pdpte-1gb-pagebits->page new-x)
           (22bits-fix page))))

Theorem: !ia32e-pdpte-1gb-pagebits->page-equiv-under-mask

(defthm !ia32e-pdpte-1gb-pagebits->page-equiv-under-mask
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->page$inline page x)))
    (ia32e-pdpte-1gb-pagebits-equiv-under-mask
         new-x x -4503598553628673)))