		Search-engine friendly clone of the ACL2 documentation.

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)))