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Ia32e-pdpte-1gb-pagebits

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

Update the |ACL2|::|P| field of a ia32e-pdpte-1gb-pagebits bit structure.

Signature
(!ia32e-pdpte-1gb-pagebits->p p x) → new-x
Arguments: p — Guard (bitp p).; 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->p$inline

(defun
     !ia32e-pdpte-1gb-pagebits->p$inline
     (p x)
     (declare (xargs :guard (and (bitp p)
                                 (ia32e-pdpte-1gb-pagebits-p x))))
     (mbe :logic (b* ((p (mbe :logic (bfix p) :exec p))
                      (x (ia32e-pdpte-1gb-pagebits-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-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->p

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

Theorem: !ia32e-pdpte-1gb-pagebits->p$inline-of-bfix-p

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

Theorem: !ia32e-pdpte-1gb-pagebits->p$inline-bit-equiv-congruence-on-p

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

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

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

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

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

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

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

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

(defthm ia32e-pdpte-1gb-pagebits->p-of-!ia32e-pdpte-1gb-pagebits->p
        (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->p$inline p x)))
            (equal (ia32e-pdpte-1gb-pagebits->p new-x)
                   (bfix p))))

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

(defthm !ia32e-pdpte-1gb-pagebits->p-equiv-under-mask
        (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->p$inline p x)))
            (ia32e-pdpte-1gb-pagebits-equiv-under-mask new-x x -2)))