		Search-engine friendly clone of the ACL2 documentation.

Ia32e-page-tablesbits

!ia32e-page-tablesbits->ps

Update the |X86ISA|::|PS| field of a ia32e-page-tablesbits bit structure.

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

Definitions and Theorems

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

(defun !ia32e-page-tablesbits->ps$inline (ps x)
 (declare (xargs :guard (and (bitp ps)
                             (ia32e-page-tablesbits-p x))))
 (mbe
     :logic
     (b* ((ps (mbe :logic (bfix ps) :exec ps))
          (x (ia32e-page-tablesbits-fix x)))
       (part-install ps x :width 1 :low 7))
     :exec (the (unsigned-byte 64)
                (logior (the (unsigned-byte 64)
                             (logand (the (unsigned-byte 64) x)
                                     (the (signed-byte 9) -129)))
                        (the (unsigned-byte 8)
                             (ash (the (unsigned-byte 1) ps) 7))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !ia32e-page-tablesbits->ps-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->ps$inline ps x)))
    (ia32e-page-tablesbits-equiv-under-mask new-x x -129)))