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Ia32e-page-tablesbits

!ia32e-page-tablesbits->res2

Update the |X86ISA|::|RES2| field of a ia32e-page-tablesbits bit structure.

Signature
(!ia32e-page-tablesbits->res2 res2 x) → new-x
Arguments: res2 — Guard (11bits-p res2).; x — Guard (ia32e-page-tablesbits-p x).
Returns: new-x — Type (ia32e-page-tablesbits-p new-x).

Definitions and Theorems

Function: !ia32e-page-tablesbits->res2$inline

(defun !ia32e-page-tablesbits->res2$inline (res2 x)
  (declare (xargs :guard (and (11bits-p res2)
                              (ia32e-page-tablesbits-p x))))
  (mbe :logic
       (b* ((res2 (mbe :logic (11bits-fix res2)
                       :exec res2))
            (x (ia32e-page-tablesbits-fix x)))
         (part-install res2 x :width 11 :low 52))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 64)
                                            -9218868437227405313)))
                          (the (unsigned-byte 63)
                               (ash (the (unsigned-byte 11) res2)
                                    52))))))

Theorem: ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->res2

(defthm ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->res2
  (b* ((new-x (!ia32e-page-tablesbits->res2$inline res2 x)))
    (ia32e-page-tablesbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-page-tablesbits->res2$inline-of-11bits-fix-res2

(defthm !ia32e-page-tablesbits->res2$inline-of-11bits-fix-res2
  (equal (!ia32e-page-tablesbits->res2$inline (11bits-fix res2)
                                              x)
         (!ia32e-page-tablesbits->res2$inline res2 x)))

Theorem: !ia32e-page-tablesbits->res2$inline-11bits-equiv-congruence-on-res2

(defthm
 !ia32e-page-tablesbits->res2$inline-11bits-equiv-congruence-on-res2
 (implies
      (11bits-equiv res2 res2-equiv)
      (equal (!ia32e-page-tablesbits->res2$inline res2 x)
             (!ia32e-page-tablesbits->res2$inline res2-equiv x)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->res2$inline-of-ia32e-page-tablesbits-fix-x

(defthm
 !ia32e-page-tablesbits->res2$inline-of-ia32e-page-tablesbits-fix-x
 (equal (!ia32e-page-tablesbits->res2$inline
             res2 (ia32e-page-tablesbits-fix x))
        (!ia32e-page-tablesbits->res2$inline res2 x)))

Theorem: !ia32e-page-tablesbits->res2$inline-ia32e-page-tablesbits-equiv-congruence-on-x

(defthm
 !ia32e-page-tablesbits->res2$inline-ia32e-page-tablesbits-equiv-congruence-on-x
 (implies
      (ia32e-page-tablesbits-equiv x x-equiv)
      (equal (!ia32e-page-tablesbits->res2$inline res2 x)
             (!ia32e-page-tablesbits->res2$inline res2 x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->res2-is-ia32e-page-tablesbits

(defthm !ia32e-page-tablesbits->res2-is-ia32e-page-tablesbits
  (equal (!ia32e-page-tablesbits->res2 res2 x)
         (change-ia32e-page-tablesbits x
                                       :res2 res2)))

Theorem: ia32e-page-tablesbits->res2-of-!ia32e-page-tablesbits->res2

(defthm ia32e-page-tablesbits->res2-of-!ia32e-page-tablesbits->res2
  (b* ((?new-x (!ia32e-page-tablesbits->res2$inline res2 x)))
    (equal (ia32e-page-tablesbits->res2 new-x)
           (11bits-fix res2))))

Theorem: !ia32e-page-tablesbits->res2-equiv-under-mask

(defthm !ia32e-page-tablesbits->res2-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->res2$inline res2 x)))
    (ia32e-page-tablesbits-equiv-under-mask
         new-x x -9218868437227405313)))