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Ia32e-pml4ebits

!ia32e-pml4ebits->res3

Update the |X86ISA|::|RES3| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->res3 res3 x) → new-x
Arguments: res3 — Guard (11bits-p res3).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->res3$inline

(defun !ia32e-pml4ebits->res3$inline (res3 x)
  (declare (xargs :guard (and (11bits-p res3)
                              (ia32e-pml4ebits-p x))))
  (mbe :logic
       (b* ((res3 (mbe :logic (11bits-fix res3)
                       :exec res3))
            (x (ia32e-pml4ebits-fix x)))
         (part-install res3 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) res3)
                                    52))))))

Theorem: ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res3

(defthm ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res3
  (b* ((new-x (!ia32e-pml4ebits->res3$inline res3 x)))
    (ia32e-pml4ebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pml4ebits->res3$inline-of-11bits-fix-res3

(defthm !ia32e-pml4ebits->res3$inline-of-11bits-fix-res3
  (equal (!ia32e-pml4ebits->res3$inline (11bits-fix res3)
                                        x)
         (!ia32e-pml4ebits->res3$inline res3 x)))

Theorem: !ia32e-pml4ebits->res3$inline-11bits-equiv-congruence-on-res3

(defthm
      !ia32e-pml4ebits->res3$inline-11bits-equiv-congruence-on-res3
  (implies (11bits-equiv res3 res3-equiv)
           (equal (!ia32e-pml4ebits->res3$inline res3 x)
                  (!ia32e-pml4ebits->res3$inline res3-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res3$inline-of-ia32e-pml4ebits-fix-x

(defthm !ia32e-pml4ebits->res3$inline-of-ia32e-pml4ebits-fix-x
 (equal (!ia32e-pml4ebits->res3$inline res3 (ia32e-pml4ebits-fix x))
        (!ia32e-pml4ebits->res3$inline res3 x)))

Theorem: !ia32e-pml4ebits->res3$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
 !ia32e-pml4ebits->res3$inline-ia32e-pml4ebits-equiv-congruence-on-x
 (implies (ia32e-pml4ebits-equiv x x-equiv)
          (equal (!ia32e-pml4ebits->res3$inline res3 x)
                 (!ia32e-pml4ebits->res3$inline res3 x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res3-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->res3-is-ia32e-pml4ebits
  (equal (!ia32e-pml4ebits->res3 res3 x)
         (change-ia32e-pml4ebits x :res3 res3)))

Theorem: ia32e-pml4ebits->res3-of-!ia32e-pml4ebits->res3

(defthm ia32e-pml4ebits->res3-of-!ia32e-pml4ebits->res3
  (b* ((?new-x (!ia32e-pml4ebits->res3$inline res3 x)))
    (equal (ia32e-pml4ebits->res3 new-x)
           (11bits-fix res3))))

Theorem: !ia32e-pml4ebits->res3-equiv-under-mask

(defthm !ia32e-pml4ebits->res3-equiv-under-mask
 (b* ((?new-x (!ia32e-pml4ebits->res3$inline res3 x)))
   (ia32e-pml4ebits-equiv-under-mask new-x x -9218868437227405313)))