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Ia32e-pml4ebits

!ia32e-pml4ebits->res2

Update the |X86ISA|::|RES2| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->res2 res2 x) → new-x
Arguments: res2 — Guard (4bits-p res2).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->res2$inline

(defun !ia32e-pml4ebits->res2$inline (res2 x)
 (declare (xargs :guard (and (4bits-p res2)
                             (ia32e-pml4ebits-p x))))
 (mbe :logic
      (b* ((res2 (mbe :logic (4bits-fix res2)
                      :exec res2))
           (x (ia32e-pml4ebits-fix x)))
        (part-install res2 x :width 4 :low 8))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 13) -3841)))
                         (the (unsigned-byte 12)
                              (ash (the (unsigned-byte 4) res2)
                                   8))))))

Theorem: ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res2

(defthm ia32e-pml4ebits-p-of-!ia32e-pml4ebits->res2
  (b* ((new-x (!ia32e-pml4ebits->res2$inline res2 x)))
    (ia32e-pml4ebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pml4ebits->res2$inline-of-4bits-fix-res2

(defthm !ia32e-pml4ebits->res2$inline-of-4bits-fix-res2
  (equal (!ia32e-pml4ebits->res2$inline (4bits-fix res2)
                                        x)
         (!ia32e-pml4ebits->res2$inline res2 x)))

Theorem: !ia32e-pml4ebits->res2$inline-4bits-equiv-congruence-on-res2

(defthm !ia32e-pml4ebits->res2$inline-4bits-equiv-congruence-on-res2
  (implies (4bits-equiv res2 res2-equiv)
           (equal (!ia32e-pml4ebits->res2$inline res2 x)
                  (!ia32e-pml4ebits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res2$inline-of-ia32e-pml4ebits-fix-x

(defthm !ia32e-pml4ebits->res2$inline-of-ia32e-pml4ebits-fix-x
 (equal (!ia32e-pml4ebits->res2$inline res2 (ia32e-pml4ebits-fix x))
        (!ia32e-pml4ebits->res2$inline res2 x)))

Theorem: !ia32e-pml4ebits->res2$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
 !ia32e-pml4ebits->res2$inline-ia32e-pml4ebits-equiv-congruence-on-x
 (implies (ia32e-pml4ebits-equiv x x-equiv)
          (equal (!ia32e-pml4ebits->res2$inline res2 x)
                 (!ia32e-pml4ebits->res2$inline res2 x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->res2-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->res2-is-ia32e-pml4ebits
  (equal (!ia32e-pml4ebits->res2 res2 x)
         (change-ia32e-pml4ebits x :res2 res2)))

Theorem: ia32e-pml4ebits->res2-of-!ia32e-pml4ebits->res2

(defthm ia32e-pml4ebits->res2-of-!ia32e-pml4ebits->res2
  (b* ((?new-x (!ia32e-pml4ebits->res2$inline res2 x)))
    (equal (ia32e-pml4ebits->res2 new-x)
           (4bits-fix res2))))

Theorem: !ia32e-pml4ebits->res2-equiv-under-mask

(defthm !ia32e-pml4ebits->res2-equiv-under-mask
  (b* ((?new-x (!ia32e-pml4ebits->res2$inline res2 x)))
    (ia32e-pml4ebits-equiv-under-mask new-x x -3841)))