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Ia32e-pml4ebits

!ia32e-pml4ebits->a

Update the |ACL2|::|A| field of a ia32e-pml4ebits bit structure.

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

Definitions and Theorems

Function: !ia32e-pml4ebits->a$inline

(defun !ia32e-pml4ebits->a$inline (a x)
 (declare (xargs :guard (and (bitp a) (ia32e-pml4ebits-p x))))
 (mbe :logic
      (b* ((a (mbe :logic (bfix a) :exec a))
           (x (ia32e-pml4ebits-fix x)))
        (part-install a x :width 1 :low 5))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 7) -33)))
                         (the (unsigned-byte 6)
                              (ash (the (unsigned-byte 1) a) 5))))))

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

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

Theorem: !ia32e-pml4ebits->a$inline-of-bfix-a

(defthm !ia32e-pml4ebits->a$inline-of-bfix-a
  (equal (!ia32e-pml4ebits->a$inline (bfix a) x)
         (!ia32e-pml4ebits->a$inline a x)))

Theorem: !ia32e-pml4ebits->a$inline-bit-equiv-congruence-on-a

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

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

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

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

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

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

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

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

(defthm ia32e-pml4ebits->a-of-!ia32e-pml4ebits->a
  (b* ((?new-x (!ia32e-pml4ebits->a$inline a x)))
    (equal (ia32e-pml4ebits->a new-x)
           (bfix a))))

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

(defthm !ia32e-pml4ebits->a-equiv-under-mask
  (b* ((?new-x (!ia32e-pml4ebits->a$inline a x)))
    (ia32e-pml4ebits-equiv-under-mask new-x x -33)))