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Cr3bits

!cr3bits->res3

Update the |X86ISA|::|RES3| field of a cr3bits bit structure.

Signature
(!cr3bits->res3 res3 x) → new-x
Arguments: res3 — Guard (12bits-p res3).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->res3$inline

(defun !cr3bits->res3$inline (res3 x)
  (declare (xargs :guard (and (12bits-p res3) (cr3bits-p x))))
  (mbe :logic
       (b* ((res3 (mbe :logic (12bits-fix res3)
                       :exec res3))
            (x (cr3bits-fix x)))
         (part-install res3 x :width 12 :low 52))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 65)
                                            -18442240474082181121)))
                          (the (unsigned-byte 64)
                               (ash (the (unsigned-byte 12) res3)
                                    52))))))

Theorem: cr3bits-p-of-!cr3bits->res3

(defthm cr3bits-p-of-!cr3bits->res3
  (b* ((new-x (!cr3bits->res3$inline res3 x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->res3$inline-of-12bits-fix-res3

(defthm !cr3bits->res3$inline-of-12bits-fix-res3
  (equal (!cr3bits->res3$inline (12bits-fix res3)
                                x)
         (!cr3bits->res3$inline res3 x)))

Theorem: !cr3bits->res3$inline-12bits-equiv-congruence-on-res3

(defthm !cr3bits->res3$inline-12bits-equiv-congruence-on-res3
  (implies (12bits-equiv res3 res3-equiv)
           (equal (!cr3bits->res3$inline res3 x)
                  (!cr3bits->res3$inline res3-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->res3$inline-of-cr3bits-fix-x

(defthm !cr3bits->res3$inline-of-cr3bits-fix-x
  (equal (!cr3bits->res3$inline res3 (cr3bits-fix x))
         (!cr3bits->res3$inline res3 x)))

Theorem: !cr3bits->res3$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->res3$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->res3$inline res3 x)
                  (!cr3bits->res3$inline res3 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->res3-is-cr3bits

(defthm !cr3bits->res3-is-cr3bits
  (equal (!cr3bits->res3 res3 x)
         (change-cr3bits x :res3 res3)))

Theorem: cr3bits->res3-of-!cr3bits->res3

(defthm cr3bits->res3-of-!cr3bits->res3
  (b* ((?new-x (!cr3bits->res3$inline res3 x)))
    (equal (cr3bits->res3 new-x)
           (12bits-fix res3))))

Theorem: !cr3bits->res3-equiv-under-mask

(defthm !cr3bits->res3-equiv-under-mask
  (b* ((?new-x (!cr3bits->res3$inline res3 x)))
    (cr3bits-equiv-under-mask new-x x 4503599627370495)))