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Cr3bits

!cr3bits->res2

Update the |X86ISA|::|RES2| field of a cr3bits bit structure.

Signature
(!cr3bits->res2 res2 x) → new-x
Arguments: res2 — Guard (7bits-p res2).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->res2$inline

(defun !cr3bits->res2$inline (res2 x)
 (declare (xargs :guard (and (7bits-p res2) (cr3bits-p x))))
 (mbe :logic
      (b* ((res2 (mbe :logic (7bits-fix res2)
                      :exec res2))
           (x (cr3bits-fix x)))
        (part-install res2 x :width 7 :low 5))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 13) -4065)))
                         (the (unsigned-byte 12)
                              (ash (the (unsigned-byte 7) res2)
                                   5))))))

Theorem: cr3bits-p-of-!cr3bits->res2

(defthm cr3bits-p-of-!cr3bits->res2
  (b* ((new-x (!cr3bits->res2$inline res2 x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->res2$inline-of-7bits-fix-res2

(defthm !cr3bits->res2$inline-of-7bits-fix-res2
  (equal (!cr3bits->res2$inline (7bits-fix res2)
                                x)
         (!cr3bits->res2$inline res2 x)))

Theorem: !cr3bits->res2$inline-7bits-equiv-congruence-on-res2

(defthm !cr3bits->res2$inline-7bits-equiv-congruence-on-res2
  (implies (7bits-equiv res2 res2-equiv)
           (equal (!cr3bits->res2$inline res2 x)
                  (!cr3bits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->res2$inline-of-cr3bits-fix-x

(defthm !cr3bits->res2$inline-of-cr3bits-fix-x
  (equal (!cr3bits->res2$inline res2 (cr3bits-fix x))
         (!cr3bits->res2$inline res2 x)))

Theorem: !cr3bits->res2$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->res2$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->res2$inline res2 x)
                  (!cr3bits->res2$inline res2 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->res2-is-cr3bits

(defthm !cr3bits->res2-is-cr3bits
  (equal (!cr3bits->res2 res2 x)
         (change-cr3bits x :res2 res2)))

Theorem: cr3bits->res2-of-!cr3bits->res2

(defthm cr3bits->res2-of-!cr3bits->res2
  (b* ((?new-x (!cr3bits->res2$inline res2 x)))
    (equal (cr3bits->res2 new-x)
           (7bits-fix res2))))

Theorem: !cr3bits->res2-equiv-under-mask

(defthm !cr3bits->res2-equiv-under-mask
  (b* ((?new-x (!cr3bits->res2$inline res2 x)))
    (cr3bits-equiv-under-mask new-x x -4065)))