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Cr0bits

!cr0bits->res3

Update the |X86ISA|::|RES3| field of a cr0bits bit structure.

Signature
(!cr0bits->res3 res3 x) → new-x
Arguments: res3 — Guard (10bits-p res3).; x — Guard (cr0bits-p x).
Returns: new-x — Type (cr0bits-p new-x).

Definitions and Theorems

Function: !cr0bits->res3$inline

(defun !cr0bits->res3$inline (res3 x)
  (declare (xargs :guard (and (10bits-p res3) (cr0bits-p x))))
  (mbe :logic
       (b* ((res3 (mbe :logic (10bits-fix res3)
                       :exec res3))
            (x (cr0bits-fix x)))
         (part-install res3 x :width 10 :low 19))
       :exec
       (the (unsigned-byte 32)
            (logior (the (unsigned-byte 32)
                         (logand (the (unsigned-byte 32) x)
                                 (the (signed-byte 30) -536346625)))
                    (the (unsigned-byte 29)
                         (ash (the (unsigned-byte 10) res3)
                              19))))))

Theorem: cr0bits-p-of-!cr0bits->res3

(defthm cr0bits-p-of-!cr0bits->res3
  (b* ((new-x (!cr0bits->res3$inline res3 x)))
    (cr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr0bits->res3$inline-of-10bits-fix-res3

(defthm !cr0bits->res3$inline-of-10bits-fix-res3
  (equal (!cr0bits->res3$inline (10bits-fix res3)
                                x)
         (!cr0bits->res3$inline res3 x)))

Theorem: !cr0bits->res3$inline-10bits-equiv-congruence-on-res3

(defthm !cr0bits->res3$inline-10bits-equiv-congruence-on-res3
  (implies (10bits-equiv res3 res3-equiv)
           (equal (!cr0bits->res3$inline res3 x)
                  (!cr0bits->res3$inline res3-equiv x)))
  :rule-classes :congruence)

Theorem: !cr0bits->res3$inline-of-cr0bits-fix-x

(defthm !cr0bits->res3$inline-of-cr0bits-fix-x
  (equal (!cr0bits->res3$inline res3 (cr0bits-fix x))
         (!cr0bits->res3$inline res3 x)))

Theorem: !cr0bits->res3$inline-cr0bits-equiv-congruence-on-x

(defthm !cr0bits->res3$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (!cr0bits->res3$inline res3 x)
                  (!cr0bits->res3$inline res3 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->res3-is-cr0bits

(defthm !cr0bits->res3-is-cr0bits
  (equal (!cr0bits->res3 res3 x)
         (change-cr0bits x :res3 res3)))

Theorem: cr0bits->res3-of-!cr0bits->res3

(defthm cr0bits->res3-of-!cr0bits->res3
  (b* ((?new-x (!cr0bits->res3$inline res3 x)))
    (equal (cr0bits->res3 new-x)
           (10bits-fix res3))))

Theorem: !cr0bits->res3-equiv-under-mask

(defthm !cr0bits->res3-equiv-under-mask
  (b* ((?new-x (!cr0bits->res3$inline res3 x)))
    (cr0bits-equiv-under-mask new-x x -536346625)))