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Cr0bits

!cr0bits->res1

Update the |X86ISA|::|RES1| field of a cr0bits bit structure.

Signature
(!cr0bits->res1 res1 x) → new-x
Arguments: res1 — Guard (10bits-p res1).; x — Guard (cr0bits-p x).
Returns: new-x — Type (cr0bits-p new-x).

Definitions and Theorems

Function: !cr0bits->res1$inline

(defun !cr0bits->res1$inline (res1 x)
 (declare (xargs :guard (and (10bits-p res1) (cr0bits-p x))))
 (mbe
     :logic
     (b* ((res1 (mbe :logic (10bits-fix res1)
                     :exec res1))
          (x (cr0bits-fix x)))
       (part-install res1 x :width 10 :low 6))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 17) -65473)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 10) res1)
                                  6))))))

Theorem: cr0bits-p-of-!cr0bits->res1

(defthm cr0bits-p-of-!cr0bits->res1
  (b* ((new-x (!cr0bits->res1$inline res1 x)))
    (cr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr0bits->res1$inline-of-10bits-fix-res1

(defthm !cr0bits->res1$inline-of-10bits-fix-res1
  (equal (!cr0bits->res1$inline (10bits-fix res1)
                                x)
         (!cr0bits->res1$inline res1 x)))

Theorem: !cr0bits->res1$inline-10bits-equiv-congruence-on-res1

(defthm !cr0bits->res1$inline-10bits-equiv-congruence-on-res1
  (implies (10bits-equiv res1 res1-equiv)
           (equal (!cr0bits->res1$inline res1 x)
                  (!cr0bits->res1$inline res1-equiv x)))
  :rule-classes :congruence)

Theorem: !cr0bits->res1$inline-of-cr0bits-fix-x

(defthm !cr0bits->res1$inline-of-cr0bits-fix-x
  (equal (!cr0bits->res1$inline res1 (cr0bits-fix x))
         (!cr0bits->res1$inline res1 x)))

Theorem: !cr0bits->res1$inline-cr0bits-equiv-congruence-on-x

(defthm !cr0bits->res1$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (!cr0bits->res1$inline res1 x)
                  (!cr0bits->res1$inline res1 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->res1-is-cr0bits

(defthm !cr0bits->res1-is-cr0bits
  (equal (!cr0bits->res1 res1 x)
         (change-cr0bits x :res1 res1)))

Theorem: cr0bits->res1-of-!cr0bits->res1

(defthm cr0bits->res1-of-!cr0bits->res1
  (b* ((?new-x (!cr0bits->res1$inline res1 x)))
    (equal (cr0bits->res1 new-x)
           (10bits-fix res1))))

Theorem: !cr0bits->res1-equiv-under-mask

(defthm !cr0bits->res1-equiv-under-mask
  (b* ((?new-x (!cr0bits->res1$inline res1 x)))
    (cr0bits-equiv-under-mask new-x x -65473)))