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Cr3bits

!cr3bits->res1

Update the |X86ISA|::|RES1| field of a cr3bits bit structure.

Signature
(!cr3bits->res1 res1 x) → new-x
Arguments: res1 — Guard (3bits-p res1).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->res1$inline

(defun !cr3bits->res1$inline (res1 x)
  (declare (xargs :guard (and (3bits-p res1) (cr3bits-p x))))
  (mbe :logic
       (b* ((res1 (mbe :logic (3bits-fix res1)
                       :exec res1))
            (x (cr3bits-fix x)))
         (part-install res1 x :width 3 :low 0))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 4) -8)))
                          (the (unsigned-byte 3) res1)))))

Theorem: cr3bits-p-of-!cr3bits->res1

(defthm cr3bits-p-of-!cr3bits->res1
  (b* ((new-x (!cr3bits->res1$inline res1 x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->res1$inline-of-3bits-fix-res1

(defthm !cr3bits->res1$inline-of-3bits-fix-res1
  (equal (!cr3bits->res1$inline (3bits-fix res1)
                                x)
         (!cr3bits->res1$inline res1 x)))

Theorem: !cr3bits->res1$inline-3bits-equiv-congruence-on-res1

(defthm !cr3bits->res1$inline-3bits-equiv-congruence-on-res1
  (implies (3bits-equiv res1 res1-equiv)
           (equal (!cr3bits->res1$inline res1 x)
                  (!cr3bits->res1$inline res1-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->res1$inline-of-cr3bits-fix-x

(defthm !cr3bits->res1$inline-of-cr3bits-fix-x
  (equal (!cr3bits->res1$inline res1 (cr3bits-fix x))
         (!cr3bits->res1$inline res1 x)))

Theorem: !cr3bits->res1$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->res1$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->res1$inline res1 x)
                  (!cr3bits->res1$inline res1 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->res1-is-cr3bits

(defthm !cr3bits->res1-is-cr3bits
  (equal (!cr3bits->res1 res1 x)
         (change-cr3bits x :res1 res1)))

Theorem: cr3bits->res1-of-!cr3bits->res1

(defthm cr3bits->res1-of-!cr3bits->res1
  (b* ((?new-x (!cr3bits->res1$inline res1 x)))
    (equal (cr3bits->res1 new-x)
           (3bits-fix res1))))

Theorem: !cr3bits->res1-equiv-under-mask

(defthm !cr3bits->res1-equiv-under-mask
  (b* ((?new-x (!cr3bits->res1$inline res1 x)))
    (cr3bits-equiv-under-mask new-x x -8)))