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Xcr0bits

!xcr0bits->res1

Update the |X86ISA|::|RES1| field of a xcr0bits bit structure.

Signature
(!xcr0bits->res1 res1 x) → new-x
Arguments: res1 — Guard (bitp res1).; x — Guard (xcr0bits-p x).
Returns: new-x — Type (xcr0bits-p new-x).

Definitions and Theorems

Function: !xcr0bits->res1$inline

(defun !xcr0bits->res1$inline (res1 x)
  (declare (xargs :guard (and (bitp res1) (xcr0bits-p x))))
  (mbe :logic
       (b* ((res1 (mbe :logic (bfix res1) :exec res1))
            (x (xcr0bits-fix x)))
         (part-install res1 x :width 1 :low 8))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 10) -257)))
                          (the (unsigned-byte 9)
                               (ash (the (unsigned-byte 1) res1)
                                    8))))))

Theorem: xcr0bits-p-of-!xcr0bits->res1

(defthm xcr0bits-p-of-!xcr0bits->res1
  (b* ((new-x (!xcr0bits->res1$inline res1 x)))
    (xcr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !xcr0bits->res1$inline-of-bfix-res1

(defthm !xcr0bits->res1$inline-of-bfix-res1
  (equal (!xcr0bits->res1$inline (bfix res1) x)
         (!xcr0bits->res1$inline res1 x)))

Theorem: !xcr0bits->res1$inline-bit-equiv-congruence-on-res1

(defthm !xcr0bits->res1$inline-bit-equiv-congruence-on-res1
  (implies (bit-equiv res1 res1-equiv)
           (equal (!xcr0bits->res1$inline res1 x)
                  (!xcr0bits->res1$inline res1-equiv x)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res1$inline-of-xcr0bits-fix-x

(defthm !xcr0bits->res1$inline-of-xcr0bits-fix-x
  (equal (!xcr0bits->res1$inline res1 (xcr0bits-fix x))
         (!xcr0bits->res1$inline res1 x)))

Theorem: !xcr0bits->res1$inline-xcr0bits-equiv-congruence-on-x

(defthm !xcr0bits->res1$inline-xcr0bits-equiv-congruence-on-x
  (implies (xcr0bits-equiv x x-equiv)
           (equal (!xcr0bits->res1$inline res1 x)
                  (!xcr0bits->res1$inline res1 x-equiv)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res1-is-xcr0bits

(defthm !xcr0bits->res1-is-xcr0bits
  (equal (!xcr0bits->res1 res1 x)
         (change-xcr0bits x :res1 res1)))

Theorem: xcr0bits->res1-of-!xcr0bits->res1

(defthm xcr0bits->res1-of-!xcr0bits->res1
  (b* ((?new-x (!xcr0bits->res1$inline res1 x)))
    (equal (xcr0bits->res1 new-x)
           (bfix res1))))

Theorem: !xcr0bits->res1-equiv-under-mask

(defthm !xcr0bits->res1-equiv-under-mask
  (b* ((?new-x (!xcr0bits->res1$inline res1 x)))
    (xcr0bits-equiv-under-mask new-x x -257)))