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Rflagsbits

!rflagsbits->ac

Update the |X86ISA|::|AC| field of a rflagsbits bit structure.

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

Definitions and Theorems

Function: !rflagsbits->ac$inline

(defun !rflagsbits->ac$inline (ac x)
 (declare (xargs :guard (and (bitp ac) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((ac (mbe :logic (bfix ac) :exec ac))
         (x (rflagsbits-fix x)))
      (part-install ac x :width 1 :low 18))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 20) -262145)))
                       (the (unsigned-byte 19)
                            (ash (the (unsigned-byte 1) ac) 18))))))

Theorem: rflagsbits-p-of-!rflagsbits->ac

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

Theorem: !rflagsbits->ac$inline-of-bfix-ac

(defthm !rflagsbits->ac$inline-of-bfix-ac
  (equal (!rflagsbits->ac$inline (bfix ac) x)
         (!rflagsbits->ac$inline ac x)))

Theorem: !rflagsbits->ac$inline-bit-equiv-congruence-on-ac

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

Theorem: !rflagsbits->ac$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->ac$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->ac$inline ac (rflagsbits-fix x))
         (!rflagsbits->ac$inline ac x)))

Theorem: !rflagsbits->ac$inline-rflagsbits-equiv-congruence-on-x

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

Theorem: !rflagsbits->ac-is-rflagsbits

(defthm !rflagsbits->ac-is-rflagsbits
  (equal (!rflagsbits->ac ac x)
         (change-rflagsbits x :ac ac)))

Theorem: rflagsbits->ac-of-!rflagsbits->ac

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

Theorem: !rflagsbits->ac-equiv-under-mask

(defthm !rflagsbits->ac-equiv-under-mask
  (b* ((?new-x (!rflagsbits->ac$inline ac x)))
    (rflagsbits-equiv-under-mask new-x x -262145)))