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Rflagsbits

!rflagsbits->res2

Update the |X86ISA|::|RES2| field of a rflagsbits bit structure.

Signature
(!rflagsbits->res2 res2 x) → new-x
Arguments: res2 — Guard (bitp res2).; x — Guard (rflagsbits-p x).
Returns: new-x — Type (rflagsbits-p new-x).

Definitions and Theorems

Function: !rflagsbits->res2$inline

(defun !rflagsbits->res2$inline (res2 x)
  (declare (xargs :guard (and (bitp res2) (rflagsbits-p x))))
  (mbe :logic
       (b* ((res2 (mbe :logic (bfix res2) :exec res2))
            (x (rflagsbits-fix x)))
         (part-install res2 x :width 1 :low 3))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 5) -9)))
                          (the (unsigned-byte 4)
                               (ash (the (unsigned-byte 1) res2)
                                    3))))))

Theorem: rflagsbits-p-of-!rflagsbits->res2

(defthm rflagsbits-p-of-!rflagsbits->res2
  (b* ((new-x (!rflagsbits->res2$inline res2 x)))
    (rflagsbits-p new-x))
  :rule-classes :rewrite)

Theorem: !rflagsbits->res2$inline-of-bfix-res2

(defthm !rflagsbits->res2$inline-of-bfix-res2
  (equal (!rflagsbits->res2$inline (bfix res2) x)
         (!rflagsbits->res2$inline res2 x)))

Theorem: !rflagsbits->res2$inline-bit-equiv-congruence-on-res2

(defthm !rflagsbits->res2$inline-bit-equiv-congruence-on-res2
  (implies (bit-equiv res2 res2-equiv)
           (equal (!rflagsbits->res2$inline res2 x)
                  (!rflagsbits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !rflagsbits->res2$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->res2$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->res2$inline res2 (rflagsbits-fix x))
         (!rflagsbits->res2$inline res2 x)))

Theorem: !rflagsbits->res2$inline-rflagsbits-equiv-congruence-on-x

(defthm !rflagsbits->res2$inline-rflagsbits-equiv-congruence-on-x
  (implies (rflagsbits-equiv x x-equiv)
           (equal (!rflagsbits->res2$inline res2 x)
                  (!rflagsbits->res2$inline res2 x-equiv)))
  :rule-classes :congruence)

Theorem: !rflagsbits->res2-is-rflagsbits

(defthm !rflagsbits->res2-is-rflagsbits
  (equal (!rflagsbits->res2 res2 x)
         (change-rflagsbits x :res2 res2)))

Theorem: rflagsbits->res2-of-!rflagsbits->res2

(defthm rflagsbits->res2-of-!rflagsbits->res2
  (b* ((?new-x (!rflagsbits->res2$inline res2 x)))
    (equal (rflagsbits->res2 new-x)
           (bfix res2))))

Theorem: !rflagsbits->res2-equiv-under-mask

(defthm !rflagsbits->res2-equiv-under-mask
  (b* ((?new-x (!rflagsbits->res2$inline res2 x)))
    (rflagsbits-equiv-under-mask new-x x -9)))