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Rflagsbits

!rflagsbits->res4

Update the |X86ISA|::|RES4| field of a rflagsbits bit structure.

Signature
(!rflagsbits->res4 res4 x) → new-x
Arguments: res4 — Guard (bitp res4).; x — Guard (rflagsbits-p x).
Returns: new-x — Type (rflagsbits-p new-x).

Definitions and Theorems

Function: !rflagsbits->res4$inline

(defun !rflagsbits->res4$inline (res4 x)
 (declare (xargs :guard (and (bitp res4) (rflagsbits-p x))))
 (mbe
     :logic
     (b* ((res4 (mbe :logic (bfix res4) :exec res4))
          (x (rflagsbits-fix x)))
       (part-install res4 x :width 1 :low 15))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 17) -32769)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 1) res4)
                                  15))))))

Theorem: rflagsbits-p-of-!rflagsbits->res4

(defthm rflagsbits-p-of-!rflagsbits->res4
  (b* ((new-x (!rflagsbits->res4$inline res4 x)))
    (rflagsbits-p new-x))
  :rule-classes :rewrite)

Theorem: !rflagsbits->res4$inline-of-bfix-res4

(defthm !rflagsbits->res4$inline-of-bfix-res4
  (equal (!rflagsbits->res4$inline (bfix res4) x)
         (!rflagsbits->res4$inline res4 x)))

Theorem: !rflagsbits->res4$inline-bit-equiv-congruence-on-res4

(defthm !rflagsbits->res4$inline-bit-equiv-congruence-on-res4
  (implies (bit-equiv res4 res4-equiv)
           (equal (!rflagsbits->res4$inline res4 x)
                  (!rflagsbits->res4$inline res4-equiv x)))
  :rule-classes :congruence)

Theorem: !rflagsbits->res4$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->res4$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->res4$inline res4 (rflagsbits-fix x))
         (!rflagsbits->res4$inline res4 x)))

Theorem: !rflagsbits->res4$inline-rflagsbits-equiv-congruence-on-x

(defthm !rflagsbits->res4$inline-rflagsbits-equiv-congruence-on-x
  (implies (rflagsbits-equiv x x-equiv)
           (equal (!rflagsbits->res4$inline res4 x)
                  (!rflagsbits->res4$inline res4 x-equiv)))
  :rule-classes :congruence)

Theorem: !rflagsbits->res4-is-rflagsbits

(defthm !rflagsbits->res4-is-rflagsbits
  (equal (!rflagsbits->res4 res4 x)
         (change-rflagsbits x :res4 res4)))

Theorem: rflagsbits->res4-of-!rflagsbits->res4

(defthm rflagsbits->res4-of-!rflagsbits->res4
  (b* ((?new-x (!rflagsbits->res4$inline res4 x)))
    (equal (rflagsbits->res4 new-x)
           (bfix res4))))

Theorem: !rflagsbits->res4-equiv-under-mask

(defthm !rflagsbits->res4-equiv-under-mask
  (b* ((?new-x (!rflagsbits->res4$inline res4 x)))
    (rflagsbits-equiv-under-mask new-x x -32769)))