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Rflagsbits

!rflagsbits->res1

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

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

Definitions and Theorems

Function: !rflagsbits->res1$inline

(defun !rflagsbits->res1$inline (res1 x)
  (declare (xargs :guard (and (bitp res1) (rflagsbits-p x))))
  (mbe :logic
       (b* ((res1 (mbe :logic (bfix res1) :exec res1))
            (x (rflagsbits-fix x)))
         (part-install res1 x :width 1 :low 1))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 3) -3)))
                          (the (unsigned-byte 2)
                               (ash (the (unsigned-byte 1) res1)
                                    1))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->res1-is-rflagsbits

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

Theorem: rflagsbits->res1-of-!rflagsbits->res1

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

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

(defthm !rflagsbits->res1-equiv-under-mask
  (b* ((?new-x (!rflagsbits->res1$inline res1 x)))
    (rflagsbits-equiv-under-mask new-x x -3)))