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Rflagsbits

!rflagsbits->nt

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

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

Definitions and Theorems

Function: !rflagsbits->nt$inline

(defun !rflagsbits->nt$inline (nt x)
 (declare (xargs :guard (and (bitp nt) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((nt (mbe :logic (bfix nt) :exec nt))
         (x (rflagsbits-fix x)))
      (part-install nt x :width 1 :low 14))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 16) -16385)))
                       (the (unsigned-byte 15)
                            (ash (the (unsigned-byte 1) nt) 14))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->nt-is-rflagsbits

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

Theorem: rflagsbits->nt-of-!rflagsbits->nt

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

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

(defthm !rflagsbits->nt-equiv-under-mask
  (b* ((?new-x (!rflagsbits->nt$inline nt x)))
    (rflagsbits-equiv-under-mask new-x x -16385)))