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Ia32_eferbits

Ia32_eferbits-fix

Fixing function for ia32_eferbits bit structures.

Signature
(ia32_eferbits-fix x) → fty::fixed
Arguments: x — Guard (ia32_eferbits-p x).
Returns: fty::fixed — Type (ia32_eferbits-p fty::fixed).

Definitions and Theorems

Function: ia32_eferbits-fix$inline

(defun ia32_eferbits-fix$inline (x)
  (declare (xargs :guard (ia32_eferbits-p x)))
  (mbe :logic (loghead 12 x) :exec x))

Theorem: ia32_eferbits-p-of-ia32_eferbits-fix

(defthm ia32_eferbits-p-of-ia32_eferbits-fix
  (b* ((fty::fixed (ia32_eferbits-fix$inline x)))
    (ia32_eferbits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: ia32_eferbits-fix-when-ia32_eferbits-p

(defthm ia32_eferbits-fix-when-ia32_eferbits-p
  (implies (ia32_eferbits-p x)
           (equal (ia32_eferbits-fix x) x)))

Function: ia32_eferbits-equiv$inline

(defun ia32_eferbits-equiv$inline (x y)
  (declare (xargs :guard (and (ia32_eferbits-p x)
                              (ia32_eferbits-p y))))
  (equal (ia32_eferbits-fix x)
         (ia32_eferbits-fix y)))

Theorem: ia32_eferbits-equiv-is-an-equivalence

(defthm ia32_eferbits-equiv-is-an-equivalence
  (and (booleanp (ia32_eferbits-equiv x y))
       (ia32_eferbits-equiv x x)
       (implies (ia32_eferbits-equiv x y)
                (ia32_eferbits-equiv y x))
       (implies (and (ia32_eferbits-equiv x y)
                     (ia32_eferbits-equiv y z))
                (ia32_eferbits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ia32_eferbits-equiv-implies-equal-ia32_eferbits-fix-1

(defthm ia32_eferbits-equiv-implies-equal-ia32_eferbits-fix-1
  (implies (ia32_eferbits-equiv x x-equiv)
           (equal (ia32_eferbits-fix x)
                  (ia32_eferbits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ia32_eferbits-fix-under-ia32_eferbits-equiv

(defthm ia32_eferbits-fix-under-ia32_eferbits-equiv
  (ia32_eferbits-equiv (ia32_eferbits-fix x)
                       x)
  :rule-classes (:rewrite :rewrite-quoted-constant))