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Gdtr/idtrbits

Gdtr/idtrbits-fix

Fixing function for gdtr/idtrbits bit structures.

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

Definitions and Theorems

Function: gdtr/idtrbits-fix

(defun gdtr/idtrbits-fix (x)
  (declare (xargs :guard (gdtr/idtrbits-p x)))
  (let ((__function__ 'gdtr/idtrbits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 80 x) :exec x)))

Theorem: gdtr/idtrbits-p-of-gdtr/idtrbits-fix

(defthm gdtr/idtrbits-p-of-gdtr/idtrbits-fix
  (b* ((fty::fixed (gdtr/idtrbits-fix x)))
    (gdtr/idtrbits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: gdtr/idtrbits-fix-when-gdtr/idtrbits-p

(defthm gdtr/idtrbits-fix-when-gdtr/idtrbits-p
  (implies (gdtr/idtrbits-p x)
           (equal (gdtr/idtrbits-fix x) x)))

Function: gdtr/idtrbits-equiv$inline

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

Theorem: gdtr/idtrbits-equiv-is-an-equivalence

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

Theorem: gdtr/idtrbits-equiv-implies-equal-gdtr/idtrbits-fix-1

(defthm gdtr/idtrbits-equiv-implies-equal-gdtr/idtrbits-fix-1
  (implies (gdtr/idtrbits-equiv x x-equiv)
           (equal (gdtr/idtrbits-fix x)
                  (gdtr/idtrbits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: gdtr/idtrbits-fix-under-gdtr/idtrbits-equiv

(defthm gdtr/idtrbits-fix-under-gdtr/idtrbits-equiv
  (gdtr/idtrbits-equiv (gdtr/idtrbits-fix x)
                       x)
  :rule-classes (:rewrite :rewrite-quoted-constant))