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Cr0bits

Cr0bits-fix

Fixing function for cr0bits bit structures.

Signature
(cr0bits-fix x) → fty::fixed
Arguments: x — Guard (cr0bits-p x).
Returns: fty::fixed — Type (cr0bits-p fty::fixed).

Definitions and Theorems

Function: cr0bits-fix$inline

(defun cr0bits-fix$inline (x)
  (declare (xargs :guard (cr0bits-p x)))
  (mbe :logic (loghead 32 x) :exec x))

Theorem: cr0bits-p-of-cr0bits-fix

(defthm cr0bits-p-of-cr0bits-fix
  (b* ((fty::fixed (cr0bits-fix$inline x)))
    (cr0bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: cr0bits-fix-when-cr0bits-p

(defthm cr0bits-fix-when-cr0bits-p
  (implies (cr0bits-p x)
           (equal (cr0bits-fix x) x)))

Function: cr0bits-equiv$inline

(defun cr0bits-equiv$inline (x y)
  (declare (xargs :guard (and (cr0bits-p x) (cr0bits-p y))))
  (equal (cr0bits-fix x) (cr0bits-fix y)))

Theorem: cr0bits-equiv-is-an-equivalence

(defthm cr0bits-equiv-is-an-equivalence
  (and (booleanp (cr0bits-equiv x y))
       (cr0bits-equiv x x)
       (implies (cr0bits-equiv x y)
                (cr0bits-equiv y x))
       (implies (and (cr0bits-equiv x y)
                     (cr0bits-equiv y z))
                (cr0bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: cr0bits-equiv-implies-equal-cr0bits-fix-1

(defthm cr0bits-equiv-implies-equal-cr0bits-fix-1
  (implies (cr0bits-equiv x x-equiv)
           (equal (cr0bits-fix x)
                  (cr0bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: cr0bits-fix-under-cr0bits-equiv

(defthm cr0bits-fix-under-cr0bits-equiv
  (cr0bits-equiv (cr0bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))