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Mxcsrbits

Mxcsrbits-fix

Fixing function for mxcsrbits bit structures.

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

Definitions and Theorems

Function: mxcsrbits-fix

(defun mxcsrbits-fix (x)
  (declare (xargs :guard (mxcsrbits-p x)))
  (let ((__function__ 'mxcsrbits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 32 x) :exec x)))

Theorem: mxcsrbits-p-of-mxcsrbits-fix

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

Theorem: mxcsrbits-fix-when-mxcsrbits-p

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

Function: mxcsrbits-equiv$inline

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

Theorem: mxcsrbits-equiv-is-an-equivalence

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

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

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

Theorem: mxcsrbits-fix-under-mxcsrbits-equiv

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