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Xcr0bits

Xcr0bits-fix

Fixing function for xcr0bits bit structures.

Signature
(xcr0bits-fix x) → fty::fixed
Arguments: x — Guard (xcr0bits-p x).
Returns: fty::fixed — Type (xcr0bits-p fty::fixed).

Definitions and Theorems

Function: xcr0bits-fix$inline

(defun xcr0bits-fix$inline (x)
  (declare (xargs :guard (xcr0bits-p x)))
  (mbe :logic (loghead 64 x) :exec x))

Theorem: xcr0bits-p-of-xcr0bits-fix

(defthm xcr0bits-p-of-xcr0bits-fix
  (b* ((fty::fixed (xcr0bits-fix$inline x)))
    (xcr0bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: xcr0bits-fix-when-xcr0bits-p

(defthm xcr0bits-fix-when-xcr0bits-p
  (implies (xcr0bits-p x)
           (equal (xcr0bits-fix x) x)))

Function: xcr0bits-equiv$inline

(defun xcr0bits-equiv$inline (x y)
  (declare (xargs :guard (and (xcr0bits-p x) (xcr0bits-p y))))
  (equal (xcr0bits-fix x)
         (xcr0bits-fix y)))

Theorem: xcr0bits-equiv-is-an-equivalence

(defthm xcr0bits-equiv-is-an-equivalence
  (and (booleanp (xcr0bits-equiv x y))
       (xcr0bits-equiv x x)
       (implies (xcr0bits-equiv x y)
                (xcr0bits-equiv y x))
       (implies (and (xcr0bits-equiv x y)
                     (xcr0bits-equiv y z))
                (xcr0bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: xcr0bits-equiv-implies-equal-xcr0bits-fix-1

(defthm xcr0bits-equiv-implies-equal-xcr0bits-fix-1
  (implies (xcr0bits-equiv x x-equiv)
           (equal (xcr0bits-fix x)
                  (xcr0bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: xcr0bits-fix-under-xcr0bits-equiv

(defthm xcr0bits-fix-under-xcr0bits-equiv
  (xcr0bits-equiv (xcr0bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))