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Sib-fix

Fixing function for sib bit structures.

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

Definitions and Theorems

Function: sib-fix$inline

(defun sib-fix$inline (x)
  (declare (xargs :guard (sib-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: sib-p-of-sib-fix

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

Theorem: sib-fix-when-sib-p

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

Function: sib-equiv$inline

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

Theorem: sib-equiv-is-an-equivalence

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

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

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

Theorem: sib-fix-under-sib-equiv

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