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Vex3-byte2

Vex3-byte2-fix

Fixing function for vex3-byte2 bit structures.

Signature
(vex3-byte2-fix x) → fty::fixed
Arguments: x — Guard (vex3-byte2-p x).
Returns: fty::fixed — Type (vex3-byte2-p fty::fixed).

Definitions and Theorems

Function: vex3-byte2-fix$inline

(defun vex3-byte2-fix$inline (x)
  (declare (xargs :guard (vex3-byte2-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: vex3-byte2-p-of-vex3-byte2-fix

(defthm vex3-byte2-p-of-vex3-byte2-fix
  (b* ((fty::fixed (vex3-byte2-fix$inline x)))
    (vex3-byte2-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex3-byte2-fix-when-vex3-byte2-p

(defthm vex3-byte2-fix-when-vex3-byte2-p
  (implies (vex3-byte2-p x)
           (equal (vex3-byte2-fix x) x)))

Function: vex3-byte2-equiv$inline

(defun vex3-byte2-equiv$inline (x y)
  (declare (xargs :guard (and (vex3-byte2-p x)
                              (vex3-byte2-p y))))
  (equal (vex3-byte2-fix x)
         (vex3-byte2-fix y)))

Theorem: vex3-byte2-equiv-is-an-equivalence

(defthm vex3-byte2-equiv-is-an-equivalence
  (and (booleanp (vex3-byte2-equiv x y))
       (vex3-byte2-equiv x x)
       (implies (vex3-byte2-equiv x y)
                (vex3-byte2-equiv y x))
       (implies (and (vex3-byte2-equiv x y)
                     (vex3-byte2-equiv y z))
                (vex3-byte2-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex3-byte2-equiv-implies-equal-vex3-byte2-fix-1

(defthm vex3-byte2-equiv-implies-equal-vex3-byte2-fix-1
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2-fix x)
                  (vex3-byte2-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex3-byte2-fix-under-vex3-byte2-equiv

(defthm vex3-byte2-fix-under-vex3-byte2-equiv
  (vex3-byte2-equiv (vex3-byte2-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))