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Vex2-byte1

Vex2-byte1-fix

Fixing function for vex2-byte1 bit structures.

Signature
(vex2-byte1-fix x) → fty::fixed
Arguments: x — Guard (vex2-byte1-p x).
Returns: fty::fixed — Type (vex2-byte1-p fty::fixed).

Definitions and Theorems

Function: vex2-byte1-fix$inline

(defun vex2-byte1-fix$inline (x)
  (declare (xargs :guard (vex2-byte1-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: vex2-byte1-p-of-vex2-byte1-fix

(defthm vex2-byte1-p-of-vex2-byte1-fix
  (b* ((fty::fixed (vex2-byte1-fix$inline x)))
    (vex2-byte1-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex2-byte1-fix-when-vex2-byte1-p

(defthm vex2-byte1-fix-when-vex2-byte1-p
  (implies (vex2-byte1-p x)
           (equal (vex2-byte1-fix x) x)))

Function: vex2-byte1-equiv$inline

(defun vex2-byte1-equiv$inline (x y)
  (declare (xargs :guard (and (vex2-byte1-p x)
                              (vex2-byte1-p y))))
  (equal (vex2-byte1-fix x)
         (vex2-byte1-fix y)))

Theorem: vex2-byte1-equiv-is-an-equivalence

(defthm vex2-byte1-equiv-is-an-equivalence
  (and (booleanp (vex2-byte1-equiv x y))
       (vex2-byte1-equiv x x)
       (implies (vex2-byte1-equiv x y)
                (vex2-byte1-equiv y x))
       (implies (and (vex2-byte1-equiv x y)
                     (vex2-byte1-equiv y z))
                (vex2-byte1-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex2-byte1-equiv-implies-equal-vex2-byte1-fix-1

(defthm vex2-byte1-equiv-implies-equal-vex2-byte1-fix-1
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1-fix x)
                  (vex2-byte1-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex2-byte1-fix-under-vex2-byte1-equiv

(defthm vex2-byte1-fix-under-vex2-byte1-equiv
  (vex2-byte1-equiv (vex2-byte1-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))