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Rflagsbits

Rflagsbits-fix

Fixing function for rflagsbits bit structures.

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

Definitions and Theorems

Function: rflagsbits-fix$inline

(defun rflagsbits-fix$inline (x)
  (declare (xargs :guard (rflagsbits-p x)))
  (mbe :logic (loghead 32 x) :exec x))

Theorem: rflagsbits-p-of-rflagsbits-fix

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

Theorem: rflagsbits-fix-when-rflagsbits-p

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

Function: rflagsbits-equiv$inline

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

Theorem: rflagsbits-equiv-is-an-equivalence

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

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

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

Theorem: rflagsbits-fix-under-rflagsbits-equiv

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