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Interp-flags

Interp-flags-fix

Fixing function for interp-flags bit structures.

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

Definitions and Theorems

Function: interp-flags-fix

(defun interp-flags-fix (x)
  (declare (xargs :guard (interp-flags-p x)))
  (let ((__function__ 'interp-flags-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 6 x) :exec x)))

Theorem: interp-flags-p-of-interp-flags-fix

(defthm interp-flags-p-of-interp-flags-fix
  (b* ((fty::fixed (interp-flags-fix x)))
    (interp-flags-p fty::fixed))
  :rule-classes :rewrite)

Theorem: interp-flags-fix-when-interp-flags-p

(defthm interp-flags-fix-when-interp-flags-p
  (implies (interp-flags-p x)
           (equal (interp-flags-fix x) x)))

Function: interp-flags-equiv$inline

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

Theorem: interp-flags-equiv-is-an-equivalence

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

Theorem: interp-flags-equiv-implies-equal-interp-flags-fix-1

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

Theorem: interp-flags-fix-under-interp-flags-equiv

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

Theorem: interp-flags-fix-of-interp-flags-fix-x

(defthm interp-flags-fix-of-interp-flags-fix-x
  (equal (interp-flags-fix (interp-flags-fix x))
         (interp-flags-fix x)))

Theorem: interp-flags-fix-interp-flags-equiv-congruence-on-x

(defthm interp-flags-fix-interp-flags-equiv-congruence-on-x
  (implies (interp-flags-equiv x x-equiv)
           (equal (interp-flags-fix x)
                  (interp-flags-fix x-equiv)))
  :rule-classes :congruence)