Fixing function for data-segment-descriptor-attributesbits bit structures.
(data-segment-descriptor-attributesbits-fix x) → fty::fixed
Function:
(defun data-segment-descriptor-attributesbits-fix (x) (declare (xargs :guard (data-segment-descriptor-attributesbits-p x))) (let ((__function__ 'data-segment-descriptor-attributesbits-fix)) (declare (ignorable __function__)) (mbe :logic (loghead 16 x) :exec x)))
Theorem:
(defthm data-segment-descriptor-attributesbits-p-of-data-segment-descriptor-attributesbits-fix (b* ((fty::fixed (data-segment-descriptor-attributesbits-fix x))) (data-segment-descriptor-attributesbits-p fty::fixed)) :rule-classes :rewrite)
Theorem:
(defthm data-segment-descriptor-attributesbits-fix-when-data-segment-descriptor-attributesbits-p (implies (data-segment-descriptor-attributesbits-p x) (equal (data-segment-descriptor-attributesbits-fix x) x)))
Function:
(defun data-segment-descriptor-attributesbits-equiv$inline (x y) (declare (xargs :guard (and (data-segment-descriptor-attributesbits-p x) (data-segment-descriptor-attributesbits-p y)))) (equal (data-segment-descriptor-attributesbits-fix x) (data-segment-descriptor-attributesbits-fix y)))
Theorem:
(defthm data-segment-descriptor-attributesbits-equiv-is-an-equivalence (and (booleanp (data-segment-descriptor-attributesbits-equiv x y)) (data-segment-descriptor-attributesbits-equiv x x) (implies (data-segment-descriptor-attributesbits-equiv x y) (data-segment-descriptor-attributesbits-equiv y x)) (implies (and (data-segment-descriptor-attributesbits-equiv x y) (data-segment-descriptor-attributesbits-equiv y z)) (data-segment-descriptor-attributesbits-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm data-segment-descriptor-attributesbits-equiv-implies-equal-data-segment-descriptor-attributesbits-fix-1 (implies (data-segment-descriptor-attributesbits-equiv x x-equiv) (equal (data-segment-descriptor-attributesbits-fix x) (data-segment-descriptor-attributesbits-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm data-segment-descriptor-attributesbits-fix-under-data-segment-descriptor-attributesbits-equiv (data-segment-descriptor-attributesbits-equiv (data-segment-descriptor-attributesbits-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))