Fixing function for hidden-segment-registerbits bit structures.
(hidden-segment-registerbits-fix x) → fty::fixed
Function:
(defun hidden-segment-registerbits-fix (x) (declare (xargs :guard (hidden-segment-registerbits-p x))) (let ((__function__ 'hidden-segment-registerbits-fix)) (declare (ignorable __function__)) (mbe :logic (loghead 112 x) :exec x)))
Theorem:
(defthm hidden-segment-registerbits-p-of-hidden-segment-registerbits-fix (b* ((fty::fixed (hidden-segment-registerbits-fix x))) (hidden-segment-registerbits-p fty::fixed)) :rule-classes :rewrite)
Theorem:
(defthm hidden-segment-registerbits-fix-when-hidden-segment-registerbits-p (implies (hidden-segment-registerbits-p x) (equal (hidden-segment-registerbits-fix x) x)))
Function:
(defun hidden-segment-registerbits-equiv$inline (x y) (declare (xargs :guard (and (hidden-segment-registerbits-p x) (hidden-segment-registerbits-p y)))) (equal (hidden-segment-registerbits-fix x) (hidden-segment-registerbits-fix y)))
Theorem:
(defthm hidden-segment-registerbits-equiv-is-an-equivalence (and (booleanp (hidden-segment-registerbits-equiv x y)) (hidden-segment-registerbits-equiv x x) (implies (hidden-segment-registerbits-equiv x y) (hidden-segment-registerbits-equiv y x)) (implies (and (hidden-segment-registerbits-equiv x y) (hidden-segment-registerbits-equiv y z)) (hidden-segment-registerbits-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm hidden-segment-registerbits-equiv-implies-equal-hidden-segment-registerbits-fix-1 (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (hidden-segment-registerbits-fix x) (hidden-segment-registerbits-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm hidden-segment-registerbits-fix-under-hidden-segment-registerbits-equiv (hidden-segment-registerbits-equiv (hidden-segment-registerbits-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))