Fixing function for ia32e-pdpte-pg-dirbits bit structures.
(ia32e-pdpte-pg-dirbits-fix x) → fty::fixed
Function:
(defun ia32e-pdpte-pg-dirbits-fix (x) (declare (xargs :guard (ia32e-pdpte-pg-dirbits-p x))) (let ((__function__ 'ia32e-pdpte-pg-dirbits-fix)) (declare (ignorable __function__)) (mbe :logic (loghead 64 x) :exec x)))
Theorem:
(defthm ia32e-pdpte-pg-dirbits-p-of-ia32e-pdpte-pg-dirbits-fix (b* ((fty::fixed (ia32e-pdpte-pg-dirbits-fix x))) (ia32e-pdpte-pg-dirbits-p fty::fixed)) :rule-classes :rewrite)
Theorem:
(defthm ia32e-pdpte-pg-dirbits-fix-when-ia32e-pdpte-pg-dirbits-p (implies (ia32e-pdpte-pg-dirbits-p x) (equal (ia32e-pdpte-pg-dirbits-fix x) x)))
Function:
(defun ia32e-pdpte-pg-dirbits-equiv$inline (x y) (declare (xargs :guard (and (ia32e-pdpte-pg-dirbits-p x) (ia32e-pdpte-pg-dirbits-p y)))) (equal (ia32e-pdpte-pg-dirbits-fix x) (ia32e-pdpte-pg-dirbits-fix y)))
Theorem:
(defthm ia32e-pdpte-pg-dirbits-equiv-is-an-equivalence (and (booleanp (ia32e-pdpte-pg-dirbits-equiv x y)) (ia32e-pdpte-pg-dirbits-equiv x x) (implies (ia32e-pdpte-pg-dirbits-equiv x y) (ia32e-pdpte-pg-dirbits-equiv y x)) (implies (and (ia32e-pdpte-pg-dirbits-equiv x y) (ia32e-pdpte-pg-dirbits-equiv y z)) (ia32e-pdpte-pg-dirbits-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm ia32e-pdpte-pg-dirbits-equiv-implies-equal-ia32e-pdpte-pg-dirbits-fix-1 (implies (ia32e-pdpte-pg-dirbits-equiv x x-equiv) (equal (ia32e-pdpte-pg-dirbits-fix x) (ia32e-pdpte-pg-dirbits-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm ia32e-pdpte-pg-dirbits-fix-under-ia32e-pdpte-pg-dirbits-equiv (ia32e-pdpte-pg-dirbits-equiv (ia32e-pdpte-pg-dirbits-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))