Update the |X86ISA|::|LIMIT15-0| field of a system-segment-descriptorbits bit structure.
(!system-segment-descriptorbits->limit15-0 limit15-0 x) → new-x
Function:
(defun !system-segment-descriptorbits->limit15-0$inline (limit15-0 x) (declare (xargs :guard (and (16bits-p limit15-0) (system-segment-descriptorbits-p x)))) (mbe :logic (b* ((limit15-0 (mbe :logic (16bits-fix limit15-0) :exec limit15-0)) (x (system-segment-descriptorbits-fix x))) (part-install limit15-0 x :width 16 :low 0)) :exec (the (unsigned-byte 128) (logior (the (unsigned-byte 128) (logand (the (unsigned-byte 128) x) (the (signed-byte 17) -65536))) (the (unsigned-byte 16) limit15-0)))))
Theorem:
(defthm system-segment-descriptorbits-p-of-!system-segment-descriptorbits->limit15-0 (b* ((new-x (!system-segment-descriptorbits->limit15-0$inline limit15-0 x))) (system-segment-descriptorbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !system-segment-descriptorbits->limit15-0$inline-of-16bits-fix-limit15-0 (equal (!system-segment-descriptorbits->limit15-0$inline (16bits-fix limit15-0) x) (!system-segment-descriptorbits->limit15-0$inline limit15-0 x)))
Theorem:
(defthm !system-segment-descriptorbits->limit15-0$inline-16bits-equiv-congruence-on-limit15-0 (implies (16bits-equiv limit15-0 limit15-0-equiv) (equal (!system-segment-descriptorbits->limit15-0$inline limit15-0 x) (!system-segment-descriptorbits->limit15-0$inline limit15-0-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !system-segment-descriptorbits->limit15-0$inline-of-system-segment-descriptorbits-fix-x (equal (!system-segment-descriptorbits->limit15-0$inline limit15-0 (system-segment-descriptorbits-fix x)) (!system-segment-descriptorbits->limit15-0$inline limit15-0 x)))
Theorem:
(defthm !system-segment-descriptorbits->limit15-0$inline-system-segment-descriptorbits-equiv-congruence-on-x (implies (system-segment-descriptorbits-equiv x x-equiv) (equal (!system-segment-descriptorbits->limit15-0$inline limit15-0 x) (!system-segment-descriptorbits->limit15-0$inline limit15-0 x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !system-segment-descriptorbits->limit15-0-is-system-segment-descriptorbits (equal (!system-segment-descriptorbits->limit15-0 limit15-0 x) (change-system-segment-descriptorbits x :limit15-0 limit15-0)))
Theorem:
(defthm system-segment-descriptorbits->limit15-0-of-!system-segment-descriptorbits->limit15-0 (b* ((?new-x (!system-segment-descriptorbits->limit15-0$inline limit15-0 x))) (equal (system-segment-descriptorbits->limit15-0 new-x) (16bits-fix limit15-0))))
Theorem:
(defthm !system-segment-descriptorbits->limit15-0-equiv-under-mask (b* ((?new-x (!system-segment-descriptorbits->limit15-0$inline limit15-0 x))) (system-segment-descriptorbits-equiv-under-mask new-x x -65536)))