Update the |X86ISA|::|D/B| field of a data-segment-descriptorbits bit structure.
(!data-segment-descriptorbits->d/b d/b x) → new-x
Function:
(defun !data-segment-descriptorbits->d/b$inline (d/b x) (declare (xargs :guard (and (bitp d/b) (data-segment-descriptorbits-p x)))) (mbe :logic (b* ((d/b (mbe :logic (bfix d/b) :exec d/b)) (x (data-segment-descriptorbits-fix x))) (part-install d/b x :width 1 :low 54)) :exec (the (unsigned-byte 64) (logior (the (unsigned-byte 64) (logand (the (unsigned-byte 64) x) (the (signed-byte 56) -18014398509481985))) (the (unsigned-byte 55) (ash (the (unsigned-byte 1) d/b) 54))))))
Theorem:
(defthm data-segment-descriptorbits-p-of-!data-segment-descriptorbits->d/b (b* ((new-x (!data-segment-descriptorbits->d/b$inline d/b x))) (data-segment-descriptorbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !data-segment-descriptorbits->d/b$inline-of-bfix-d/b (equal (!data-segment-descriptorbits->d/b$inline (bfix d/b) x) (!data-segment-descriptorbits->d/b$inline d/b x)))
Theorem:
(defthm !data-segment-descriptorbits->d/b$inline-bit-equiv-congruence-on-d/b (implies (bit-equiv d/b d/b-equiv) (equal (!data-segment-descriptorbits->d/b$inline d/b x) (!data-segment-descriptorbits->d/b$inline d/b-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !data-segment-descriptorbits->d/b$inline-of-data-segment-descriptorbits-fix-x (equal (!data-segment-descriptorbits->d/b$inline d/b (data-segment-descriptorbits-fix x)) (!data-segment-descriptorbits->d/b$inline d/b x)))
Theorem:
(defthm !data-segment-descriptorbits->d/b$inline-data-segment-descriptorbits-equiv-congruence-on-x (implies (data-segment-descriptorbits-equiv x x-equiv) (equal (!data-segment-descriptorbits->d/b$inline d/b x) (!data-segment-descriptorbits->d/b$inline d/b x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !data-segment-descriptorbits->d/b-is-data-segment-descriptorbits (equal (!data-segment-descriptorbits->d/b d/b x) (change-data-segment-descriptorbits x :d/b d/b)))
Theorem:
(defthm data-segment-descriptorbits->d/b-of-!data-segment-descriptorbits->d/b (b* ((?new-x (!data-segment-descriptorbits->d/b$inline d/b x))) (equal (data-segment-descriptorbits->d/b new-x) (bfix d/b))))
Theorem:
(defthm !data-segment-descriptorbits->d/b-equiv-under-mask (b* ((?new-x (!data-segment-descriptorbits->d/b$inline d/b x))) (data-segment-descriptorbits-equiv-under-mask new-x x -18014398509481985)))