Update the |X86ISA|::|BASE31-24| field of a system-segment-descriptorbits bit structure.
(!system-segment-descriptorbits->base31-24 base31-24 x) → new-x
Function:
(defun !system-segment-descriptorbits->base31-24$inline (base31-24 x) (declare (xargs :guard (and (8bits-p base31-24) (system-segment-descriptorbits-p x)))) (mbe :logic (b* ((base31-24 (mbe :logic (8bits-fix base31-24) :exec base31-24)) (x (system-segment-descriptorbits-fix x))) (part-install base31-24 x :width 8 :low 56)) :exec (the (unsigned-byte 128) (logior (the (unsigned-byte 128) (logand (the (unsigned-byte 128) x) (the (signed-byte 65) -18374686479671623681))) (the (unsigned-byte 64) (ash (the (unsigned-byte 8) base31-24) 56))))))
Theorem:
(defthm system-segment-descriptorbits-p-of-!system-segment-descriptorbits->base31-24 (b* ((new-x (!system-segment-descriptorbits->base31-24$inline base31-24 x))) (system-segment-descriptorbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !system-segment-descriptorbits->base31-24$inline-of-8bits-fix-base31-24 (equal (!system-segment-descriptorbits->base31-24$inline (8bits-fix base31-24) x) (!system-segment-descriptorbits->base31-24$inline base31-24 x)))
Theorem:
(defthm !system-segment-descriptorbits->base31-24$inline-8bits-equiv-congruence-on-base31-24 (implies (8bits-equiv base31-24 base31-24-equiv) (equal (!system-segment-descriptorbits->base31-24$inline base31-24 x) (!system-segment-descriptorbits->base31-24$inline base31-24-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !system-segment-descriptorbits->base31-24$inline-of-system-segment-descriptorbits-fix-x (equal (!system-segment-descriptorbits->base31-24$inline base31-24 (system-segment-descriptorbits-fix x)) (!system-segment-descriptorbits->base31-24$inline base31-24 x)))
Theorem:
(defthm !system-segment-descriptorbits->base31-24$inline-system-segment-descriptorbits-equiv-congruence-on-x (implies (system-segment-descriptorbits-equiv x x-equiv) (equal (!system-segment-descriptorbits->base31-24$inline base31-24 x) (!system-segment-descriptorbits->base31-24$inline base31-24 x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !system-segment-descriptorbits->base31-24-is-system-segment-descriptorbits (equal (!system-segment-descriptorbits->base31-24 base31-24 x) (change-system-segment-descriptorbits x :base31-24 base31-24)))
Theorem:
(defthm system-segment-descriptorbits->base31-24-of-!system-segment-descriptorbits->base31-24 (b* ((?new-x (!system-segment-descriptorbits->base31-24$inline base31-24 x))) (equal (system-segment-descriptorbits->base31-24 new-x) (8bits-fix base31-24))))
Theorem:
(defthm !system-segment-descriptorbits->base31-24-equiv-under-mask (b* ((?new-x (!system-segment-descriptorbits->base31-24$inline base31-24 x))) (system-segment-descriptorbits-equiv-under-mask new-x x -18374686479671623681)))