Intel manual, Dec'23, Vol. 3A, Figure 3-7.
This is a bitstruct type introduced by defbitstruct, represented as a unsigned 112-bit integer.
Function:
(defun hidden-segment-registerbits-p (x) (declare (xargs :guard t)) (let ((__function__ 'hidden-segment-registerbits-p)) (declare (ignorable __function__)) (mbe :logic (unsigned-byte-p 112 x) :exec (and (natp x) (< x 5192296858534827628530496329220096)))))
Theorem:
(defthm hidden-segment-registerbits-p-when-unsigned-byte-p (implies (unsigned-byte-p 112 x) (hidden-segment-registerbits-p x)))
Theorem:
(defthm unsigned-byte-p-when-hidden-segment-registerbits-p (implies (hidden-segment-registerbits-p x) (unsigned-byte-p 112 x)))
Theorem:
(defthm hidden-segment-registerbits-p-compound-recognizer (implies (hidden-segment-registerbits-p x) (natp x)) :rule-classes :compound-recognizer)
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))
Function:
(defun hidden-segment-registerbits (base-addr limit attr) (declare (xargs :guard (and (64bits-p base-addr) (32bits-p limit) (16bits-p attr)))) (let ((__function__ 'hidden-segment-registerbits)) (declare (ignorable __function__)) (b* ((base-addr (mbe :logic (64bits-fix base-addr) :exec base-addr)) (limit (mbe :logic (32bits-fix limit) :exec limit)) (attr (mbe :logic (16bits-fix attr) :exec attr))) (logapp 64 base-addr (logapp 32 limit attr)))))
Theorem:
(defthm hidden-segment-registerbits-p-of-hidden-segment-registerbits (b* ((hidden-segment-registerbits (hidden-segment-registerbits base-addr limit attr))) (hidden-segment-registerbits-p hidden-segment-registerbits)) :rule-classes :rewrite)
Theorem:
(defthm hidden-segment-registerbits-of-64bits-fix-base-addr (equal (hidden-segment-registerbits (64bits-fix base-addr) limit attr) (hidden-segment-registerbits base-addr limit attr)))
Theorem:
(defthm hidden-segment-registerbits-64bits-equiv-congruence-on-base-addr (implies (64bits-equiv base-addr base-addr-equiv) (equal (hidden-segment-registerbits base-addr limit attr) (hidden-segment-registerbits base-addr-equiv limit attr))) :rule-classes :congruence)
Theorem:
(defthm hidden-segment-registerbits-of-32bits-fix-limit (equal (hidden-segment-registerbits base-addr (32bits-fix limit) attr) (hidden-segment-registerbits base-addr limit attr)))
Theorem:
(defthm hidden-segment-registerbits-32bits-equiv-congruence-on-limit (implies (32bits-equiv limit limit-equiv) (equal (hidden-segment-registerbits base-addr limit attr) (hidden-segment-registerbits base-addr limit-equiv attr))) :rule-classes :congruence)
Theorem:
(defthm hidden-segment-registerbits-of-16bits-fix-attr (equal (hidden-segment-registerbits base-addr limit (16bits-fix attr)) (hidden-segment-registerbits base-addr limit attr)))
Theorem:
(defthm hidden-segment-registerbits-16bits-equiv-congruence-on-attr (implies (16bits-equiv attr attr-equiv) (equal (hidden-segment-registerbits base-addr limit attr) (hidden-segment-registerbits base-addr limit attr-equiv))) :rule-classes :congruence)
Function:
(defun hidden-segment-registerbits-equiv-under-mask (x x1 mask) (declare (xargs :guard (and (hidden-segment-registerbits-p x) (hidden-segment-registerbits-p x1) (integerp mask)))) (let ((__function__ 'hidden-segment-registerbits-equiv-under-mask)) (declare (ignorable __function__)) (fty::int-equiv-under-mask (hidden-segment-registerbits-fix x) (hidden-segment-registerbits-fix x1) mask)))
Function:
(defun hidden-segment-registerbits->base-addr$inline (x) (declare (xargs :guard (hidden-segment-registerbits-p x))) (mbe :logic (let ((x (hidden-segment-registerbits-fix x))) (part-select x :low 0 :width 64)) :exec (the (unsigned-byte 64) (logand (the (unsigned-byte 64) 18446744073709551615) (the (unsigned-byte 112) x)))))
Theorem:
(defthm 64bits-p-of-hidden-segment-registerbits->base-addr (b* ((base-addr (hidden-segment-registerbits->base-addr$inline x))) (64bits-p base-addr)) :rule-classes :rewrite)
Theorem:
(defthm hidden-segment-registerbits->base-addr$inline-of-hidden-segment-registerbits-fix-x (equal (hidden-segment-registerbits->base-addr$inline (hidden-segment-registerbits-fix x)) (hidden-segment-registerbits->base-addr$inline x)))
Theorem:
(defthm hidden-segment-registerbits->base-addr$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (hidden-segment-registerbits->base-addr$inline x) (hidden-segment-registerbits->base-addr$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm hidden-segment-registerbits->base-addr-of-hidden-segment-registerbits (equal (hidden-segment-registerbits->base-addr (hidden-segment-registerbits base-addr limit attr)) (64bits-fix base-addr)))
Theorem:
(defthm hidden-segment-registerbits->base-addr-of-write-with-mask (implies (and (fty::bitstruct-read-over-write-hyps x hidden-segment-registerbits-equiv-under-mask) (hidden-segment-registerbits-equiv-under-mask x y fty::mask) (equal (logand (lognot fty::mask) 18446744073709551615) 0)) (equal (hidden-segment-registerbits->base-addr x) (hidden-segment-registerbits->base-addr y))))
Function:
(defun hidden-segment-registerbits->limit$inline (x) (declare (xargs :guard (hidden-segment-registerbits-p x))) (mbe :logic (let ((x (hidden-segment-registerbits-fix x))) (part-select x :low 64 :width 32)) :exec (the (unsigned-byte 32) (logand (the (unsigned-byte 32) 4294967295) (the (unsigned-byte 48) (ash (the (unsigned-byte 112) x) -64))))))
Theorem:
(defthm 32bits-p-of-hidden-segment-registerbits->limit (b* ((limit (hidden-segment-registerbits->limit$inline x))) (32bits-p limit)) :rule-classes :rewrite)
Theorem:
(defthm hidden-segment-registerbits->limit$inline-of-hidden-segment-registerbits-fix-x (equal (hidden-segment-registerbits->limit$inline (hidden-segment-registerbits-fix x)) (hidden-segment-registerbits->limit$inline x)))
Theorem:
(defthm hidden-segment-registerbits->limit$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (hidden-segment-registerbits->limit$inline x) (hidden-segment-registerbits->limit$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm hidden-segment-registerbits->limit-of-hidden-segment-registerbits (equal (hidden-segment-registerbits->limit (hidden-segment-registerbits base-addr limit attr)) (32bits-fix limit)))
Theorem:
(defthm hidden-segment-registerbits->limit-of-write-with-mask (implies (and (fty::bitstruct-read-over-write-hyps x hidden-segment-registerbits-equiv-under-mask) (hidden-segment-registerbits-equiv-under-mask x y fty::mask) (equal (logand (lognot fty::mask) 79228162495817593519834398720) 0)) (equal (hidden-segment-registerbits->limit x) (hidden-segment-registerbits->limit y))))
Function:
(defun hidden-segment-registerbits->attr$inline (x) (declare (xargs :guard (hidden-segment-registerbits-p x))) (mbe :logic (let ((x (hidden-segment-registerbits-fix x))) (part-select x :low 96 :width 16)) :exec (the (unsigned-byte 16) (logand (the (unsigned-byte 16) 65535) (the (unsigned-byte 16) (ash (the (unsigned-byte 112) x) -96))))))
Theorem:
(defthm 16bits-p-of-hidden-segment-registerbits->attr (b* ((attr (hidden-segment-registerbits->attr$inline x))) (16bits-p attr)) :rule-classes :rewrite)
Theorem:
(defthm hidden-segment-registerbits->attr$inline-of-hidden-segment-registerbits-fix-x (equal (hidden-segment-registerbits->attr$inline (hidden-segment-registerbits-fix x)) (hidden-segment-registerbits->attr$inline x)))
Theorem:
(defthm hidden-segment-registerbits->attr$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (hidden-segment-registerbits->attr$inline x) (hidden-segment-registerbits->attr$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm hidden-segment-registerbits->attr-of-hidden-segment-registerbits (equal (hidden-segment-registerbits->attr (hidden-segment-registerbits base-addr limit attr)) (16bits-fix attr)))
Theorem:
(defthm hidden-segment-registerbits->attr-of-write-with-mask (implies (and (fty::bitstruct-read-over-write-hyps x hidden-segment-registerbits-equiv-under-mask) (hidden-segment-registerbits-equiv-under-mask x y fty::mask) (equal (logand (lognot fty::mask) 5192217630372313364192902785269760) 0)) (equal (hidden-segment-registerbits->attr x) (hidden-segment-registerbits->attr y))))
Theorem:
(defthm hidden-segment-registerbits-fix-in-terms-of-hidden-segment-registerbits (equal (hidden-segment-registerbits-fix x) (change-hidden-segment-registerbits x)))
Function:
(defun !hidden-segment-registerbits->base-addr$inline (base-addr x) (declare (xargs :guard (and (64bits-p base-addr) (hidden-segment-registerbits-p x)))) (mbe :logic (b* ((base-addr (mbe :logic (64bits-fix base-addr) :exec base-addr)) (x (hidden-segment-registerbits-fix x))) (part-install base-addr x :width 64 :low 0)) :exec (the (unsigned-byte 112) (logior (the (unsigned-byte 112) (logand (the (unsigned-byte 112) x) (the (signed-byte 65) -18446744073709551616))) (the (unsigned-byte 64) base-addr)))))
Theorem:
(defthm hidden-segment-registerbits-p-of-!hidden-segment-registerbits->base-addr (b* ((new-x (!hidden-segment-registerbits->base-addr$inline base-addr x))) (hidden-segment-registerbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !hidden-segment-registerbits->base-addr$inline-of-64bits-fix-base-addr (equal (!hidden-segment-registerbits->base-addr$inline (64bits-fix base-addr) x) (!hidden-segment-registerbits->base-addr$inline base-addr x)))
Theorem:
(defthm !hidden-segment-registerbits->base-addr$inline-64bits-equiv-congruence-on-base-addr (implies (64bits-equiv base-addr base-addr-equiv) (equal (!hidden-segment-registerbits->base-addr$inline base-addr x) (!hidden-segment-registerbits->base-addr$inline base-addr-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->base-addr$inline-of-hidden-segment-registerbits-fix-x (equal (!hidden-segment-registerbits->base-addr$inline base-addr (hidden-segment-registerbits-fix x)) (!hidden-segment-registerbits->base-addr$inline base-addr x)))
Theorem:
(defthm !hidden-segment-registerbits->base-addr$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (!hidden-segment-registerbits->base-addr$inline base-addr x) (!hidden-segment-registerbits->base-addr$inline base-addr x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->base-addr-is-hidden-segment-registerbits (equal (!hidden-segment-registerbits->base-addr base-addr x) (change-hidden-segment-registerbits x :base-addr base-addr)))
Theorem:
(defthm hidden-segment-registerbits->base-addr-of-!hidden-segment-registerbits->base-addr (b* ((?new-x (!hidden-segment-registerbits->base-addr$inline base-addr x))) (equal (hidden-segment-registerbits->base-addr new-x) (64bits-fix base-addr))))
Theorem:
(defthm !hidden-segment-registerbits->base-addr-equiv-under-mask (b* ((?new-x (!hidden-segment-registerbits->base-addr$inline base-addr x))) (hidden-segment-registerbits-equiv-under-mask new-x x -18446744073709551616)))
Function:
(defun !hidden-segment-registerbits->limit$inline (limit x) (declare (xargs :guard (and (32bits-p limit) (hidden-segment-registerbits-p x)))) (mbe :logic (b* ((limit (mbe :logic (32bits-fix limit) :exec limit)) (x (hidden-segment-registerbits-fix x))) (part-install limit x :width 32 :low 64)) :exec (the (unsigned-byte 112) (logior (the (unsigned-byte 112) (logand (the (unsigned-byte 112) x) (the (signed-byte 97) -79228162495817593519834398721))) (the (unsigned-byte 96) (ash (the (unsigned-byte 32) limit) 64))))))
Theorem:
(defthm hidden-segment-registerbits-p-of-!hidden-segment-registerbits->limit (b* ((new-x (!hidden-segment-registerbits->limit$inline limit x))) (hidden-segment-registerbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !hidden-segment-registerbits->limit$inline-of-32bits-fix-limit (equal (!hidden-segment-registerbits->limit$inline (32bits-fix limit) x) (!hidden-segment-registerbits->limit$inline limit x)))
Theorem:
(defthm !hidden-segment-registerbits->limit$inline-32bits-equiv-congruence-on-limit (implies (32bits-equiv limit limit-equiv) (equal (!hidden-segment-registerbits->limit$inline limit x) (!hidden-segment-registerbits->limit$inline limit-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->limit$inline-of-hidden-segment-registerbits-fix-x (equal (!hidden-segment-registerbits->limit$inline limit (hidden-segment-registerbits-fix x)) (!hidden-segment-registerbits->limit$inline limit x)))
Theorem:
(defthm !hidden-segment-registerbits->limit$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (!hidden-segment-registerbits->limit$inline limit x) (!hidden-segment-registerbits->limit$inline limit x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->limit-is-hidden-segment-registerbits (equal (!hidden-segment-registerbits->limit limit x) (change-hidden-segment-registerbits x :limit limit)))
Theorem:
(defthm hidden-segment-registerbits->limit-of-!hidden-segment-registerbits->limit (b* ((?new-x (!hidden-segment-registerbits->limit$inline limit x))) (equal (hidden-segment-registerbits->limit new-x) (32bits-fix limit))))
Theorem:
(defthm !hidden-segment-registerbits->limit-equiv-under-mask (b* ((?new-x (!hidden-segment-registerbits->limit$inline limit x))) (hidden-segment-registerbits-equiv-under-mask new-x x -79228162495817593519834398721)))
Function:
(defun !hidden-segment-registerbits->attr$inline (attr x) (declare (xargs :guard (and (16bits-p attr) (hidden-segment-registerbits-p x)))) (mbe :logic (b* ((attr (mbe :logic (16bits-fix attr) :exec attr)) (x (hidden-segment-registerbits-fix x))) (part-install attr x :width 16 :low 96)) :exec (the (unsigned-byte 112) (logior (the (unsigned-byte 112) (logand (the (unsigned-byte 112) x) (the (signed-byte 113) -5192217630372313364192902785269761))) (the (unsigned-byte 112) (ash (the (unsigned-byte 16) attr) 96))))))
Theorem:
(defthm hidden-segment-registerbits-p-of-!hidden-segment-registerbits->attr (b* ((new-x (!hidden-segment-registerbits->attr$inline attr x))) (hidden-segment-registerbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !hidden-segment-registerbits->attr$inline-of-16bits-fix-attr (equal (!hidden-segment-registerbits->attr$inline (16bits-fix attr) x) (!hidden-segment-registerbits->attr$inline attr x)))
Theorem:
(defthm !hidden-segment-registerbits->attr$inline-16bits-equiv-congruence-on-attr (implies (16bits-equiv attr attr-equiv) (equal (!hidden-segment-registerbits->attr$inline attr x) (!hidden-segment-registerbits->attr$inline attr-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->attr$inline-of-hidden-segment-registerbits-fix-x (equal (!hidden-segment-registerbits->attr$inline attr (hidden-segment-registerbits-fix x)) (!hidden-segment-registerbits->attr$inline attr x)))
Theorem:
(defthm !hidden-segment-registerbits->attr$inline-hidden-segment-registerbits-equiv-congruence-on-x (implies (hidden-segment-registerbits-equiv x x-equiv) (equal (!hidden-segment-registerbits->attr$inline attr x) (!hidden-segment-registerbits->attr$inline attr x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !hidden-segment-registerbits->attr-is-hidden-segment-registerbits (equal (!hidden-segment-registerbits->attr attr x) (change-hidden-segment-registerbits x :attr attr)))
Theorem:
(defthm hidden-segment-registerbits->attr-of-!hidden-segment-registerbits->attr (b* ((?new-x (!hidden-segment-registerbits->attr$inline attr x))) (equal (hidden-segment-registerbits->attr new-x) (16bits-fix attr))))
Theorem:
(defthm !hidden-segment-registerbits->attr-equiv-under-mask (b* ((?new-x (!hidden-segment-registerbits->attr$inline attr x))) (hidden-segment-registerbits-equiv-under-mask new-x x 79228162514264337593543950335)))
Function:
(defun hidden-segment-registerbits-debug (x) (declare (xargs :guard (hidden-segment-registerbits-p x))) (let ((__function__ 'hidden-segment-registerbits-debug)) (declare (ignorable __function__)) (b* (((hidden-segment-registerbits x))) (cons (cons 'base-addr x.base-addr) (cons (cons 'limit x.limit) (cons (cons 'attr x.attr) nil))))))