Update the |ACL2|::|A| field of a code-segment-descriptor-attributesbits bit structure.
(!code-segment-descriptor-attributesbits->a a x) → new-x
Function:
(defun !code-segment-descriptor-attributesbits->a$inline (a x) (declare (xargs :guard (and (bitp a) (code-segment-descriptor-attributesbits-p x)))) (mbe :logic (b* ((a (mbe :logic (bfix a) :exec a)) (x (code-segment-descriptor-attributesbits-fix x))) (part-install a x :width 1 :low 0)) :exec (the (unsigned-byte 16) (logior (the (unsigned-byte 16) (logand (the (unsigned-byte 16) x) (the (signed-byte 2) -2))) (the (unsigned-byte 1) a)))))
Theorem:
(defthm code-segment-descriptor-attributesbits-p-of-!code-segment-descriptor-attributesbits->a (b* ((new-x (!code-segment-descriptor-attributesbits->a$inline a x))) (code-segment-descriptor-attributesbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !code-segment-descriptor-attributesbits->a$inline-of-bfix-a (equal (!code-segment-descriptor-attributesbits->a$inline (bfix a) x) (!code-segment-descriptor-attributesbits->a$inline a x)))
Theorem:
(defthm !code-segment-descriptor-attributesbits->a$inline-bit-equiv-congruence-on-a (implies (bit-equiv a a-equiv) (equal (!code-segment-descriptor-attributesbits->a$inline a x) (!code-segment-descriptor-attributesbits->a$inline a-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !code-segment-descriptor-attributesbits->a$inline-of-code-segment-descriptor-attributesbits-fix-x (equal (!code-segment-descriptor-attributesbits->a$inline a (code-segment-descriptor-attributesbits-fix x)) (!code-segment-descriptor-attributesbits->a$inline a x)))
Theorem:
(defthm !code-segment-descriptor-attributesbits->a$inline-code-segment-descriptor-attributesbits-equiv-congruence-on-x (implies (code-segment-descriptor-attributesbits-equiv x x-equiv) (equal (!code-segment-descriptor-attributesbits->a$inline a x) (!code-segment-descriptor-attributesbits->a$inline a x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !code-segment-descriptor-attributesbits->a-is-code-segment-descriptor-attributesbits (equal (!code-segment-descriptor-attributesbits->a a x) (change-code-segment-descriptor-attributesbits x :a a)))
Theorem:
(defthm code-segment-descriptor-attributesbits->a-of-!code-segment-descriptor-attributesbits->a (b* ((?new-x (!code-segment-descriptor-attributesbits->a$inline a x))) (equal (code-segment-descriptor-attributesbits->a new-x) (bfix a))))
Theorem:
(defthm !code-segment-descriptor-attributesbits->a-equiv-under-mask (b* ((?new-x (!code-segment-descriptor-attributesbits->a$inline a x))) (code-segment-descriptor-attributesbits-equiv-under-mask new-x x -2)))