Update the |X86ISA|::|IST| field of a interrupt/trap-gate-descriptor-attributesbits bit structure.
(!interrupt/trap-gate-descriptor-attributesbits->ist ist x) → new-x
Function:
(defun !interrupt/trap-gate-descriptor-attributesbits->ist$inline (ist x) (declare (xargs :guard (and (3bits-p ist) (interrupt/trap-gate-descriptor-attributesbits-p x)))) (mbe :logic (b* ((ist (mbe :logic (3bits-fix ist) :exec ist)) (x (interrupt/trap-gate-descriptor-attributesbits-fix x))) (part-install ist x :width 3 :low 0)) :exec (the (unsigned-byte 16) (logior (the (unsigned-byte 16) (logand (the (unsigned-byte 16) x) (the (signed-byte 4) -8))) (the (unsigned-byte 3) ist)))))
Theorem:
(defthm interrupt/trap-gate-descriptor-attributesbits-p-of-!interrupt/trap-gate-descriptor-attributesbits->ist (b* ((new-x (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x))) (interrupt/trap-gate-descriptor-attributesbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist$inline-of-3bits-fix-ist (equal (!interrupt/trap-gate-descriptor-attributesbits->ist$inline (3bits-fix ist) x) (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x)))
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist$inline-3bits-equiv-congruence-on-ist (implies (3bits-equiv ist ist-equiv) (equal (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x) (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist$inline-of-interrupt/trap-gate-descriptor-attributesbits-fix-x (equal (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist (interrupt/trap-gate-descriptor-attributesbits-fix x)) (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x)))
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist$inline-interrupt/trap-gate-descriptor-attributesbits-equiv-congruence-on-x (implies (interrupt/trap-gate-descriptor-attributesbits-equiv x x-equiv) (equal (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x) (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist-is-interrupt/trap-gate-descriptor-attributesbits (equal (!interrupt/trap-gate-descriptor-attributesbits->ist ist x) (change-interrupt/trap-gate-descriptor-attributesbits x :ist ist)))
Theorem:
(defthm interrupt/trap-gate-descriptor-attributesbits->ist-of-!interrupt/trap-gate-descriptor-attributesbits->ist (b* ((?new-x (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x))) (equal (interrupt/trap-gate-descriptor-attributesbits->ist new-x) (3bits-fix ist))))
Theorem:
(defthm !interrupt/trap-gate-descriptor-attributesbits->ist-equiv-under-mask (b* ((?new-x (!interrupt/trap-gate-descriptor-attributesbits->ist$inline ist x))) (interrupt/trap-gate-descriptor-attributesbits-equiv-under-mask new-x x -8)))