Update the |X86ISA|::|BYTE0| field of a vex-prefixes bit structure.
(!vex-prefixes->byte0 byte0 x) → new-x
Function:
(defun !vex-prefixes->byte0$inline (byte0 x) (declare (xargs :guard (and (8bits-p byte0) (vex-prefixes-p x)))) (mbe :logic (b* ((byte0 (mbe :logic (8bits-fix byte0) :exec byte0)) (x (vex-prefixes-fix x))) (part-install byte0 x :width 8 :low 0)) :exec (the (unsigned-byte 24) (logior (the (unsigned-byte 24) (logand (the (unsigned-byte 24) x) (the (signed-byte 9) -256))) (the (unsigned-byte 8) byte0)))))
Theorem:
(defthm vex-prefixes-p-of-!vex-prefixes->byte0 (b* ((new-x (!vex-prefixes->byte0$inline byte0 x))) (vex-prefixes-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !vex-prefixes->byte0$inline-of-8bits-fix-byte0 (equal (!vex-prefixes->byte0$inline (8bits-fix byte0) x) (!vex-prefixes->byte0$inline byte0 x)))
Theorem:
(defthm !vex-prefixes->byte0$inline-8bits-equiv-congruence-on-byte0 (implies (8bits-equiv byte0 byte0-equiv) (equal (!vex-prefixes->byte0$inline byte0 x) (!vex-prefixes->byte0$inline byte0-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !vex-prefixes->byte0$inline-of-vex-prefixes-fix-x (equal (!vex-prefixes->byte0$inline byte0 (vex-prefixes-fix x)) (!vex-prefixes->byte0$inline byte0 x)))
Theorem:
(defthm !vex-prefixes->byte0$inline-vex-prefixes-equiv-congruence-on-x (implies (vex-prefixes-equiv x x-equiv) (equal (!vex-prefixes->byte0$inline byte0 x) (!vex-prefixes->byte0$inline byte0 x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !vex-prefixes->byte0-is-vex-prefixes (equal (!vex-prefixes->byte0 byte0 x) (change-vex-prefixes x :byte0 byte0)))
Theorem:
(defthm vex-prefixes->byte0-of-!vex-prefixes->byte0 (b* ((?new-x (!vex-prefixes->byte0$inline byte0 x))) (equal (vex-prefixes->byte0 new-x) (8bits-fix byte0))))
Theorem:
(defthm !vex-prefixes->byte0-equiv-under-mask (b* ((?new-x (!vex-prefixes->byte0$inline byte0 x))) (vex-prefixes-equiv-under-mask new-x x -256)))