Update the |FGL|::|SPLIT-IFS| field of a fgl-function-mode bit structure.
(!fgl-function-mode->split-ifs split-ifs x) → new-x
Function:
(defun !fgl-function-mode->split-ifs (split-ifs x) (declare (xargs :guard (and (booleanp split-ifs) (fgl-function-mode-p x)))) (mbe :logic (b* ((split-ifs (bool->bit split-ifs)) (x (fgl-function-mode-fix x))) (acl2::part-install split-ifs x :width 1 :low 0)) :exec (the (unsigned-byte 6) (logior (the (unsigned-byte 6) (logand (the (unsigned-byte 6) x) (the (signed-byte 2) -2))) (the (unsigned-byte 1) (bool->bit split-ifs))))))
Theorem:
(defthm fgl-function-mode-p-of-!fgl-function-mode->split-ifs (b* ((new-x (!fgl-function-mode->split-ifs split-ifs x))) (fgl-function-mode-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !fgl-function-mode->split-ifs-of-bool-fix-split-ifs (equal (!fgl-function-mode->split-ifs (bool-fix split-ifs) x) (!fgl-function-mode->split-ifs split-ifs x)))
Theorem:
(defthm !fgl-function-mode->split-ifs-iff-congruence-on-split-ifs (implies (iff split-ifs split-ifs-equiv) (equal (!fgl-function-mode->split-ifs split-ifs x) (!fgl-function-mode->split-ifs split-ifs-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->split-ifs-of-fgl-function-mode-fix-x (equal (!fgl-function-mode->split-ifs split-ifs (fgl-function-mode-fix x)) (!fgl-function-mode->split-ifs split-ifs x)))
Theorem:
(defthm !fgl-function-mode->split-ifs-fgl-function-mode-equiv-congruence-on-x (implies (fgl-function-mode-equiv x x-equiv) (equal (!fgl-function-mode->split-ifs split-ifs x) (!fgl-function-mode->split-ifs split-ifs x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->split-ifs-is-fgl-function-mode (equal (!fgl-function-mode->split-ifs split-ifs x) (change-fgl-function-mode x :split-ifs split-ifs)))
Theorem:
(defthm fgl-function-mode->split-ifs-of-!fgl-function-mode->split-ifs (b* ((?new-x (!fgl-function-mode->split-ifs split-ifs x))) (equal (fgl-function-mode->split-ifs new-x) (bool-fix split-ifs))))
Theorem:
(defthm !fgl-function-mode->split-ifs-equiv-under-mask (b* ((?new-x (!fgl-function-mode->split-ifs split-ifs x))) (fgl-function-mode-equiv-under-mask new-x x -2)))