Update the |FGL|::|DONT-REWRITE| field of a fgl-function-mode bit structure.
(!fgl-function-mode->dont-rewrite dont-rewrite x) → new-x
Function:
(defun !fgl-function-mode->dont-rewrite (dont-rewrite x) (declare (xargs :guard (and (booleanp dont-rewrite) (fgl-function-mode-p x)))) (mbe :logic (b* ((dont-rewrite (bool->bit dont-rewrite)) (x (fgl-function-mode-fix x))) (acl2::part-install dont-rewrite x :width 1 :low 3)) :exec (the (unsigned-byte 6) (logior (the (unsigned-byte 6) (logand (the (unsigned-byte 6) x) (the (signed-byte 5) -9))) (the (unsigned-byte 4) (ash (the (unsigned-byte 1) (bool->bit dont-rewrite)) 3))))))
Theorem:
(defthm fgl-function-mode-p-of-!fgl-function-mode->dont-rewrite (b* ((new-x (!fgl-function-mode->dont-rewrite dont-rewrite x))) (fgl-function-mode-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-of-bool-fix-dont-rewrite (equal (!fgl-function-mode->dont-rewrite (bool-fix dont-rewrite) x) (!fgl-function-mode->dont-rewrite dont-rewrite x)))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-iff-congruence-on-dont-rewrite (implies (iff dont-rewrite dont-rewrite-equiv) (equal (!fgl-function-mode->dont-rewrite dont-rewrite x) (!fgl-function-mode->dont-rewrite dont-rewrite-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-of-fgl-function-mode-fix-x (equal (!fgl-function-mode->dont-rewrite dont-rewrite (fgl-function-mode-fix x)) (!fgl-function-mode->dont-rewrite dont-rewrite x)))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-fgl-function-mode-equiv-congruence-on-x (implies (fgl-function-mode-equiv x x-equiv) (equal (!fgl-function-mode->dont-rewrite dont-rewrite x) (!fgl-function-mode->dont-rewrite dont-rewrite x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-is-fgl-function-mode (equal (!fgl-function-mode->dont-rewrite dont-rewrite x) (change-fgl-function-mode x :dont-rewrite dont-rewrite)))
Theorem:
(defthm fgl-function-mode->dont-rewrite-of-!fgl-function-mode->dont-rewrite (b* ((?new-x (!fgl-function-mode->dont-rewrite dont-rewrite x))) (equal (fgl-function-mode->dont-rewrite new-x) (bool-fix dont-rewrite))))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-equiv-under-mask (b* ((?new-x (!fgl-function-mode->dont-rewrite dont-rewrite x))) (fgl-function-mode-equiv-under-mask new-x x -9)))