Fixing function for phase-fsm-params structures.
(phase-fsm-params-fix x) → new-x
Function:
(defun phase-fsm-params-fix$inline (x) (declare (xargs :guard (phase-fsm-params-p x))) (let ((__function__ 'phase-fsm-params-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((scc-selfcompose-limit (acl2::maybe-natp-fix (cdr (std::da-nth 0 x)))) (rewrite (bool-fix (cdr (std::da-nth 1 x))))) (list (cons 'scc-selfcompose-limit scc-selfcompose-limit) (cons 'rewrite rewrite))) :exec x)))
Theorem:
(defthm phase-fsm-params-p-of-phase-fsm-params-fix (b* ((new-x (phase-fsm-params-fix$inline x))) (phase-fsm-params-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm phase-fsm-params-fix-when-phase-fsm-params-p (implies (phase-fsm-params-p x) (equal (phase-fsm-params-fix x) x)))
Function:
(defun phase-fsm-params-equiv$inline (x y) (declare (xargs :guard (and (phase-fsm-params-p x) (phase-fsm-params-p y)))) (equal (phase-fsm-params-fix x) (phase-fsm-params-fix y)))
Theorem:
(defthm phase-fsm-params-equiv-is-an-equivalence (and (booleanp (phase-fsm-params-equiv x y)) (phase-fsm-params-equiv x x) (implies (phase-fsm-params-equiv x y) (phase-fsm-params-equiv y x)) (implies (and (phase-fsm-params-equiv x y) (phase-fsm-params-equiv y z)) (phase-fsm-params-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm phase-fsm-params-equiv-implies-equal-phase-fsm-params-fix-1 (implies (phase-fsm-params-equiv x x-equiv) (equal (phase-fsm-params-fix x) (phase-fsm-params-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm phase-fsm-params-fix-under-phase-fsm-params-equiv (phase-fsm-params-equiv (phase-fsm-params-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-phase-fsm-params-fix-1-forward-to-phase-fsm-params-equiv (implies (equal (phase-fsm-params-fix x) y) (phase-fsm-params-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-phase-fsm-params-fix-2-forward-to-phase-fsm-params-equiv (implies (equal x (phase-fsm-params-fix y)) (phase-fsm-params-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm phase-fsm-params-equiv-of-phase-fsm-params-fix-1-forward (implies (phase-fsm-params-equiv (phase-fsm-params-fix x) y) (phase-fsm-params-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm phase-fsm-params-equiv-of-phase-fsm-params-fix-2-forward (implies (phase-fsm-params-equiv x (phase-fsm-params-fix y)) (phase-fsm-params-equiv x y)) :rule-classes :forward-chaining)