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