Fixing function for svex-scc-consts structures.
(svex-scc-consts-fix x) → new-x
Function:
(defun svex-scc-consts-fix$inline (x) (declare (xargs :guard (svex-scc-consts-p x))) (let ((__function__ 'svex-scc-consts-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((final-masks (svex-mask-alist-fix (std::prod-car (std::prod-car x)))) (loop-vars (svar-key-alist-fix (std::prod-cdr (std::prod-car x)))) (compose-iter-limit (acl2::maybe-natp-fix (std::prod-car (std::prod-cdr x)))) (updates (svex-alist-fix (std::prod-cdr (std::prod-cdr x))))) (std::prod-cons (std::prod-cons final-masks loop-vars) (std::prod-cons compose-iter-limit updates))) :exec x)))
Theorem:
(defthm svex-scc-consts-p-of-svex-scc-consts-fix (b* ((new-x (svex-scc-consts-fix$inline x))) (svex-scc-consts-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm svex-scc-consts-fix-when-svex-scc-consts-p (implies (svex-scc-consts-p x) (equal (svex-scc-consts-fix x) x)))
Function:
(defun svex-scc-consts-equiv$inline (x y) (declare (xargs :guard (and (svex-scc-consts-p x) (svex-scc-consts-p y)))) (equal (svex-scc-consts-fix x) (svex-scc-consts-fix y)))
Theorem:
(defthm svex-scc-consts-equiv-is-an-equivalence (and (booleanp (svex-scc-consts-equiv x y)) (svex-scc-consts-equiv x x) (implies (svex-scc-consts-equiv x y) (svex-scc-consts-equiv y x)) (implies (and (svex-scc-consts-equiv x y) (svex-scc-consts-equiv y z)) (svex-scc-consts-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm svex-scc-consts-equiv-implies-equal-svex-scc-consts-fix-1 (implies (svex-scc-consts-equiv x x-equiv) (equal (svex-scc-consts-fix x) (svex-scc-consts-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svex-scc-consts-fix-under-svex-scc-consts-equiv (svex-scc-consts-equiv (svex-scc-consts-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-svex-scc-consts-fix-1-forward-to-svex-scc-consts-equiv (implies (equal (svex-scc-consts-fix x) y) (svex-scc-consts-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-svex-scc-consts-fix-2-forward-to-svex-scc-consts-equiv (implies (equal x (svex-scc-consts-fix y)) (svex-scc-consts-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svex-scc-consts-equiv-of-svex-scc-consts-fix-1-forward (implies (svex-scc-consts-equiv (svex-scc-consts-fix x) y) (svex-scc-consts-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svex-scc-consts-equiv-of-svex-scc-consts-fix-2-forward (implies (svex-scc-consts-equiv x (svex-scc-consts-fix y)) (svex-scc-consts-equiv x y)) :rule-classes :forward-chaining)