Fixing function for overridekey-syntaxcheck-data structures.
(overridekey-syntaxcheck-data-fix x) → new-x
Function:
(defun overridekey-syntaxcheck-data-fix$inline (x) (declare (xargs :guard (overridekey-syntaxcheck-data-p x))) (let ((__function__ 'overridekey-syntaxcheck-data-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((keys (svarlist-fix (cdr (std::da-nth 0 x)))) (values (svex-alist-fix (cdr (std::da-nth 1 x))))) (list (cons 'keys keys) (cons 'values values))) :exec x)))
Theorem:
(defthm overridekey-syntaxcheck-data-p-of-overridekey-syntaxcheck-data-fix (b* ((new-x (overridekey-syntaxcheck-data-fix$inline x))) (overridekey-syntaxcheck-data-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm overridekey-syntaxcheck-data-fix-when-overridekey-syntaxcheck-data-p (implies (overridekey-syntaxcheck-data-p x) (equal (overridekey-syntaxcheck-data-fix x) x)))
Function:
(defun overridekey-syntaxcheck-data-equiv$inline (x y) (declare (xargs :guard (and (overridekey-syntaxcheck-data-p x) (overridekey-syntaxcheck-data-p y)))) (equal (overridekey-syntaxcheck-data-fix x) (overridekey-syntaxcheck-data-fix y)))
Theorem:
(defthm overridekey-syntaxcheck-data-equiv-is-an-equivalence (and (booleanp (overridekey-syntaxcheck-data-equiv x y)) (overridekey-syntaxcheck-data-equiv x x) (implies (overridekey-syntaxcheck-data-equiv x y) (overridekey-syntaxcheck-data-equiv y x)) (implies (and (overridekey-syntaxcheck-data-equiv x y) (overridekey-syntaxcheck-data-equiv y z)) (overridekey-syntaxcheck-data-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm overridekey-syntaxcheck-data-equiv-implies-equal-overridekey-syntaxcheck-data-fix-1 (implies (overridekey-syntaxcheck-data-equiv x x-equiv) (equal (overridekey-syntaxcheck-data-fix x) (overridekey-syntaxcheck-data-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm overridekey-syntaxcheck-data-fix-under-overridekey-syntaxcheck-data-equiv (overridekey-syntaxcheck-data-equiv (overridekey-syntaxcheck-data-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-overridekey-syntaxcheck-data-fix-1-forward-to-overridekey-syntaxcheck-data-equiv (implies (equal (overridekey-syntaxcheck-data-fix x) y) (overridekey-syntaxcheck-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-overridekey-syntaxcheck-data-fix-2-forward-to-overridekey-syntaxcheck-data-equiv (implies (equal x (overridekey-syntaxcheck-data-fix y)) (overridekey-syntaxcheck-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm overridekey-syntaxcheck-data-equiv-of-overridekey-syntaxcheck-data-fix-1-forward (implies (overridekey-syntaxcheck-data-equiv (overridekey-syntaxcheck-data-fix x) y) (overridekey-syntaxcheck-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm overridekey-syntaxcheck-data-equiv-of-overridekey-syntaxcheck-data-fix-2-forward (implies (overridekey-syntaxcheck-data-equiv x (overridekey-syntaxcheck-data-fix y)) (overridekey-syntaxcheck-data-equiv x y)) :rule-classes :forward-chaining)