(string-stringlist-alist-fix x) is an fty alist fixing function that follows the fix-keys strategy.
(string-stringlist-alist-fix x) → fty::newx
Note that in the execution this is just an inline identity function.
Function:
(defun string-stringlist-alist-fix$inline (x) (declare (xargs :guard (string-stringlist-alistp x))) (let ((__function__ 'string-stringlist-alist-fix)) (declare (ignorable __function__)) (mbe :logic (if (atom x) nil (if (consp (car x)) (cons (cons (str-fix (caar x)) (str::string-list-fix (cdar x))) (string-stringlist-alist-fix (cdr x))) (string-stringlist-alist-fix (cdr x)))) :exec x)))
Theorem:
(defthm string-stringlist-alistp-of-string-stringlist-alist-fix (b* ((fty::newx (string-stringlist-alist-fix$inline x))) (string-stringlist-alistp fty::newx)) :rule-classes :rewrite)
Theorem:
(defthm string-stringlist-alist-fix-when-string-stringlist-alistp (implies (string-stringlist-alistp x) (equal (string-stringlist-alist-fix x) x)))
Function:
(defun string-stringlist-alist-equiv$inline (x y) (declare (xargs :guard (and (string-stringlist-alistp x) (string-stringlist-alistp y)))) (equal (string-stringlist-alist-fix x) (string-stringlist-alist-fix y)))
Theorem:
(defthm string-stringlist-alist-equiv-is-an-equivalence (and (booleanp (string-stringlist-alist-equiv x y)) (string-stringlist-alist-equiv x x) (implies (string-stringlist-alist-equiv x y) (string-stringlist-alist-equiv y x)) (implies (and (string-stringlist-alist-equiv x y) (string-stringlist-alist-equiv y z)) (string-stringlist-alist-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm string-stringlist-alist-equiv-implies-equal-string-stringlist-alist-fix-1 (implies (string-stringlist-alist-equiv x x-equiv) (equal (string-stringlist-alist-fix x) (string-stringlist-alist-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm string-stringlist-alist-fix-under-string-stringlist-alist-equiv (string-stringlist-alist-equiv (string-stringlist-alist-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-string-stringlist-alist-fix-1-forward-to-string-stringlist-alist-equiv (implies (equal (string-stringlist-alist-fix x) y) (string-stringlist-alist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-string-stringlist-alist-fix-2-forward-to-string-stringlist-alist-equiv (implies (equal x (string-stringlist-alist-fix y)) (string-stringlist-alist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm string-stringlist-alist-equiv-of-string-stringlist-alist-fix-1-forward (implies (string-stringlist-alist-equiv (string-stringlist-alist-fix x) y) (string-stringlist-alist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm string-stringlist-alist-equiv-of-string-stringlist-alist-fix-2-forward (implies (string-stringlist-alist-equiv x (string-stringlist-alist-fix y)) (string-stringlist-alist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm cons-of-str-fix-k-under-string-stringlist-alist-equiv (string-stringlist-alist-equiv (cons (cons (str-fix k) v) x) (cons (cons k v) x)))
Theorem:
(defthm cons-streqv-congruence-on-k-under-string-stringlist-alist-equiv (implies (streqv k k-equiv) (string-stringlist-alist-equiv (cons (cons k v) x) (cons (cons k-equiv v) x))) :rule-classes :congruence)
Theorem:
(defthm cons-of-string-list-fix-v-under-string-stringlist-alist-equiv (string-stringlist-alist-equiv (cons (cons k (str::string-list-fix v)) x) (cons (cons k v) x)))
Theorem:
(defthm cons-string-list-equiv-congruence-on-v-under-string-stringlist-alist-equiv (implies (str::string-list-equiv v v-equiv) (string-stringlist-alist-equiv (cons (cons k v) x) (cons (cons k v-equiv) x))) :rule-classes :congruence)
Theorem:
(defthm cons-of-string-stringlist-alist-fix-y-under-string-stringlist-alist-equiv (string-stringlist-alist-equiv (cons x (string-stringlist-alist-fix y)) (cons x y)))
Theorem:
(defthm cons-string-stringlist-alist-equiv-congruence-on-y-under-string-stringlist-alist-equiv (implies (string-stringlist-alist-equiv y y-equiv) (string-stringlist-alist-equiv (cons x y) (cons x y-equiv))) :rule-classes :congruence)
Theorem:
(defthm string-stringlist-alist-fix-of-acons (equal (string-stringlist-alist-fix (cons (cons a b) x)) (cons (cons (str-fix a) (str::string-list-fix b)) (string-stringlist-alist-fix x))))
Theorem:
(defthm string-stringlist-alist-fix-of-append (equal (string-stringlist-alist-fix (append std::a std::b)) (append (string-stringlist-alist-fix std::a) (string-stringlist-alist-fix std::b))))
Theorem:
(defthm consp-car-of-string-stringlist-alist-fix (equal (consp (car (string-stringlist-alist-fix x))) (consp (string-stringlist-alist-fix x))))