Recognizer for svl-module-alist.
(svl-module-alist-p x) → *
Function:
(defun svl-module-alist-p (x) (declare (xargs :guard t)) (let ((acl2::__function__ 'svl-module-alist-p)) (declare (ignorable acl2::__function__)) (if (atom x) (eq x nil) (and (consp (car x)) (sv::modname-p (caar x)) (svl-module-p (cdar x)) (svl-module-alist-p (cdr x))))))
Theorem:
(defthm svl-module-alist-p-of-butlast (implies (svl-module-alist-p (double-rewrite acl2::x)) (svl-module-alist-p (butlast acl2::x acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-append (equal (svl-module-alist-p (append acl2::a acl2::b)) (and (svl-module-alist-p (list-fix acl2::a)) (svl-module-alist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-repeat (iff (svl-module-alist-p (repeat acl2::n acl2::x)) (or (and (consp acl2::x) (sv::modname-p (car acl2::x)) (svl-module-p (cdr acl2::x))) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-rev (equal (svl-module-alist-p (rev acl2::x)) (svl-module-alist-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-list-fix (implies (svl-module-alist-p acl2::x) (svl-module-alist-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-svl-module-alist-p-compound-recognizer (implies (svl-module-alist-p acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm svl-module-alist-p-when-not-consp (implies (not (consp acl2::x)) (equal (svl-module-alist-p acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-cdr-when-svl-module-alist-p (implies (svl-module-alist-p (double-rewrite acl2::x)) (svl-module-alist-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-cons (equal (svl-module-alist-p (cons acl2::a acl2::x)) (and (and (consp acl2::a) (sv::modname-p (car acl2::a)) (svl-module-p (cdr acl2::a))) (svl-module-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-remove-assoc (implies (svl-module-alist-p acl2::x) (svl-module-alist-p (remove-assoc-equal acl2::name acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-put-assoc (implies (and (svl-module-alist-p acl2::x)) (iff (svl-module-alist-p (put-assoc-equal acl2::name acl2::val acl2::x)) (and (sv::modname-p acl2::name) (svl-module-p acl2::val)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-fast-alist-clean (implies (svl-module-alist-p acl2::x) (svl-module-alist-p (fast-alist-clean acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-hons-shrink-alist (implies (and (svl-module-alist-p acl2::x) (svl-module-alist-p acl2::y)) (svl-module-alist-p (hons-shrink-alist acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-alist-p-of-hons-acons (equal (svl-module-alist-p (hons-acons acl2::a acl2::n acl2::x)) (and (sv::modname-p acl2::a) (svl-module-p acl2::n) (svl-module-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-module-p-of-cdr-of-hons-assoc-equal-when-svl-module-alist-p (implies (svl-module-alist-p acl2::x) (iff (svl-module-p (cdr (hons-assoc-equal acl2::k acl2::x))) (or (hons-assoc-equal acl2::k acl2::x) (svl-module-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm alistp-when-svl-module-alist-p-rewrite (implies (svl-module-alist-p acl2::x) (alistp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm alistp-when-svl-module-alist-p (implies (svl-module-alist-p acl2::x) (alistp acl2::x)) :rule-classes :tau-system)
Theorem:
(defthm svl-module-p-of-cdar-when-svl-module-alist-p (implies (svl-module-alist-p acl2::x) (iff (svl-module-p (cdar acl2::x)) (or (consp acl2::x) (svl-module-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm modname-p-of-caar-when-svl-module-alist-p (implies (svl-module-alist-p acl2::x) (iff (sv::modname-p (caar acl2::x)) (or (consp acl2::x) (sv::modname-p nil)))) :rule-classes ((:rewrite)))