Recognizer for svl-env-alist.
(svl-env-alist-p x) → *
Theorem:
(defthm svl-env-alist-p-of-butlast (implies (svl-env-alist-p (double-rewrite acl2::x)) (svl-env-alist-p (butlast acl2::x acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-repeat (iff (svl-env-alist-p (repeat acl2::n acl2::x)) (or (and (consp acl2::x) (svl-env-p (cdr acl2::x))) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-rev (equal (svl-env-alist-p (rev acl2::x)) (svl-env-alist-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-list-fix (equal (svl-env-alist-p (list-fix acl2::x)) (svl-env-alist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-append (equal (svl-env-alist-p (append acl2::a acl2::b)) (and (svl-env-alist-p acl2::a) (svl-env-alist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-when-not-consp (implies (not (consp acl2::x)) (svl-env-alist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-cdr-when-svl-env-alist-p (implies (svl-env-alist-p (double-rewrite acl2::x)) (svl-env-alist-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-cons (equal (svl-env-alist-p (cons acl2::a acl2::x)) (and (and (consp acl2::a) (svl-env-p (cdr acl2::a))) (svl-env-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-fast-alist-clean (implies (svl-env-alist-p acl2::x) (svl-env-alist-p (fast-alist-clean acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-hons-shrink-alist (implies (and (svl-env-alist-p acl2::x) (svl-env-alist-p acl2::y)) (svl-env-alist-p (hons-shrink-alist acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-alist-p-of-hons-acons (equal (svl-env-alist-p (hons-acons acl2::a acl2::n acl2::x)) (and t (svl-env-p acl2::n) (svl-env-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-p-of-cdr-of-hons-assoc-equal-when-svl-env-alist-p (implies (svl-env-alist-p acl2::x) (iff (svl-env-p (cdr (hons-assoc-equal acl2::k acl2::x))) (or (hons-assoc-equal acl2::k acl2::x) (svl-env-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svl-env-p-of-cdar-when-svl-env-alist-p (implies (svl-env-alist-p acl2::x) (iff (svl-env-p (cdar acl2::x)) (or (consp acl2::x) (svl-env-p nil)))) :rule-classes ((:rewrite)))