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