Basic theorems about atc-formal-affectable-listp, generated by std::deflist.
Theorem:
(defthm atc-formal-affectable-listp-of-cons (equal (atc-formal-affectable-listp (cons acl2::a acl2::x) typed-formals) (and (atc-formal-affectablep acl2::a typed-formals) (atc-formal-affectable-listp acl2::x typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-cdr-when-atc-formal-affectable-listp (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (atc-formal-affectable-listp (cdr acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-when-not-consp (implies (not (consp acl2::x)) (equal (atc-formal-affectable-listp acl2::x typed-formals) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectablep-of-car-when-atc-formal-affectable-listp (implies (atc-formal-affectable-listp acl2::x typed-formals) (iff (atc-formal-affectablep (car acl2::x) typed-formals) (or (consp acl2::x) (atc-formal-affectablep nil typed-formals)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-atc-formal-affectable-listp (implies (atc-formal-affectable-listp acl2::x typed-formals) (true-listp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-list-fix (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (list-fix acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-sfix (iff (atc-formal-affectable-listp (sfix acl2::x) typed-formals) (or (atc-formal-affectable-listp acl2::x typed-formals) (not (setp acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-insert (iff (atc-formal-affectable-listp (insert acl2::a acl2::x) typed-formals) (and (atc-formal-affectable-listp (sfix acl2::x) typed-formals) (atc-formal-affectablep acl2::a typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-delete (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (delete acl2::k acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-mergesort (iff (atc-formal-affectable-listp (mergesort acl2::x) typed-formals) (atc-formal-affectable-listp (list-fix acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-union (iff (atc-formal-affectable-listp (union acl2::x acl2::y) typed-formals) (and (atc-formal-affectable-listp (sfix acl2::x) typed-formals) (atc-formal-affectable-listp (sfix acl2::y) typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-intersect-1 (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (intersect acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-intersect-2 (implies (atc-formal-affectable-listp acl2::y typed-formals) (atc-formal-affectable-listp (intersect acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-difference (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (difference acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-duplicated-members (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (duplicated-members acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-rev (equal (atc-formal-affectable-listp (rev acl2::x) typed-formals) (atc-formal-affectable-listp (list-fix acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-append (equal (atc-formal-affectable-listp (append acl2::a acl2::b) typed-formals) (and (atc-formal-affectable-listp (list-fix acl2::a) typed-formals) (atc-formal-affectable-listp acl2::b typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-rcons (iff (atc-formal-affectable-listp (rcons acl2::a acl2::x) typed-formals) (and (atc-formal-affectablep acl2::a typed-formals) (atc-formal-affectable-listp (list-fix acl2::x) typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectablep-when-member-equal-of-atc-formal-affectable-listp (and (implies (and (member-equal acl2::a acl2::x) (atc-formal-affectable-listp acl2::x typed-formals)) (atc-formal-affectablep acl2::a typed-formals)) (implies (and (atc-formal-affectable-listp acl2::x typed-formals) (member-equal acl2::a acl2::x)) (atc-formal-affectablep acl2::a typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-when-subsetp-equal (and (implies (and (subsetp-equal acl2::x acl2::y) (atc-formal-affectable-listp acl2::y typed-formals)) (equal (atc-formal-affectable-listp acl2::x typed-formals) (true-listp acl2::x))) (implies (and (atc-formal-affectable-listp acl2::y typed-formals) (subsetp-equal acl2::x acl2::y)) (equal (atc-formal-affectable-listp acl2::x typed-formals) (true-listp acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-set-difference-equal (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (set-difference-equal acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-intersection-equal-1 (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (atc-formal-affectable-listp (intersection-equal acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-intersection-equal-2 (implies (atc-formal-affectable-listp (double-rewrite acl2::y) typed-formals) (atc-formal-affectable-listp (intersection-equal acl2::x acl2::y) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-union-equal (equal (atc-formal-affectable-listp (union-equal acl2::x acl2::y) typed-formals) (and (atc-formal-affectable-listp (list-fix acl2::x) typed-formals) (atc-formal-affectable-listp (double-rewrite acl2::y) typed-formals))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-take (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (iff (atc-formal-affectable-listp (take acl2::n acl2::x) typed-formals) (or (atc-formal-affectablep nil typed-formals) (<= (nfix acl2::n) (len acl2::x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-repeat (iff (atc-formal-affectable-listp (repeat acl2::n acl2::x) typed-formals) (or (atc-formal-affectablep acl2::x typed-formals) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectablep-of-nth-when-atc-formal-affectable-listp (implies (and (atc-formal-affectable-listp acl2::x typed-formals) (< (nfix acl2::n) (len acl2::x))) (atc-formal-affectablep (nth acl2::n acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-update-nth (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (iff (atc-formal-affectable-listp (update-nth acl2::n acl2::y acl2::x) typed-formals) (and (atc-formal-affectablep acl2::y typed-formals) (or (<= (nfix acl2::n) (len acl2::x)) (atc-formal-affectablep nil typed-formals))))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-butlast (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (atc-formal-affectable-listp (butlast acl2::x acl2::n) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-nthcdr (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (atc-formal-affectable-listp (nthcdr acl2::n acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-last (implies (atc-formal-affectable-listp (double-rewrite acl2::x) typed-formals) (atc-formal-affectable-listp (last acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-remove (implies (atc-formal-affectable-listp acl2::x typed-formals) (atc-formal-affectable-listp (remove acl2::a acl2::x) typed-formals)) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-formal-affectable-listp-of-revappend (equal (atc-formal-affectable-listp (revappend acl2::x acl2::y) typed-formals) (and (atc-formal-affectable-listp (list-fix acl2::x) typed-formals) (atc-formal-affectable-listp acl2::y typed-formals))) :rule-classes ((:rewrite)))