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• Atc-formal-affectable-listp

Atc-formal-affectable-listp-basics

Basic theorems about atc-formal-affectable-listp, generated by std::deflist.

Definitions and Theorems

Theorem: atc-formal-affectable-listp-of-cons

(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: atc-formal-affectable-listp-of-cdr-when-atc-formal-affectable-listp

(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: atc-formal-affectable-listp-when-not-consp

(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: atc-formal-affectablep-of-car-when-atc-formal-affectable-listp

(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: true-listp-when-atc-formal-affectable-listp

(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: atc-formal-affectable-listp-of-list-fix

(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: atc-formal-affectable-listp-of-sfix

(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: atc-formal-affectable-listp-of-insert

(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: atc-formal-affectable-listp-of-delete

(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: atc-formal-affectable-listp-of-mergesort

(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: atc-formal-affectable-listp-of-union

(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: atc-formal-affectable-listp-of-intersect-1

(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: atc-formal-affectable-listp-of-intersect-2

(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: atc-formal-affectable-listp-of-difference

(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: atc-formal-affectable-listp-of-duplicated-members

(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: atc-formal-affectable-listp-of-rev

(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: atc-formal-affectable-listp-of-append

(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: atc-formal-affectable-listp-of-rcons

(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: atc-formal-affectablep-when-member-equal-of-atc-formal-affectable-listp

(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: atc-formal-affectable-listp-when-subsetp-equal

(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: atc-formal-affectable-listp-of-set-difference-equal

(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: atc-formal-affectable-listp-of-intersection-equal-1

(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: atc-formal-affectable-listp-of-intersection-equal-2

(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: atc-formal-affectable-listp-of-union-equal

(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: atc-formal-affectable-listp-of-take

(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: atc-formal-affectable-listp-of-repeat

(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: atc-formal-affectablep-of-nth-when-atc-formal-affectable-listp

(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: atc-formal-affectable-listp-of-update-nth

(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: atc-formal-affectable-listp-of-butlast

(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: atc-formal-affectable-listp-of-nthcdr

(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: atc-formal-affectable-listp-of-last

(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: atc-formal-affectable-listp-of-remove

(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: atc-formal-affectable-listp-of-revappend

(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)))