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Ubdd-to-aignet-memo

Ubdd-to-aignet-memo-fix

(ubdd-to-aignet-memo-fix x) is an ACL2::fty alist fixing function that follows the drop-keys strategy.

Signature
(ubdd-to-aignet-memo-fix x) → fty::newx
Arguments: x — Guard (ubdd-to-aignet-memo-p x).
Returns: fty::newx — Type (ubdd-to-aignet-memo-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: ubdd-to-aignet-memo-fix$inline

(defun ubdd-to-aignet-memo-fix$inline (x)
  (declare (xargs :guard (ubdd-to-aignet-memo-p x)))
  (let ((__function__ 'ubdd-to-aignet-memo-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (let ((rest (ubdd-to-aignet-memo-fix (cdr x))))
             (if (and (consp (car x))
                      (ubdd/level-p (caar x)))
                 (let ((fty::first-key (caar x))
                       (fty::first-val (lit-fix (cdar x))))
                   (cons (cons fty::first-key fty::first-val)
                         rest))
               rest)))
         :exec x)))

Theorem: ubdd-to-aignet-memo-p-of-ubdd-to-aignet-memo-fix

(defthm ubdd-to-aignet-memo-p-of-ubdd-to-aignet-memo-fix
  (b* ((fty::newx (ubdd-to-aignet-memo-fix$inline x)))
    (ubdd-to-aignet-memo-p fty::newx))
  :rule-classes :rewrite)

Theorem: ubdd-to-aignet-memo-fix-when-ubdd-to-aignet-memo-p

(defthm ubdd-to-aignet-memo-fix-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p x)
           (equal (ubdd-to-aignet-memo-fix x) x)))

Function: ubdd-to-aignet-memo-equiv$inline

(defun ubdd-to-aignet-memo-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (ubdd-to-aignet-memo-p x)
                              (ubdd-to-aignet-memo-p acl2::y))))
  (equal (ubdd-to-aignet-memo-fix x)
         (ubdd-to-aignet-memo-fix acl2::y)))

Theorem: ubdd-to-aignet-memo-equiv-is-an-equivalence

(defthm ubdd-to-aignet-memo-equiv-is-an-equivalence
  (and (booleanp (ubdd-to-aignet-memo-equiv x y))
       (ubdd-to-aignet-memo-equiv x x)
       (implies (ubdd-to-aignet-memo-equiv x y)
                (ubdd-to-aignet-memo-equiv y x))
       (implies (and (ubdd-to-aignet-memo-equiv x y)
                     (ubdd-to-aignet-memo-equiv y z))
                (ubdd-to-aignet-memo-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubdd-to-aignet-memo-equiv-implies-equal-ubdd-to-aignet-memo-fix-1

(defthm
  ubdd-to-aignet-memo-equiv-implies-equal-ubdd-to-aignet-memo-fix-1
  (implies (ubdd-to-aignet-memo-equiv x x-equiv)
           (equal (ubdd-to-aignet-memo-fix x)
                  (ubdd-to-aignet-memo-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubdd-to-aignet-memo-fix-under-ubdd-to-aignet-memo-equiv

(defthm ubdd-to-aignet-memo-fix-under-ubdd-to-aignet-memo-equiv
  (ubdd-to-aignet-memo-equiv (ubdd-to-aignet-memo-fix x)
                             x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubdd-to-aignet-memo-fix-1-forward-to-ubdd-to-aignet-memo-equiv

(defthm
 equal-of-ubdd-to-aignet-memo-fix-1-forward-to-ubdd-to-aignet-memo-equiv
 (implies (equal (ubdd-to-aignet-memo-fix x)
                 acl2::y)
          (ubdd-to-aignet-memo-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-ubdd-to-aignet-memo-fix-2-forward-to-ubdd-to-aignet-memo-equiv

(defthm
 equal-of-ubdd-to-aignet-memo-fix-2-forward-to-ubdd-to-aignet-memo-equiv
 (implies (equal x (ubdd-to-aignet-memo-fix acl2::y))
          (ubdd-to-aignet-memo-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-1-forward

(defthm
     ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-1-forward
  (implies (ubdd-to-aignet-memo-equiv (ubdd-to-aignet-memo-fix x)
                                      acl2::y)
           (ubdd-to-aignet-memo-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-2-forward

(defthm
     ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-2-forward
 (implies
     (ubdd-to-aignet-memo-equiv x (ubdd-to-aignet-memo-fix acl2::y))
     (ubdd-to-aignet-memo-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: cons-of-lit-fix-v-under-ubdd-to-aignet-memo-equiv

(defthm cons-of-lit-fix-v-under-ubdd-to-aignet-memo-equiv
  (ubdd-to-aignet-memo-equiv (cons (cons acl2::k (lit-fix acl2::v))
                                   x)
                             (cons (cons acl2::k acl2::v) x)))

Theorem: cons-lit-equiv-congruence-on-v-under-ubdd-to-aignet-memo-equiv

(defthm
     cons-lit-equiv-congruence-on-v-under-ubdd-to-aignet-memo-equiv
  (implies
       (lit-equiv acl2::v v-equiv)
       (ubdd-to-aignet-memo-equiv (cons (cons acl2::k acl2::v) x)
                                  (cons (cons acl2::k v-equiv) x)))
  :rule-classes :congruence)

Theorem: cons-of-ubdd-to-aignet-memo-fix-y-under-ubdd-to-aignet-memo-equiv

(defthm
  cons-of-ubdd-to-aignet-memo-fix-y-under-ubdd-to-aignet-memo-equiv
  (ubdd-to-aignet-memo-equiv
       (cons x (ubdd-to-aignet-memo-fix acl2::y))
       (cons x acl2::y)))

Theorem: cons-ubdd-to-aignet-memo-equiv-congruence-on-y-under-ubdd-to-aignet-memo-equiv

(defthm
 cons-ubdd-to-aignet-memo-equiv-congruence-on-y-under-ubdd-to-aignet-memo-equiv
 (implies (ubdd-to-aignet-memo-equiv acl2::y y-equiv)
          (ubdd-to-aignet-memo-equiv (cons x acl2::y)
                                     (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: ubdd-to-aignet-memo-fix-of-acons

(defthm ubdd-to-aignet-memo-fix-of-acons
  (equal (ubdd-to-aignet-memo-fix (cons (cons acl2::a acl2::b) x))
         (let ((rest (ubdd-to-aignet-memo-fix x)))
           (if (and (ubdd/level-p acl2::a))
               (let ((fty::first-key acl2::a)
                     (fty::first-val (lit-fix acl2::b)))
                 (cons (cons fty::first-key fty::first-val)
                       rest))
             rest))))

Theorem: hons-assoc-equal-of-ubdd-to-aignet-memo-fix

(defthm hons-assoc-equal-of-ubdd-to-aignet-memo-fix
  (equal (hons-assoc-equal acl2::k (ubdd-to-aignet-memo-fix x))
         (let ((fty::pair (hons-assoc-equal acl2::k x)))
           (and (ubdd/level-p acl2::k)
                fty::pair
                (cons acl2::k (lit-fix (cdr fty::pair)))))))

Theorem: ubdd-to-aignet-memo-fix-of-append

(defthm ubdd-to-aignet-memo-fix-of-append
  (equal (ubdd-to-aignet-memo-fix (append std::a std::b))
         (append (ubdd-to-aignet-memo-fix std::a)
                 (ubdd-to-aignet-memo-fix std::b))))

Theorem: consp-car-of-ubdd-to-aignet-memo-fix

(defthm consp-car-of-ubdd-to-aignet-memo-fix
  (equal (consp (car (ubdd-to-aignet-memo-fix x)))
         (consp (ubdd-to-aignet-memo-fix x))))