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• Svar-boolmasks

Svar-boolmasks-fix

(svar-boolmasks-fix x) is an fty alist fixing function that follows the drop-keys strategy.

Signature

(svar-boolmasks-fix x) → fty::newx

Arguments

x — Guard (svar-boolmasks-p x).

Returns

fty::newx — Type (svar-boolmasks-p fty::newx).

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

Definitions and Theorems

Function: svar-boolmasks-fix$inline

(defun svar-boolmasks-fix$inline (x)
  (declare (xargs :guard (svar-boolmasks-p x)))
  (let ((__function__ 'svar-boolmasks-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             x
           (let ((rest (svar-boolmasks-fix (cdr x))))
             (if (and (consp (car x)) (svar-p (caar x)))
                 (let ((fty::first-key (caar x))
                       (fty::first-val (ifix (cdar x))))
                   (cons (cons fty::first-key fty::first-val)
                         rest))
               rest)))
         :exec x)))

Theorem: svar-boolmasks-p-of-svar-boolmasks-fix

(defthm svar-boolmasks-p-of-svar-boolmasks-fix
  (b* ((fty::newx (svar-boolmasks-fix$inline x)))
    (svar-boolmasks-p fty::newx))
  :rule-classes :rewrite)

Theorem: svar-boolmasks-fix-when-svar-boolmasks-p

(defthm svar-boolmasks-fix-when-svar-boolmasks-p
  (implies (svar-boolmasks-p x)
           (equal (svar-boolmasks-fix x) x)))

Function: svar-boolmasks-equiv$inline

(defun svar-boolmasks-equiv$inline (x y)
  (declare (xargs :guard (and (svar-boolmasks-p x)
                              (svar-boolmasks-p y))))
  (equal (svar-boolmasks-fix x)
         (svar-boolmasks-fix y)))

Theorem: svar-boolmasks-equiv-is-an-equivalence

(defthm svar-boolmasks-equiv-is-an-equivalence
  (and (booleanp (svar-boolmasks-equiv x y))
       (svar-boolmasks-equiv x x)
       (implies (svar-boolmasks-equiv x y)
                (svar-boolmasks-equiv y x))
       (implies (and (svar-boolmasks-equiv x y)
                     (svar-boolmasks-equiv y z))
                (svar-boolmasks-equiv x z)))
  :rule-classes (:equivalence))

Theorem: svar-boolmasks-equiv-implies-equal-svar-boolmasks-fix-1

(defthm svar-boolmasks-equiv-implies-equal-svar-boolmasks-fix-1
  (implies (svar-boolmasks-equiv x x-equiv)
           (equal (svar-boolmasks-fix x)
                  (svar-boolmasks-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svar-boolmasks-fix-under-svar-boolmasks-equiv

(defthm svar-boolmasks-fix-under-svar-boolmasks-equiv
  (svar-boolmasks-equiv (svar-boolmasks-fix x)
                        x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svar-boolmasks-fix-1-forward-to-svar-boolmasks-equiv

(defthm
      equal-of-svar-boolmasks-fix-1-forward-to-svar-boolmasks-equiv
  (implies (equal (svar-boolmasks-fix x) y)
           (svar-boolmasks-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-svar-boolmasks-fix-2-forward-to-svar-boolmasks-equiv

(defthm
      equal-of-svar-boolmasks-fix-2-forward-to-svar-boolmasks-equiv
  (implies (equal x (svar-boolmasks-fix y))
           (svar-boolmasks-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svar-boolmasks-equiv-of-svar-boolmasks-fix-1-forward

(defthm svar-boolmasks-equiv-of-svar-boolmasks-fix-1-forward
  (implies (svar-boolmasks-equiv (svar-boolmasks-fix x)
                                 y)
           (svar-boolmasks-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svar-boolmasks-equiv-of-svar-boolmasks-fix-2-forward

(defthm svar-boolmasks-equiv-of-svar-boolmasks-fix-2-forward
  (implies (svar-boolmasks-equiv x (svar-boolmasks-fix y))
           (svar-boolmasks-equiv x y))
  :rule-classes :forward-chaining)

Theorem: cons-of-ifix-v-under-svar-boolmasks-equiv

(defthm cons-of-ifix-v-under-svar-boolmasks-equiv
  (svar-boolmasks-equiv (cons (cons acl2::k (ifix acl2::v)) x)
                        (cons (cons acl2::k acl2::v) x)))

Theorem: cons-int-equiv-congruence-on-v-under-svar-boolmasks-equiv

(defthm cons-int-equiv-congruence-on-v-under-svar-boolmasks-equiv
  (implies (int-equiv acl2::v v-equiv)
           (svar-boolmasks-equiv (cons (cons acl2::k acl2::v) x)
                                 (cons (cons acl2::k v-equiv) x)))
  :rule-classes :congruence)

Theorem: cons-of-svar-boolmasks-fix-y-under-svar-boolmasks-equiv

(defthm cons-of-svar-boolmasks-fix-y-under-svar-boolmasks-equiv
  (svar-boolmasks-equiv (cons x (svar-boolmasks-fix y))
                        (cons x y)))

Theorem: cons-svar-boolmasks-equiv-congruence-on-y-under-svar-boolmasks-equiv

(defthm
 cons-svar-boolmasks-equiv-congruence-on-y-under-svar-boolmasks-equiv
 (implies (svar-boolmasks-equiv y y-equiv)
          (svar-boolmasks-equiv (cons x y)
                                (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: svar-boolmasks-fix-of-acons

(defthm svar-boolmasks-fix-of-acons
  (equal (svar-boolmasks-fix (cons (cons acl2::a acl2::b) x))
         (let ((rest (svar-boolmasks-fix x)))
           (if (and (svar-p acl2::a))
               (let ((fty::first-key acl2::a)
                     (fty::first-val (ifix acl2::b)))
                 (cons (cons fty::first-key fty::first-val)
                       rest))
             rest))))

Theorem: hons-assoc-equal-of-svar-boolmasks-fix

(defthm hons-assoc-equal-of-svar-boolmasks-fix
  (equal (hons-assoc-equal acl2::k (svar-boolmasks-fix x))
         (let ((fty::pair (hons-assoc-equal acl2::k x)))
           (and (svar-p acl2::k)
                fty::pair
                (cons acl2::k (ifix (cdr fty::pair)))))))

Theorem: svar-boolmasks-fix-of-append

(defthm svar-boolmasks-fix-of-append
  (equal (svar-boolmasks-fix (append std::a std::b))
         (append (svar-boolmasks-fix std::a)
                 (svar-boolmasks-fix std::b))))

Theorem: consp-car-of-svar-boolmasks-fix

(defthm consp-car-of-svar-boolmasks-fix
  (equal (consp (car (svar-boolmasks-fix x)))
         (consp (svar-boolmasks-fix x))))