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• Sv::maybe-4veclist

Sv::maybe-4veclist-fix

(sv::maybe-4veclist-fix acl2::x) is a usual fty list fixing function.

Signature

(sv::maybe-4veclist-fix acl2::x) → fty::newx

Arguments

acl2::x — Guard (sv::maybe-4veclist-p acl2::x).

Returns

fty::newx — Type (sv::maybe-4veclist-p fty::newx).

In the logic, we apply sv::maybe-4vec-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.

Definitions and Theorems

Function: maybe-4veclist-fix$inline

(defun sv::maybe-4veclist-fix$inline (acl2::x)
  (declare (xargs :guard (sv::maybe-4veclist-p acl2::x)))
  (let ((__function__ 'sv::maybe-4veclist-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom acl2::x)
             nil
           (cons (sv::maybe-4vec-fix (car acl2::x))
                 (sv::maybe-4veclist-fix (cdr acl2::x))))
         :exec acl2::x)))

Theorem: maybe-4veclist-p-of-maybe-4veclist-fix

(defthm sv::maybe-4veclist-p-of-maybe-4veclist-fix
  (b* ((fty::newx (sv::maybe-4veclist-fix$inline acl2::x)))
    (sv::maybe-4veclist-p fty::newx))
  :rule-classes :rewrite)

Theorem: maybe-4veclist-fix-when-maybe-4veclist-p

(defthm sv::maybe-4veclist-fix-when-maybe-4veclist-p
  (implies (sv::maybe-4veclist-p acl2::x)
           (equal (sv::maybe-4veclist-fix acl2::x)
                  acl2::x)))

Function: maybe-4veclist-equiv$inline

(defun sv::maybe-4veclist-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (sv::maybe-4veclist-p acl2::x)
                              (sv::maybe-4veclist-p acl2::y))))
  (equal (sv::maybe-4veclist-fix acl2::x)
         (sv::maybe-4veclist-fix acl2::y)))

Theorem: maybe-4veclist-equiv-is-an-equivalence

(defthm sv::maybe-4veclist-equiv-is-an-equivalence
  (and (booleanp (sv::maybe-4veclist-equiv acl2::x acl2::y))
       (sv::maybe-4veclist-equiv acl2::x acl2::x)
       (implies (sv::maybe-4veclist-equiv acl2::x acl2::y)
                (sv::maybe-4veclist-equiv acl2::y acl2::x))
       (implies (and (sv::maybe-4veclist-equiv acl2::x acl2::y)
                     (sv::maybe-4veclist-equiv acl2::y acl2::z))
                (sv::maybe-4veclist-equiv acl2::x acl2::z)))
  :rule-classes (:equivalence))

Theorem: maybe-4veclist-equiv-implies-equal-maybe-4veclist-fix-1

(defthm sv::maybe-4veclist-equiv-implies-equal-maybe-4veclist-fix-1
  (implies (sv::maybe-4veclist-equiv acl2::x sv::x-equiv)
           (equal (sv::maybe-4veclist-fix acl2::x)
                  (sv::maybe-4veclist-fix sv::x-equiv)))
  :rule-classes (:congruence))

Theorem: maybe-4veclist-fix-under-maybe-4veclist-equiv

(defthm sv::maybe-4veclist-fix-under-maybe-4veclist-equiv
  (sv::maybe-4veclist-equiv (sv::maybe-4veclist-fix acl2::x)
                            acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-maybe-4veclist-fix-1-forward-to-maybe-4veclist-equiv

(defthm
  sv::equal-of-maybe-4veclist-fix-1-forward-to-maybe-4veclist-equiv
  (implies (equal (sv::maybe-4veclist-fix acl2::x)
                  acl2::y)
           (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-maybe-4veclist-fix-2-forward-to-maybe-4veclist-equiv

(defthm
  sv::equal-of-maybe-4veclist-fix-2-forward-to-maybe-4veclist-equiv
  (implies (equal acl2::x
                  (sv::maybe-4veclist-fix acl2::y))
           (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: maybe-4veclist-equiv-of-maybe-4veclist-fix-1-forward

(defthm sv::maybe-4veclist-equiv-of-maybe-4veclist-fix-1-forward
 (implies (sv::maybe-4veclist-equiv (sv::maybe-4veclist-fix acl2::x)
                                    acl2::y)
          (sv::maybe-4veclist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: maybe-4veclist-equiv-of-maybe-4veclist-fix-2-forward

(defthm sv::maybe-4veclist-equiv-of-maybe-4veclist-fix-2-forward
  (implies
       (sv::maybe-4veclist-equiv acl2::x
                                 (sv::maybe-4veclist-fix acl2::y))
       (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: car-of-maybe-4veclist-fix-x-under-maybe-4vec-equiv

(defthm sv::car-of-maybe-4veclist-fix-x-under-maybe-4vec-equiv
  (sv::maybe-4vec-equiv (car (sv::maybe-4veclist-fix acl2::x))
                        (car acl2::x)))

Theorem: car-maybe-4veclist-equiv-congruence-on-x-under-maybe-4vec-equiv

(defthm
 sv::car-maybe-4veclist-equiv-congruence-on-x-under-maybe-4vec-equiv
 (implies (sv::maybe-4veclist-equiv acl2::x sv::x-equiv)
          (sv::maybe-4vec-equiv (car acl2::x)
                                (car sv::x-equiv)))
 :rule-classes :congruence)

Theorem: cdr-of-maybe-4veclist-fix-x-under-maybe-4veclist-equiv

(defthm sv::cdr-of-maybe-4veclist-fix-x-under-maybe-4veclist-equiv
  (sv::maybe-4veclist-equiv (cdr (sv::maybe-4veclist-fix acl2::x))
                            (cdr acl2::x)))

Theorem: cdr-maybe-4veclist-equiv-congruence-on-x-under-maybe-4veclist-equiv

(defthm
 sv::cdr-maybe-4veclist-equiv-congruence-on-x-under-maybe-4veclist-equiv
 (implies (sv::maybe-4veclist-equiv acl2::x sv::x-equiv)
          (sv::maybe-4veclist-equiv (cdr acl2::x)
                                    (cdr sv::x-equiv)))
 :rule-classes :congruence)

Theorem: cons-of-maybe-4vec-fix-x-under-maybe-4veclist-equiv

(defthm sv::cons-of-maybe-4vec-fix-x-under-maybe-4veclist-equiv
  (sv::maybe-4veclist-equiv (cons (sv::maybe-4vec-fix acl2::x)
                                  acl2::y)
                            (cons acl2::x acl2::y)))

Theorem: cons-maybe-4vec-equiv-congruence-on-x-under-maybe-4veclist-equiv

(defthm
 sv::cons-maybe-4vec-equiv-congruence-on-x-under-maybe-4veclist-equiv
 (implies (sv::maybe-4vec-equiv acl2::x sv::x-equiv)
          (sv::maybe-4veclist-equiv (cons acl2::x acl2::y)
                                    (cons sv::x-equiv acl2::y)))
 :rule-classes :congruence)

Theorem: cons-of-maybe-4veclist-fix-y-under-maybe-4veclist-equiv

(defthm sv::cons-of-maybe-4veclist-fix-y-under-maybe-4veclist-equiv
  (sv::maybe-4veclist-equiv (cons acl2::x
                                  (sv::maybe-4veclist-fix acl2::y))
                            (cons acl2::x acl2::y)))

Theorem: cons-maybe-4veclist-equiv-congruence-on-y-under-maybe-4veclist-equiv

(defthm
 sv::cons-maybe-4veclist-equiv-congruence-on-y-under-maybe-4veclist-equiv
 (implies (sv::maybe-4veclist-equiv acl2::y sv::y-equiv)
          (sv::maybe-4veclist-equiv (cons acl2::x acl2::y)
                                    (cons acl2::x sv::y-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-maybe-4veclist-fix

(defthm sv::consp-of-maybe-4veclist-fix
  (equal (consp (sv::maybe-4veclist-fix acl2::x))
         (consp acl2::x)))

Theorem: maybe-4veclist-fix-under-iff

(defthm sv::maybe-4veclist-fix-under-iff
  (iff (sv::maybe-4veclist-fix acl2::x)
       (consp acl2::x)))

Theorem: maybe-4veclist-fix-of-cons

(defthm sv::maybe-4veclist-fix-of-cons
  (equal (sv::maybe-4veclist-fix (cons sv::a acl2::x))
         (cons (sv::maybe-4vec-fix sv::a)
               (sv::maybe-4veclist-fix acl2::x))))

Theorem: len-of-maybe-4veclist-fix

(defthm sv::len-of-maybe-4veclist-fix
  (equal (len (sv::maybe-4veclist-fix acl2::x))
         (len acl2::x)))

Theorem: maybe-4veclist-fix-of-append

(defthm sv::maybe-4veclist-fix-of-append
  (equal (sv::maybe-4veclist-fix (append std::a std::b))
         (append (sv::maybe-4veclist-fix std::a)
                 (sv::maybe-4veclist-fix std::b))))

Theorem: maybe-4veclist-fix-of-repeat

(defthm sv::maybe-4veclist-fix-of-repeat
  (equal (sv::maybe-4veclist-fix (repeat acl2::n acl2::x))
         (repeat acl2::n (sv::maybe-4vec-fix acl2::x))))

Theorem: list-equiv-refines-maybe-4veclist-equiv

(defthm sv::list-equiv-refines-maybe-4veclist-equiv
  (implies (list-equiv acl2::x acl2::y)
           (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :refinement)

Theorem: nth-of-maybe-4veclist-fix

(defthm sv::nth-of-maybe-4veclist-fix
  (equal (nth acl2::n
              (sv::maybe-4veclist-fix acl2::x))
         (if (< (nfix acl2::n) (len acl2::x))
             (sv::maybe-4vec-fix (nth acl2::n acl2::x))
           nil)))

Theorem: maybe-4veclist-equiv-implies-maybe-4veclist-equiv-append-1

(defthm
     sv::maybe-4veclist-equiv-implies-maybe-4veclist-equiv-append-1
  (implies (sv::maybe-4veclist-equiv acl2::x fty::x-equiv)
           (sv::maybe-4veclist-equiv (append acl2::x acl2::y)
                                     (append fty::x-equiv acl2::y)))
  :rule-classes (:congruence))

Theorem: maybe-4veclist-equiv-implies-maybe-4veclist-equiv-append-2

(defthm
     sv::maybe-4veclist-equiv-implies-maybe-4veclist-equiv-append-2
  (implies (sv::maybe-4veclist-equiv acl2::y fty::y-equiv)
           (sv::maybe-4veclist-equiv (append acl2::x acl2::y)
                                     (append acl2::x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: maybe-4veclist-equiv-implies-maybe-4veclist-equiv-nthcdr-2

(defthm maybe-4veclist-equiv-implies-maybe-4veclist-equiv-nthcdr-2
  (implies (sv::maybe-4veclist-equiv acl2::l l-equiv)
           (sv::maybe-4veclist-equiv (nthcdr acl2::n acl2::l)
                                     (nthcdr acl2::n l-equiv)))
  :rule-classes (:congruence))

Theorem: maybe-4veclist-equiv-implies-maybe-4veclist-equiv-take-2

(defthm maybe-4veclist-equiv-implies-maybe-4veclist-equiv-take-2
  (implies (sv::maybe-4veclist-equiv acl2::l l-equiv)
           (sv::maybe-4veclist-equiv (take acl2::n acl2::l)
                                     (take acl2::n l-equiv)))
  :rule-classes (:congruence))