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    • Vl-maybe-string-list

    Vl-maybe-string-list-fix

    (vl-maybe-string-list-fix x) is a usual fty list fixing function.

    Signature
    (vl-maybe-string-list-fix x) → fty::newx
    Arguments
    x — Guard (vl-maybe-string-list-p x).
    Returns
    fty::newx — Type (vl-maybe-string-list-p fty::newx).

    In the logic, we apply maybe-string-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: vl-maybe-string-list-fix$inline

    (defun vl-maybe-string-list-fix$inline (x)
      (declare (xargs :guard (vl-maybe-string-list-p x)))
      (let ((__function__ 'vl-maybe-string-list-fix))
        (declare (ignorable __function__))
        (mbe :logic
             (if (atom x)
                 x
               (cons (maybe-string-fix (car x))
                     (vl-maybe-string-list-fix (cdr x))))
             :exec x)))

    Theorem: vl-maybe-string-list-p-of-vl-maybe-string-list-fix

    (defthm vl-maybe-string-list-p-of-vl-maybe-string-list-fix
      (b* ((fty::newx (vl-maybe-string-list-fix$inline x)))
        (vl-maybe-string-list-p fty::newx))
      :rule-classes :rewrite)

    Theorem: vl-maybe-string-list-fix-when-vl-maybe-string-list-p

    (defthm vl-maybe-string-list-fix-when-vl-maybe-string-list-p
      (implies (vl-maybe-string-list-p x)
               (equal (vl-maybe-string-list-fix x) x)))

    Function: vl-maybe-string-list-equiv$inline

    (defun vl-maybe-string-list-equiv$inline (acl2::x acl2::y)
      (declare (xargs :guard (and (vl-maybe-string-list-p acl2::x)
                                  (vl-maybe-string-list-p acl2::y))))
      (equal (vl-maybe-string-list-fix acl2::x)
             (vl-maybe-string-list-fix acl2::y)))

    Theorem: vl-maybe-string-list-equiv-is-an-equivalence

    (defthm vl-maybe-string-list-equiv-is-an-equivalence
      (and (booleanp (vl-maybe-string-list-equiv x y))
           (vl-maybe-string-list-equiv x x)
           (implies (vl-maybe-string-list-equiv x y)
                    (vl-maybe-string-list-equiv y x))
           (implies (and (vl-maybe-string-list-equiv x y)
                         (vl-maybe-string-list-equiv y z))
                    (vl-maybe-string-list-equiv x z)))
      :rule-classes (:equivalence))

    Theorem: vl-maybe-string-list-equiv-implies-equal-vl-maybe-string-list-fix-1

    (defthm
     vl-maybe-string-list-equiv-implies-equal-vl-maybe-string-list-fix-1
     (implies (vl-maybe-string-list-equiv acl2::x x-equiv)
              (equal (vl-maybe-string-list-fix acl2::x)
                     (vl-maybe-string-list-fix x-equiv)))
     :rule-classes (:congruence))

    Theorem: vl-maybe-string-list-fix-under-vl-maybe-string-list-equiv

    (defthm vl-maybe-string-list-fix-under-vl-maybe-string-list-equiv
      (vl-maybe-string-list-equiv (vl-maybe-string-list-fix acl2::x)
                                  acl2::x)
      :rule-classes (:rewrite :rewrite-quoted-constant))

    Theorem: equal-of-vl-maybe-string-list-fix-1-forward-to-vl-maybe-string-list-equiv

    (defthm
     equal-of-vl-maybe-string-list-fix-1-forward-to-vl-maybe-string-list-equiv
     (implies (equal (vl-maybe-string-list-fix acl2::x)
                     acl2::y)
              (vl-maybe-string-list-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

    Theorem: equal-of-vl-maybe-string-list-fix-2-forward-to-vl-maybe-string-list-equiv

    (defthm
     equal-of-vl-maybe-string-list-fix-2-forward-to-vl-maybe-string-list-equiv
     (implies (equal acl2::x
                     (vl-maybe-string-list-fix acl2::y))
              (vl-maybe-string-list-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

    Theorem: vl-maybe-string-list-equiv-of-vl-maybe-string-list-fix-1-forward

    (defthm
       vl-maybe-string-list-equiv-of-vl-maybe-string-list-fix-1-forward
     (implies
          (vl-maybe-string-list-equiv (vl-maybe-string-list-fix acl2::x)
                                      acl2::y)
          (vl-maybe-string-list-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

    Theorem: vl-maybe-string-list-equiv-of-vl-maybe-string-list-fix-2-forward

    (defthm
       vl-maybe-string-list-equiv-of-vl-maybe-string-list-fix-2-forward
     (implies
         (vl-maybe-string-list-equiv acl2::x
                                     (vl-maybe-string-list-fix acl2::y))
         (vl-maybe-string-list-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

    Theorem: car-of-vl-maybe-string-list-fix-x-under-maybe-string-equiv

    (defthm car-of-vl-maybe-string-list-fix-x-under-maybe-string-equiv
      (maybe-string-equiv (car (vl-maybe-string-list-fix acl2::x))
                          (car acl2::x)))

    Theorem: car-vl-maybe-string-list-equiv-congruence-on-x-under-maybe-string-equiv

    (defthm
     car-vl-maybe-string-list-equiv-congruence-on-x-under-maybe-string-equiv
     (implies (vl-maybe-string-list-equiv acl2::x x-equiv)
              (maybe-string-equiv (car acl2::x)
                                  (car x-equiv)))
     :rule-classes :congruence)

    Theorem: cdr-of-vl-maybe-string-list-fix-x-under-vl-maybe-string-list-equiv

    (defthm
     cdr-of-vl-maybe-string-list-fix-x-under-vl-maybe-string-list-equiv
     (vl-maybe-string-list-equiv
          (cdr (vl-maybe-string-list-fix acl2::x))
          (cdr acl2::x)))

    Theorem: cdr-vl-maybe-string-list-equiv-congruence-on-x-under-vl-maybe-string-list-equiv

    (defthm
     cdr-vl-maybe-string-list-equiv-congruence-on-x-under-vl-maybe-string-list-equiv
     (implies (vl-maybe-string-list-equiv acl2::x x-equiv)
              (vl-maybe-string-list-equiv (cdr acl2::x)
                                          (cdr x-equiv)))
     :rule-classes :congruence)

    Theorem: cons-of-maybe-string-fix-x-under-vl-maybe-string-list-equiv

    (defthm cons-of-maybe-string-fix-x-under-vl-maybe-string-list-equiv
      (vl-maybe-string-list-equiv (cons (maybe-string-fix acl2::x)
                                        acl2::y)
                                  (cons acl2::x acl2::y)))

    Theorem: cons-maybe-string-equiv-congruence-on-x-under-vl-maybe-string-list-equiv

    (defthm
     cons-maybe-string-equiv-congruence-on-x-under-vl-maybe-string-list-equiv
     (implies (maybe-string-equiv acl2::x x-equiv)
              (vl-maybe-string-list-equiv (cons acl2::x acl2::y)
                                          (cons x-equiv acl2::y)))
     :rule-classes :congruence)

    Theorem: cons-of-vl-maybe-string-list-fix-y-under-vl-maybe-string-list-equiv

    (defthm
     cons-of-vl-maybe-string-list-fix-y-under-vl-maybe-string-list-equiv
     (vl-maybe-string-list-equiv
          (cons acl2::x
                (vl-maybe-string-list-fix acl2::y))
          (cons acl2::x acl2::y)))

    Theorem: cons-vl-maybe-string-list-equiv-congruence-on-y-under-vl-maybe-string-list-equiv

    (defthm
     cons-vl-maybe-string-list-equiv-congruence-on-y-under-vl-maybe-string-list-equiv
     (implies (vl-maybe-string-list-equiv acl2::y y-equiv)
              (vl-maybe-string-list-equiv (cons acl2::x acl2::y)
                                          (cons acl2::x y-equiv)))
     :rule-classes :congruence)

    Theorem: consp-of-vl-maybe-string-list-fix

    (defthm consp-of-vl-maybe-string-list-fix
      (equal (consp (vl-maybe-string-list-fix acl2::x))
             (consp acl2::x)))

    Theorem: vl-maybe-string-list-fix-of-cons

    (defthm vl-maybe-string-list-fix-of-cons
      (equal (vl-maybe-string-list-fix (cons a x))
             (cons (maybe-string-fix a)
                   (vl-maybe-string-list-fix x))))

    Theorem: len-of-vl-maybe-string-list-fix

    (defthm len-of-vl-maybe-string-list-fix
      (equal (len (vl-maybe-string-list-fix acl2::x))
             (len acl2::x)))

    Theorem: vl-maybe-string-list-fix-of-append

    (defthm vl-maybe-string-list-fix-of-append
      (equal (vl-maybe-string-list-fix (append std::a std::b))
             (append (vl-maybe-string-list-fix std::a)
                     (vl-maybe-string-list-fix std::b))))

    Theorem: vl-maybe-string-list-fix-of-repeat

    (defthm vl-maybe-string-list-fix-of-repeat
      (equal (vl-maybe-string-list-fix (repeat acl2::n acl2::x))
             (repeat acl2::n (maybe-string-fix acl2::x))))

    Theorem: nth-of-vl-maybe-string-list-fix

    (defthm nth-of-vl-maybe-string-list-fix
      (equal (nth acl2::n
                  (vl-maybe-string-list-fix acl2::x))
             (if (< (nfix acl2::n) (len acl2::x))
                 (maybe-string-fix (nth acl2::n acl2::x))
               nil)))

    Theorem: vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-append-1

    (defthm
     vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-append-1
     (implies
          (vl-maybe-string-list-equiv acl2::x fty::x-equiv)
          (vl-maybe-string-list-equiv (append acl2::x acl2::y)
                                      (append fty::x-equiv acl2::y)))
     :rule-classes (:congruence))

    Theorem: vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-append-2

    (defthm
     vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-append-2
     (implies
          (vl-maybe-string-list-equiv acl2::y fty::y-equiv)
          (vl-maybe-string-list-equiv (append acl2::x acl2::y)
                                      (append acl2::x fty::y-equiv)))
     :rule-classes (:congruence))

    Theorem: vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-nthcdr-2

    (defthm
     vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-nthcdr-2
     (implies (vl-maybe-string-list-equiv acl2::l l-equiv)
              (vl-maybe-string-list-equiv (nthcdr acl2::n acl2::l)
                                          (nthcdr acl2::n l-equiv)))
     :rule-classes (:congruence))

    Theorem: vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-take-2

    (defthm
     vl-maybe-string-list-equiv-implies-vl-maybe-string-list-equiv-take-2
     (implies (vl-maybe-string-list-equiv acl2::l l-equiv)
              (vl-maybe-string-list-equiv (take acl2::n acl2::l)
                                          (take acl2::n l-equiv)))
     :rule-classes (:congruence))