		Search-engine friendly clone of the ACL2 documentation.

Snippet-table

Snippet-table-fix

(snippet-table-fix x) is a usual ACL2::fty list fixing function.

Signature
(snippet-table-fix x) → fty::newx
Arguments: x — Guard (snippet-table-p x).
Returns: fty::newx — Type (snippet-table-p fty::newx).

In the logic, we apply snippet-info-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: snippet-table-fix$inline

(defun snippet-table-fix$inline (x)
  (declare (xargs :guard (snippet-table-p x)))
  (let ((__function__ 'snippet-table-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (snippet-info-fix (car x))
                 (snippet-table-fix (cdr x))))
         :exec x)))

Theorem: snippet-table-p-of-snippet-table-fix

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

Theorem: snippet-table-fix-when-snippet-table-p

(defthm snippet-table-fix-when-snippet-table-p
  (implies (snippet-table-p x)
           (equal (snippet-table-fix x) x)))

Function: snippet-table-equiv$inline

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

Theorem: snippet-table-equiv-is-an-equivalence

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

Theorem: snippet-table-equiv-implies-equal-snippet-table-fix-1

(defthm snippet-table-equiv-implies-equal-snippet-table-fix-1
  (implies (snippet-table-equiv x x-equiv)
           (equal (snippet-table-fix x)
                  (snippet-table-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: snippet-table-fix-under-snippet-table-equiv

(defthm snippet-table-fix-under-snippet-table-equiv
  (snippet-table-equiv (snippet-table-fix x)
                       x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-snippet-table-fix-1-forward-to-snippet-table-equiv

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

Theorem: equal-of-snippet-table-fix-2-forward-to-snippet-table-equiv

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

Theorem: snippet-table-equiv-of-snippet-table-fix-1-forward

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

Theorem: snippet-table-equiv-of-snippet-table-fix-2-forward

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

Theorem: car-of-snippet-table-fix-x-under-snippet-info-equiv

(defthm car-of-snippet-table-fix-x-under-snippet-info-equiv
  (snippet-info-equiv (car (snippet-table-fix x))
                      (car x)))

Theorem: car-snippet-table-equiv-congruence-on-x-under-snippet-info-equiv

(defthm
   car-snippet-table-equiv-congruence-on-x-under-snippet-info-equiv
  (implies (snippet-table-equiv x x-equiv)
           (snippet-info-equiv (car x)
                               (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-snippet-table-fix-x-under-snippet-table-equiv

(defthm cdr-of-snippet-table-fix-x-under-snippet-table-equiv
  (snippet-table-equiv (cdr (snippet-table-fix x))
                       (cdr x)))

Theorem: cdr-snippet-table-equiv-congruence-on-x-under-snippet-table-equiv

(defthm
  cdr-snippet-table-equiv-congruence-on-x-under-snippet-table-equiv
  (implies (snippet-table-equiv x x-equiv)
           (snippet-table-equiv (cdr x)
                                (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-snippet-info-fix-x-under-snippet-table-equiv

(defthm cons-of-snippet-info-fix-x-under-snippet-table-equiv
  (snippet-table-equiv (cons (snippet-info-fix x) y)
                       (cons x y)))

Theorem: cons-snippet-info-equiv-congruence-on-x-under-snippet-table-equiv

(defthm
  cons-snippet-info-equiv-congruence-on-x-under-snippet-table-equiv
  (implies (snippet-info-equiv x x-equiv)
           (snippet-table-equiv (cons x y)
                                (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-snippet-table-fix-y-under-snippet-table-equiv

(defthm cons-of-snippet-table-fix-y-under-snippet-table-equiv
  (snippet-table-equiv (cons x (snippet-table-fix y))
                       (cons x y)))

Theorem: cons-snippet-table-equiv-congruence-on-y-under-snippet-table-equiv

(defthm
 cons-snippet-table-equiv-congruence-on-y-under-snippet-table-equiv
 (implies (snippet-table-equiv y y-equiv)
          (snippet-table-equiv (cons x y)
                               (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-snippet-table-fix

(defthm consp-of-snippet-table-fix
  (equal (consp (snippet-table-fix x))
         (consp x)))

Theorem: snippet-table-fix-under-iff

(defthm snippet-table-fix-under-iff
  (iff (snippet-table-fix x) (consp x)))

Theorem: snippet-table-fix-of-cons

(defthm snippet-table-fix-of-cons
  (equal (snippet-table-fix (cons a x))
         (cons (snippet-info-fix a)
               (snippet-table-fix x))))

Theorem: len-of-snippet-table-fix

(defthm len-of-snippet-table-fix
  (equal (len (snippet-table-fix x))
         (len x)))

Theorem: snippet-table-fix-of-append

(defthm snippet-table-fix-of-append
  (equal (snippet-table-fix (append std::a std::b))
         (append (snippet-table-fix std::a)
                 (snippet-table-fix std::b))))

Theorem: snippet-table-fix-of-repeat

(defthm snippet-table-fix-of-repeat
  (equal (snippet-table-fix (acl2::repeat n x))
         (acl2::repeat n (snippet-info-fix x))))

Theorem: list-equiv-refines-snippet-table-equiv

(defthm list-equiv-refines-snippet-table-equiv
  (implies (acl2::list-equiv x y)
           (snippet-table-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-snippet-table-fix

(defthm nth-of-snippet-table-fix
  (equal (nth n (snippet-table-fix x))
         (if (< (nfix n) (len x))
             (snippet-info-fix (nth n x))
           nil)))

Theorem: snippet-table-equiv-implies-snippet-table-equiv-append-1

(defthm snippet-table-equiv-implies-snippet-table-equiv-append-1
  (implies (snippet-table-equiv x fty::x-equiv)
           (snippet-table-equiv (append x y)
                                (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: snippet-table-equiv-implies-snippet-table-equiv-append-2

(defthm snippet-table-equiv-implies-snippet-table-equiv-append-2
  (implies (snippet-table-equiv y fty::y-equiv)
           (snippet-table-equiv (append x y)
                                (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: snippet-table-equiv-implies-snippet-table-equiv-nthcdr-2

(defthm snippet-table-equiv-implies-snippet-table-equiv-nthcdr-2
  (implies (snippet-table-equiv l l-equiv)
           (snippet-table-equiv (nthcdr n l)
                                (nthcdr n l-equiv)))
  :rule-classes (:congruence))

Theorem: snippet-table-equiv-implies-snippet-table-equiv-take-2

(defthm snippet-table-equiv-implies-snippet-table-equiv-take-2
  (implies (snippet-table-equiv l l-equiv)
           (snippet-table-equiv (take n l)
                                (take n l-equiv)))
  :rule-classes (:congruence))