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Dimb-table

Dimb-table-fix

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

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

In the logic, we apply dimb-scope-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: dimb-table-fix$inline

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

Theorem: dimb-tablep-of-dimb-table-fix

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

Theorem: dimb-table-fix-when-dimb-tablep

(defthm dimb-table-fix-when-dimb-tablep
  (implies (dimb-tablep x)
           (equal (dimb-table-fix x) x)))

Function: dimb-table-equiv$inline

(defun dimb-table-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (dimb-tablep acl2::x)
                              (dimb-tablep acl2::y))))
  (equal (dimb-table-fix acl2::x)
         (dimb-table-fix acl2::y)))

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

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

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

(defthm dimb-table-equiv-implies-equal-dimb-table-fix-1
  (implies (dimb-table-equiv acl2::x x-equiv)
           (equal (dimb-table-fix acl2::x)
                  (dimb-table-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: dimb-table-fix-under-dimb-table-equiv

(defthm dimb-table-fix-under-dimb-table-equiv
  (dimb-table-equiv (dimb-table-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-dimb-table-fix-1-forward-to-dimb-table-equiv
  (implies (equal (dimb-table-fix acl2::x) acl2::y)
           (dimb-table-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-dimb-table-fix-2-forward-to-dimb-table-equiv
  (implies (equal acl2::x (dimb-table-fix acl2::y))
           (dimb-table-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm dimb-table-equiv-of-dimb-table-fix-1-forward
  (implies (dimb-table-equiv (dimb-table-fix acl2::x)
                             acl2::y)
           (dimb-table-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm dimb-table-equiv-of-dimb-table-fix-2-forward
  (implies (dimb-table-equiv acl2::x (dimb-table-fix acl2::y))
           (dimb-table-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: car-of-dimb-table-fix-x-under-dimb-scope-equiv

(defthm car-of-dimb-table-fix-x-under-dimb-scope-equiv
  (dimb-scope-equiv (car (dimb-table-fix acl2::x))
                    (car acl2::x)))

Theorem: car-dimb-table-equiv-congruence-on-x-under-dimb-scope-equiv

(defthm car-dimb-table-equiv-congruence-on-x-under-dimb-scope-equiv
  (implies (dimb-table-equiv acl2::x x-equiv)
           (dimb-scope-equiv (car acl2::x)
                             (car x-equiv)))
  :rule-classes :congruence)

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

(defthm cdr-of-dimb-table-fix-x-under-dimb-table-equiv
  (dimb-table-equiv (cdr (dimb-table-fix acl2::x))
                    (cdr acl2::x)))

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

(defthm cdr-dimb-table-equiv-congruence-on-x-under-dimb-table-equiv
  (implies (dimb-table-equiv acl2::x x-equiv)
           (dimb-table-equiv (cdr acl2::x)
                             (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-dimb-scope-fix-x-under-dimb-table-equiv

(defthm cons-of-dimb-scope-fix-x-under-dimb-table-equiv
  (dimb-table-equiv (cons (dimb-scope-fix acl2::x) acl2::y)
                    (cons acl2::x acl2::y)))

Theorem: cons-dimb-scope-equiv-congruence-on-x-under-dimb-table-equiv

(defthm cons-dimb-scope-equiv-congruence-on-x-under-dimb-table-equiv
  (implies (dimb-scope-equiv acl2::x x-equiv)
           (dimb-table-equiv (cons acl2::x acl2::y)
                             (cons x-equiv acl2::y)))
  :rule-classes :congruence)

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

(defthm cons-of-dimb-table-fix-y-under-dimb-table-equiv
  (dimb-table-equiv (cons acl2::x (dimb-table-fix acl2::y))
                    (cons acl2::x acl2::y)))

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

(defthm cons-dimb-table-equiv-congruence-on-y-under-dimb-table-equiv
  (implies (dimb-table-equiv acl2::y y-equiv)
           (dimb-table-equiv (cons acl2::x acl2::y)
                             (cons acl2::x y-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-dimb-table-fix

(defthm consp-of-dimb-table-fix
  (equal (consp (dimb-table-fix acl2::x))
         (consp acl2::x)))

Theorem: dimb-table-fix-under-iff

(defthm dimb-table-fix-under-iff
  (iff (dimb-table-fix acl2::x)
       (consp acl2::x)))

Theorem: dimb-table-fix-of-cons

(defthm dimb-table-fix-of-cons
  (equal (dimb-table-fix (cons a x))
         (cons (dimb-scope-fix a)
               (dimb-table-fix x))))

Theorem: len-of-dimb-table-fix

(defthm len-of-dimb-table-fix
  (equal (len (dimb-table-fix acl2::x))
         (len acl2::x)))

Theorem: dimb-table-fix-of-append

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

Theorem: dimb-table-fix-of-repeat

(defthm dimb-table-fix-of-repeat
  (equal (dimb-table-fix (repeat acl2::n acl2::x))
         (repeat acl2::n (dimb-scope-fix acl2::x))))

Theorem: list-equiv-refines-dimb-table-equiv

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

Theorem: nth-of-dimb-table-fix

(defthm nth-of-dimb-table-fix
  (equal (nth acl2::n (dimb-table-fix acl2::x))
         (if (< (nfix acl2::n) (len acl2::x))
             (dimb-scope-fix (nth acl2::n acl2::x))
           nil)))

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

(defthm dimb-table-equiv-implies-dimb-table-equiv-append-1
  (implies (dimb-table-equiv acl2::x fty::x-equiv)
           (dimb-table-equiv (append acl2::x acl2::y)
                             (append fty::x-equiv acl2::y)))
  :rule-classes (:congruence))

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

(defthm dimb-table-equiv-implies-dimb-table-equiv-append-2
  (implies (dimb-table-equiv acl2::y fty::y-equiv)
           (dimb-table-equiv (append acl2::x acl2::y)
                             (append acl2::x fty::y-equiv)))
  :rule-classes (:congruence))

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

(defthm dimb-table-equiv-implies-dimb-table-equiv-nthcdr-2
  (implies (dimb-table-equiv acl2::l l-equiv)
           (dimb-table-equiv (nthcdr acl2::n acl2::l)
                             (nthcdr acl2::n l-equiv)))
  :rule-classes (:congruence))

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

(defthm dimb-table-equiv-implies-dimb-table-equiv-take-2
  (implies (dimb-table-equiv acl2::l l-equiv)
           (dimb-table-equiv (take acl2::n acl2::l)
                             (take acl2::n l-equiv)))
  :rule-classes (:congruence))