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Constraint-tuplelist

Constraint-tuplelist-fix

(constraint-tuplelist-fix x) is a usual ACL2::fty list fixing function.

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

In the logic, we apply constraint-tuple-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: constraint-tuplelist-fix$inline

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

Theorem: constraint-tuplelist-p-of-constraint-tuplelist-fix

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

Theorem: constraint-tuplelist-fix-when-constraint-tuplelist-p

(defthm constraint-tuplelist-fix-when-constraint-tuplelist-p
  (implies (constraint-tuplelist-p x)
           (equal (constraint-tuplelist-fix x) x)))

Function: constraint-tuplelist-equiv$inline

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

Theorem: constraint-tuplelist-equiv-is-an-equivalence

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

Theorem: constraint-tuplelist-equiv-implies-equal-constraint-tuplelist-fix-1

(defthm
 constraint-tuplelist-equiv-implies-equal-constraint-tuplelist-fix-1
 (implies (constraint-tuplelist-equiv x x-equiv)
          (equal (constraint-tuplelist-fix x)
                 (constraint-tuplelist-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: constraint-tuplelist-fix-under-constraint-tuplelist-equiv

(defthm constraint-tuplelist-fix-under-constraint-tuplelist-equiv
  (constraint-tuplelist-equiv (constraint-tuplelist-fix x)
                              x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-constraint-tuplelist-fix-1-forward-to-constraint-tuplelist-equiv

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

Theorem: equal-of-constraint-tuplelist-fix-2-forward-to-constraint-tuplelist-equiv

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

Theorem: constraint-tuplelist-equiv-of-constraint-tuplelist-fix-1-forward

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

Theorem: constraint-tuplelist-equiv-of-constraint-tuplelist-fix-2-forward

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

Theorem: car-of-constraint-tuplelist-fix-x-under-constraint-tuple-equiv

(defthm
     car-of-constraint-tuplelist-fix-x-under-constraint-tuple-equiv
  (constraint-tuple-equiv (car (constraint-tuplelist-fix x))
                          (car x)))

Theorem: car-constraint-tuplelist-equiv-congruence-on-x-under-constraint-tuple-equiv

(defthm
 car-constraint-tuplelist-equiv-congruence-on-x-under-constraint-tuple-equiv
 (implies (constraint-tuplelist-equiv x x-equiv)
          (constraint-tuple-equiv (car x)
                                  (car x-equiv)))
 :rule-classes :congruence)

Theorem: cdr-of-constraint-tuplelist-fix-x-under-constraint-tuplelist-equiv

(defthm
 cdr-of-constraint-tuplelist-fix-x-under-constraint-tuplelist-equiv
 (constraint-tuplelist-equiv (cdr (constraint-tuplelist-fix x))
                             (cdr x)))

Theorem: cdr-constraint-tuplelist-equiv-congruence-on-x-under-constraint-tuplelist-equiv

(defthm
 cdr-constraint-tuplelist-equiv-congruence-on-x-under-constraint-tuplelist-equiv
 (implies (constraint-tuplelist-equiv x x-equiv)
          (constraint-tuplelist-equiv (cdr x)
                                      (cdr x-equiv)))
 :rule-classes :congruence)

Theorem: cons-of-constraint-tuple-fix-x-under-constraint-tuplelist-equiv

(defthm
    cons-of-constraint-tuple-fix-x-under-constraint-tuplelist-equiv
  (constraint-tuplelist-equiv (cons (constraint-tuple-fix x) y)
                              (cons x y)))

Theorem: cons-constraint-tuple-equiv-congruence-on-x-under-constraint-tuplelist-equiv

(defthm
 cons-constraint-tuple-equiv-congruence-on-x-under-constraint-tuplelist-equiv
 (implies (constraint-tuple-equiv x x-equiv)
          (constraint-tuplelist-equiv (cons x y)
                                      (cons x-equiv y)))
 :rule-classes :congruence)

Theorem: cons-of-constraint-tuplelist-fix-y-under-constraint-tuplelist-equiv

(defthm
 cons-of-constraint-tuplelist-fix-y-under-constraint-tuplelist-equiv
 (constraint-tuplelist-equiv (cons x (constraint-tuplelist-fix y))
                             (cons x y)))

Theorem: cons-constraint-tuplelist-equiv-congruence-on-y-under-constraint-tuplelist-equiv

(defthm
 cons-constraint-tuplelist-equiv-congruence-on-y-under-constraint-tuplelist-equiv
 (implies (constraint-tuplelist-equiv y y-equiv)
          (constraint-tuplelist-equiv (cons x y)
                                      (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-constraint-tuplelist-fix

(defthm consp-of-constraint-tuplelist-fix
  (equal (consp (constraint-tuplelist-fix x))
         (consp x)))

Theorem: constraint-tuplelist-fix-under-iff

(defthm constraint-tuplelist-fix-under-iff
  (iff (constraint-tuplelist-fix x)
       (consp x)))

Theorem: constraint-tuplelist-fix-of-cons

(defthm constraint-tuplelist-fix-of-cons
  (equal (constraint-tuplelist-fix (cons a x))
         (cons (constraint-tuple-fix a)
               (constraint-tuplelist-fix x))))

Theorem: len-of-constraint-tuplelist-fix

(defthm len-of-constraint-tuplelist-fix
  (equal (len (constraint-tuplelist-fix x))
         (len x)))

Theorem: constraint-tuplelist-fix-of-append

(defthm constraint-tuplelist-fix-of-append
  (equal (constraint-tuplelist-fix (append std::a std::b))
         (append (constraint-tuplelist-fix std::a)
                 (constraint-tuplelist-fix std::b))))

Theorem: constraint-tuplelist-fix-of-repeat

(defthm constraint-tuplelist-fix-of-repeat
  (equal (constraint-tuplelist-fix (acl2::repeat n x))
         (acl2::repeat n (constraint-tuple-fix x))))

Theorem: list-equiv-refines-constraint-tuplelist-equiv

(defthm list-equiv-refines-constraint-tuplelist-equiv
  (implies (acl2::list-equiv x y)
           (constraint-tuplelist-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-constraint-tuplelist-fix

(defthm nth-of-constraint-tuplelist-fix
  (equal (nth n (constraint-tuplelist-fix x))
         (if (< (nfix n) (len x))
             (constraint-tuple-fix (nth n x))
           nil)))

Theorem: constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-append-1

(defthm
 constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-append-1
 (implies (constraint-tuplelist-equiv x fty::x-equiv)
          (constraint-tuplelist-equiv (append x y)
                                      (append fty::x-equiv y)))
 :rule-classes (:congruence))

Theorem: constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-append-2

(defthm
 constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-append-2
 (implies (constraint-tuplelist-equiv y fty::y-equiv)
          (constraint-tuplelist-equiv (append x y)
                                      (append x fty::y-equiv)))
 :rule-classes (:congruence))

Theorem: constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-nthcdr-2

(defthm
 constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-nthcdr-2
 (implies (constraint-tuplelist-equiv l l-equiv)
          (constraint-tuplelist-equiv (nthcdr n l)
                                      (nthcdr n l-equiv)))
 :rule-classes (:congruence))

Theorem: constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-take-2

(defthm
 constraint-tuplelist-equiv-implies-constraint-tuplelist-equiv-take-2
 (implies (constraint-tuplelist-equiv l l-equiv)
          (constraint-tuplelist-equiv (take n l)
                                      (take n l-equiv)))
 :rule-classes (:congruence))