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Constraint-sig-set

Constraint-sig-set-fix

(constraint-sig-set-fix x) is an ACL2::fty alist fixing function that follows the drop-keys strategy.

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

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: constraint-sig-set-fix$inline

(defun constraint-sig-set-fix$inline (x)
  (declare (xargs :guard (constraint-sig-set-p x)))
  (let ((__function__ 'constraint-sig-set-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (let ((rest (constraint-sig-set-fix (cdr x))))
             (if (and (consp (car x))
                      (fgl-objectlist-p (caar x)))
                 (let ((fty::first-key (caar x))
                       (fty::first-val (cdar x)))
                   (cons (cons fty::first-key fty::first-val)
                         rest))
               rest)))
         :exec x)))

Theorem: constraint-sig-set-p-of-constraint-sig-set-fix

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

Theorem: constraint-sig-set-fix-when-constraint-sig-set-p

(defthm constraint-sig-set-fix-when-constraint-sig-set-p
  (implies (constraint-sig-set-p x)
           (equal (constraint-sig-set-fix x) x)))

Function: constraint-sig-set-equiv$inline

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

Theorem: constraint-sig-set-equiv-is-an-equivalence

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

Theorem: constraint-sig-set-equiv-implies-equal-constraint-sig-set-fix-1

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

Theorem: constraint-sig-set-fix-under-constraint-sig-set-equiv

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

Theorem: equal-of-constraint-sig-set-fix-1-forward-to-constraint-sig-set-equiv

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

Theorem: equal-of-constraint-sig-set-fix-2-forward-to-constraint-sig-set-equiv

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

Theorem: constraint-sig-set-equiv-of-constraint-sig-set-fix-1-forward

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

Theorem: constraint-sig-set-equiv-of-constraint-sig-set-fix-2-forward

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

Theorem: cons-of-constraint-sig-set-fix-y-under-constraint-sig-set-equiv

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

Theorem: cons-constraint-sig-set-equiv-congruence-on-y-under-constraint-sig-set-equiv

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

Theorem: constraint-sig-set-fix-of-acons

(defthm constraint-sig-set-fix-of-acons
  (equal (constraint-sig-set-fix (cons (cons a b) x))
         (let ((rest (constraint-sig-set-fix x)))
           (if (and (fgl-objectlist-p a))
               (let ((fty::first-key a) (fty::first-val b))
                 (cons (cons fty::first-key fty::first-val)
                       rest))
             rest))))

Theorem: hons-assoc-equal-of-constraint-sig-set-fix

(defthm hons-assoc-equal-of-constraint-sig-set-fix
  (equal (hons-assoc-equal k (constraint-sig-set-fix x))
         (let ((fty::pair (hons-assoc-equal k x)))
           (and (fgl-objectlist-p k)
                fty::pair (cons k (cdr fty::pair))))))

Theorem: constraint-sig-set-fix-of-append

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

Theorem: consp-car-of-constraint-sig-set-fix

(defthm consp-car-of-constraint-sig-set-fix
  (equal (consp (car (constraint-sig-set-fix x)))
         (consp (constraint-sig-set-fix x))))