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Name+value

Name+value-fix

Fixing function for name+value structures.

Signature
(name+value-fix x) → new-x
Arguments: x — Guard (name+value-p x).
Returns: new-x — Type (name+value-p new-x).

Definitions and Theorems

Function: name+value-fix$inline

(defun name+value-fix$inline (x)
  (declare (xargs :guard (name+value-p x)))
  (let ((__function__ 'name+value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (identifier-fix (cdr (std::da-nth 0 (cdr x)))))
              (value (value-fix (cdr (std::da-nth 1 (cdr x))))))
           (cons :name+value (list (cons 'name name)
                                   (cons 'value value))))
         :exec x)))

Theorem: name+value-p-of-name+value-fix

(defthm name+value-p-of-name+value-fix
  (b* ((new-x (name+value-fix$inline x)))
    (name+value-p new-x))
  :rule-classes :rewrite)

Theorem: name+value-fix-when-name+value-p

(defthm name+value-fix-when-name+value-p
  (implies (name+value-p x)
           (equal (name+value-fix x) x)))

Function: name+value-equiv$inline

(defun name+value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (name+value-p acl2::x)
                              (name+value-p acl2::y))))
  (equal (name+value-fix acl2::x)
         (name+value-fix acl2::y)))

Theorem: name+value-equiv-is-an-equivalence

(defthm name+value-equiv-is-an-equivalence
  (and (booleanp (name+value-equiv x y))
       (name+value-equiv x x)
       (implies (name+value-equiv x y)
                (name+value-equiv y x))
       (implies (and (name+value-equiv x y)
                     (name+value-equiv y z))
                (name+value-equiv x z)))
  :rule-classes (:equivalence))

Theorem: name+value-equiv-implies-equal-name+value-fix-1

(defthm name+value-equiv-implies-equal-name+value-fix-1
  (implies (name+value-equiv acl2::x x-equiv)
           (equal (name+value-fix acl2::x)
                  (name+value-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: name+value-fix-under-name+value-equiv

(defthm name+value-fix-under-name+value-equiv
  (name+value-equiv (name+value-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-name+value-fix-1-forward-to-name+value-equiv

(defthm equal-of-name+value-fix-1-forward-to-name+value-equiv
  (implies (equal (name+value-fix acl2::x) acl2::y)
           (name+value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-name+value-fix-2-forward-to-name+value-equiv

(defthm equal-of-name+value-fix-2-forward-to-name+value-equiv
  (implies (equal acl2::x (name+value-fix acl2::y))
           (name+value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: name+value-equiv-of-name+value-fix-1-forward

(defthm name+value-equiv-of-name+value-fix-1-forward
  (implies (name+value-equiv (name+value-fix acl2::x)
                             acl2::y)
           (name+value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: name+value-equiv-of-name+value-fix-2-forward

(defthm name+value-equiv-of-name+value-fix-2-forward
  (implies (name+value-equiv acl2::x (name+value-fix acl2::y))
           (name+value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)