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• Committee

Committee-fix

Fixing function for committee structures.

Signature

(committee-fix x) → new-x

Arguments

x — Guard (committeep x).

Returns

new-x — Type (committeep new-x).

Definitions and Theorems

Function: committee-fix$inline

(defun committee-fix$inline (x)
  (declare (xargs :guard (committeep x)))
  (let ((__function__ 'committee-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((addresses (address-set-fix (cdr (std::da-nth 0 x)))))
           (let ((addresses (if (emptyp addresses)
                                (insert (address nil) nil)
                              addresses)))
             (list (cons 'addresses addresses))))
         :exec x)))

Theorem: committeep-of-committee-fix

(defthm committeep-of-committee-fix
  (b* ((new-x (committee-fix$inline x)))
    (committeep new-x))
  :rule-classes :rewrite)

Theorem: committee-fix-when-committeep

(defthm committee-fix-when-committeep
  (implies (committeep x)
           (equal (committee-fix x) x)))

Function: committee-equiv$inline

(defun committee-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (committeep acl2::x)
                              (committeep acl2::y))))
  (equal (committee-fix acl2::x)
         (committee-fix acl2::y)))

Theorem: committee-equiv-is-an-equivalence

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

Theorem: committee-equiv-implies-equal-committee-fix-1

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

Theorem: committee-fix-under-committee-equiv

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

Theorem: equal-of-committee-fix-1-forward-to-committee-equiv

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

Theorem: equal-of-committee-fix-2-forward-to-committee-equiv

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

Theorem: committee-equiv-of-committee-fix-1-forward

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

Theorem: committee-equiv-of-committee-fix-2-forward

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