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Constraint-db

Constraint-db-fix

Fixing function for constraint-db structures.

Signature
(constraint-db-fix x) → new-x
Arguments: x — Guard (constraint-db-p x).
Returns: new-x — Type (constraint-db-p new-x).

Definitions and Theorems

Function: constraint-db-fix$inline

(defun constraint-db-fix$inline (x)
 (declare (xargs :guard (constraint-db-p x)))
 (let ((__function__ 'constraint-db-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((tab (constraint-table-fix (cdr (std::da-nth 0 x))))
     (complete
          (constraint-completed-table-fix (cdr (std::da-nth 1 x)))))
    (list (cons 'tab tab)
          (cons 'complete complete)))
   :exec x)))

Theorem: constraint-db-p-of-constraint-db-fix

(defthm constraint-db-p-of-constraint-db-fix
  (b* ((new-x (constraint-db-fix$inline x)))
    (constraint-db-p new-x))
  :rule-classes :rewrite)

Theorem: constraint-db-fix-when-constraint-db-p

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

Function: constraint-db-equiv$inline

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

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

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

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

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

Theorem: constraint-db-fix-under-constraint-db-equiv

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

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

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

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

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

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

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

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

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