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Constraint-db

Constraint-db->complete

Get the complete field from a constraint-db.

Signature
(constraint-db->complete x) → complete
Arguments: x — Guard (constraint-db-p x).
Returns: complete — Type (constraint-completed-table-p complete).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: constraint-db->complete$inline

(defun constraint-db->complete$inline (x)
  (declare (xargs :guard (constraint-db-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'constraint-db->complete))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (constraint-completed-table-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: constraint-completed-table-p-of-constraint-db->complete

(defthm constraint-completed-table-p-of-constraint-db->complete
  (b* ((complete (constraint-db->complete$inline x)))
    (constraint-completed-table-p complete))
  :rule-classes :rewrite)

Theorem: constraint-db->complete$inline-of-constraint-db-fix-x

(defthm constraint-db->complete$inline-of-constraint-db-fix-x
  (equal (constraint-db->complete$inline (constraint-db-fix x))
         (constraint-db->complete$inline x)))

Theorem: constraint-db->complete$inline-constraint-db-equiv-congruence-on-x

(defthm
 constraint-db->complete$inline-constraint-db-equiv-congruence-on-x
 (implies (constraint-db-equiv x x-equiv)
          (equal (constraint-db->complete$inline x)
                 (constraint-db->complete$inline x-equiv)))
 :rule-classes :congruence)