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• Abstract-syntax-operations

Constraint-list-rels

Set of (names of) relations in a list of constraints.

Signature

(constraint-list-rels constrs) → rels

Arguments

constrs — Guard (constraint-listp constrs).

Returns

rels — Type (string-setp rels).

We collect all the relation names.

Definitions and Theorems

Function: constraint-list-rels

(defun constraint-list-rels (constrs)
  (declare (xargs :guard (constraint-listp constrs)))
  (let ((__function__ 'constraint-list-rels))
    (declare (ignorable __function__))
    (cond ((endp constrs) nil)
          (t (union (constraint-rels (car constrs))
                    (constraint-list-rels (cdr constrs)))))))

Theorem: string-setp-of-constraint-list-rels

(defthm string-setp-of-constraint-list-rels
  (b* ((rels (constraint-list-rels constrs)))
    (string-setp rels))
  :rule-classes :rewrite)

Theorem: constraint-list-rels-of-constraint-list-fix-constrs

(defthm constraint-list-rels-of-constraint-list-fix-constrs
  (equal (constraint-list-rels (constraint-list-fix constrs))
         (constraint-list-rels constrs)))

Theorem: constraint-list-rels-constraint-list-equiv-congruence-on-constrs

(defthm
   constraint-list-rels-constraint-list-equiv-congruence-on-constrs
  (implies (constraint-list-equiv constrs constrs-equiv)
           (equal (constraint-list-rels constrs)
                  (constraint-list-rels constrs-equiv)))
  :rule-classes :congruence)