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• Abstract-syntax-operations

Constraint-list-constrels

Set of relation constraints in a list of constraints.

Signature

(constraint-list-constrels constrs) → crels

Arguments

constrs — Guard (constraint-listp constrs).

Returns

crels — Type (constrel-setp crels).

In essence, we select the relation constraints and we turn them into the constrel form.

Definitions and Theorems

Function: constraint-list-constrels

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

Theorem: constrel-setp-of-constraint-list-constrels

(defthm constrel-setp-of-constraint-list-constrels
  (b* ((crels (constraint-list-constrels constrs)))
    (constrel-setp crels))
  :rule-classes :rewrite)

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

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

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

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