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• Acre-internals

Matches-add-backref

Signature

(matches-add-backref name start-index matches) → new-matches

Arguments

start-index — Guard (natp start-index).

matches — Guard (matchstatelist-p matches).

Returns

new-matches — Type (matchstatelist-p new-matches).

Definitions and Theorems

Function: matches-add-backref

(defun matches-add-backref (name start-index matches)
 (declare (xargs :guard (and (natp start-index)
                             (matchstatelist-p matches))))
 (declare
    (xargs :guard (matchstatelist-indices-gte start-index matches)))
 (let ((__function__ 'matches-add-backref))
   (declare (ignorable __function__))
   (if (atom matches)
       nil
     (cons (match-add-backref name start-index (car matches))
           (matches-add-backref name start-index (cdr matches))))))

Theorem: matchstatelist-p-of-matches-add-backref

(defthm matchstatelist-p-of-matches-add-backref
  (b* ((new-matches (matches-add-backref name start-index matches)))
    (matchstatelist-p new-matches))
  :rule-classes :rewrite)

Theorem: matches-add-backref-preserves-matchstatelist-indices-gte

(defthm matches-add-backref-preserves-matchstatelist-indices-gte
 (b* ((?new-matches (matches-add-backref name start-index matches)))
   (implies (matchstatelist-indices-gte n matches)
            (matchstatelist-indices-gte n new-matches))))

Theorem: consp-of-matches-add-backref

(defthm consp-of-matches-add-backref
 (b* ((?new-matches (matches-add-backref name start-index matches)))
   (equal (consp new-matches)
          (consp matches))))

Theorem: matchstatelist-indices-gte-of-add-backref

(defthm matchstatelist-indices-gte-of-add-backref
 (iff
   (matchstatelist-indices-gte n (matches-add-backref name start x))
   (matchstatelist-indices-gte n x)))

Theorem: matchstatelist-indices-lte-of-add-backref

(defthm matchstatelist-indices-lte-of-add-backref
 (iff
   (matchstatelist-indices-lte n (matches-add-backref name start x))
   (matchstatelist-indices-lte n x)))

Theorem: matches-add-backref-of-nfix-start-index

(defthm matches-add-backref-of-nfix-start-index
  (equal (matches-add-backref name (nfix start-index)
                              matches)
         (matches-add-backref name start-index matches)))

Theorem: matches-add-backref-nat-equiv-congruence-on-start-index

(defthm matches-add-backref-nat-equiv-congruence-on-start-index
  (implies
       (acl2::nat-equiv start-index start-index-equiv)
       (equal (matches-add-backref name start-index matches)
              (matches-add-backref name start-index-equiv matches)))
  :rule-classes :congruence)

Theorem: matches-add-backref-of-matchstatelist-fix-matches

(defthm matches-add-backref-of-matchstatelist-fix-matches
  (equal (matches-add-backref name start-index
                              (matchstatelist-fix matches))
         (matches-add-backref name start-index matches)))

Theorem: matches-add-backref-matchstatelist-equiv-congruence-on-matches

(defthm
     matches-add-backref-matchstatelist-equiv-congruence-on-matches
  (implies
       (matchstatelist-equiv matches matches-equiv)
       (equal (matches-add-backref name start-index matches)
              (matches-add-backref name start-index matches-equiv)))
  :rule-classes :congruence)