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• Acre-internals

Matchstatelist-all-have-backref

Signature

(matchstatelist-all-have-backref name x) → *

Arguments

x — Guard (matchstatelist-p x).

Definitions and Theorems

Function: matchstatelist-all-have-backref

(defun matchstatelist-all-have-backref (name x)
  (declare (xargs :guard (matchstatelist-p x)))
  (let ((__function__ 'matchstatelist-all-have-backref))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (assoc-equal name (matchstate->backrefs (car x)))
           (matchstatelist-all-have-backref name (cdr x))))))

Theorem: matchstatelist-all-have-backref-of-remove

(defthm matchstatelist-all-have-backref-of-remove
 (implies
     (assoc-equal name (matchstate->backrefs x1))
     (iff (matchstatelist-all-have-backref name (remove-equal x1 x))
          (matchstatelist-all-have-backref name x))))

Theorem: matchstatelist-all-have-backref-of-undup

(defthm matchstatelist-all-have-backref-of-undup
  (iff (matchstatelist-all-have-backref name (undup x))
       (matchstatelist-all-have-backref name x)))

Theorem: matchstatelist-all-have-backref-of-nil

(defthm matchstatelist-all-have-backref-of-nil
  (matchstatelist-all-have-backref name nil))

Theorem: matchstatelist-all-have-backref-of-append

(defthm matchstatelist-all-have-backref-of-append
  (iff (matchstatelist-all-have-backref name (append x y))
       (and (matchstatelist-all-have-backref name x)
            (matchstatelist-all-have-backref name y))))

Theorem: matchstatelist-all-have-backref-of-set-difference

(defthm matchstatelist-all-have-backref-of-set-difference
  (implies (matchstatelist-all-have-backref name x)
           (matchstatelist-all-have-backref
                name (set-difference-equal x y))))

Theorem: matchstatelist-all-have-backref-of-matches-remove-zero-length

(defthm
      matchstatelist-all-have-backref-of-matches-remove-zero-length
  (implies (matchstatelist-all-have-backref name x)
           (matchstatelist-all-have-backref
                name (matches-remove-zero-length n x))))

Theorem: matchstatelist-all-have-backref-of-cons

(defthm matchstatelist-all-have-backref-of-cons
  (equal (matchstatelist-all-have-backref name (cons a b))
         (and (assoc-equal name (matchstate->backrefs a))
              (matchstatelist-all-have-backref name b))))

Theorem: matchstatelist-all-have-backref-of-rev

(defthm matchstatelist-all-have-backref-of-rev
  (iff (matchstatelist-all-have-backref name (rev x))
       (matchstatelist-all-have-backref name x)))

Theorem: matchstatelist-all-have-backref-of-matches-add-backref

(defthm matchstatelist-all-have-backref-of-matches-add-backref
  (implies (matchstatelist-all-have-backref name x)
           (matchstatelist-all-have-backref
                name
                (matches-add-backref name1 start-idx x))))

Theorem: matchstatelist-all-have-backref-of-matches-add-backref-same

(defthm matchstatelist-all-have-backref-of-matches-add-backref-same
  (matchstatelist-all-have-backref
       name
       (matches-add-backref name start-idx x)))

Theorem: matchstatelist-all-have-backref-of-matchstatelist-fix-x

(defthm matchstatelist-all-have-backref-of-matchstatelist-fix-x
  (equal
       (matchstatelist-all-have-backref name (matchstatelist-fix x))
       (matchstatelist-all-have-backref name x)))

Theorem: matchstatelist-all-have-backref-matchstatelist-equiv-congruence-on-x

(defthm
 matchstatelist-all-have-backref-matchstatelist-equiv-congruence-on-x
 (implies (matchstatelist-equiv x x-equiv)
          (equal (matchstatelist-all-have-backref name x)
                 (matchstatelist-all-have-backref name x-equiv)))
 :rule-classes :congruence)