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• Acre-internals

Matchstatelist-min-index

Signature

(matchstatelist-min-index sts) → index

Arguments

sts — Guard (matchstatelist-p sts).

Returns

index — Type (natp index).

Definitions and Theorems

Function: matchstatelist-min-index

(defun matchstatelist-min-index (sts)
  (declare (xargs :guard (matchstatelist-p sts)))
  (declare (xargs :guard (consp sts)))
  (let ((__function__ 'matchstatelist-min-index))
    (declare (ignorable __function__))
    (if (atom (cdr sts))
        (matchstate->index (car sts))
      (min (matchstate->index (car sts))
           (matchstatelist-min-index (cdr sts))))))

Theorem: natp-of-matchstatelist-min-index

(defthm natp-of-matchstatelist-min-index
  (b* ((index (matchstatelist-min-index sts)))
    (natp index))
  :rule-classes :type-prescription)

Theorem: matchstatelist-min-index-of-append

(defthm matchstatelist-min-index-of-append
  (implies (or (consp a) (consp b))
           (equal (matchstatelist-min-index (append a b))
                  (if (consp a)
                      (if (consp b)
                          (min (matchstatelist-min-index a)
                               (matchstatelist-min-index b))
                        (matchstatelist-min-index a))
                    (matchstatelist-min-index b)))))

Theorem: matchstatelist-min-index-of-rev

(defthm matchstatelist-min-index-of-rev
  (equal (matchstatelist-min-index (rev x))
         (matchstatelist-min-index x)))

Theorem: matchstatelist-min-index-of-matches-add-backref

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

Theorem: matchstatelist-indices-gte-by-matchstatelist-min-index

(defthm matchstatelist-indices-gte-by-matchstatelist-min-index
  (implies (<= (nfix idx)
               (matchstatelist-min-index x))
           (matchstatelist-indices-gte idx x)))

Theorem: matchstatelist-min-index-of-matchstatelist-fix-sts

(defthm matchstatelist-min-index-of-matchstatelist-fix-sts
  (equal (matchstatelist-min-index (matchstatelist-fix sts))
         (matchstatelist-min-index sts)))

Theorem: matchstatelist-min-index-matchstatelist-equiv-congruence-on-sts

(defthm
    matchstatelist-min-index-matchstatelist-equiv-congruence-on-sts
  (implies (matchstatelist-equiv sts sts-equiv)
           (equal (matchstatelist-min-index sts)
                  (matchstatelist-min-index sts-equiv)))
  :rule-classes :congruence)