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Regex-backref

Regex-backref->index

Get the index field from a regex-backref.

Signature
(regex-backref->index x) → fty::x.name
Arguments: x — Guard (regex-p x).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: regex-backref->index$inline

(defun regex-backref->index$inline (x)
  (declare (xargs :guard (regex-p x)))
  (declare (xargs :guard (equal (regex-kind x) :backref)))
  (let ((__function__ 'regex-backref->index))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (regex-kind x) :backref)
                      x)))
           (std::da-nth 0 (cdr x)))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: regex-backref->index$inline-of-regex-fix-x

(defthm regex-backref->index$inline-of-regex-fix-x
  (equal (regex-backref->index$inline (regex-fix x))
         (regex-backref->index$inline x)))

Theorem: regex-backref->index$inline-regex-equiv-congruence-on-x

(defthm regex-backref->index$inline-regex-equiv-congruence-on-x
  (implies (regex-equiv x x-equiv)
           (equal (regex-backref->index$inline x)
                  (regex-backref->index$inline x-equiv)))
  :rule-classes :congruence)

Theorem: regex-backref->index-when-wrong-kind

(defthm regex-backref->index-when-wrong-kind
  (implies (not (equal (regex-kind x) :backref))
           (equal (regex-backref->index x) nil)))