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Matchresult

Matchresult->backrefs

Get the backrefs field from a matchresult.

Signature
(matchresult->backrefs x) → backrefs
Arguments: x — Guard (matchresult-p x).
Returns: backrefs — Type (backref-alist-p backrefs).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: matchresult->backrefs$inline

(defun matchresult->backrefs$inline (x)
  (declare (xargs :guard (matchresult-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'matchresult->backrefs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (backref-alist-fix (std::da-nth 3 x)))
         :exec (std::da-nth 3 x))))

Theorem: backref-alist-p-of-matchresult->backrefs

(defthm backref-alist-p-of-matchresult->backrefs
  (b* ((backrefs (matchresult->backrefs$inline x)))
    (backref-alist-p backrefs))
  :rule-classes :rewrite)

Theorem: matchresult->backrefs$inline-of-matchresult-fix-x

(defthm matchresult->backrefs$inline-of-matchresult-fix-x
  (equal (matchresult->backrefs$inline (matchresult-fix x))
         (matchresult->backrefs$inline x)))

Theorem: matchresult->backrefs$inline-matchresult-equiv-congruence-on-x

(defthm
     matchresult->backrefs$inline-matchresult-equiv-congruence-on-x
  (implies (matchresult-equiv x x-equiv)
           (equal (matchresult->backrefs$inline x)
                  (matchresult->backrefs$inline x-equiv)))
  :rule-classes :congruence)