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Matchstate

Matchstate->backrefs

Get the backrefs field from a matchstate.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: matchstate->backrefs$inline

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

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

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

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

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

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

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