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Backref

Backref->loc

Get the loc field from a backref.

Signature
(backref->loc x) → loc
Arguments: x — Guard (backref-p x).
Returns: loc — Type (natp loc).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: backref->loc$inline

(defun backref->loc$inline (x)
  (declare (xargs :guard (backref-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'backref->loc))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (std::prod-car x)))
         :exec (std::prod-car x))))

Theorem: natp-of-backref->loc

(defthm natp-of-backref->loc
  (b* ((loc (backref->loc$inline x)))
    (natp loc))
  :rule-classes :type-prescription)

Theorem: backref->loc$inline-of-backref-fix-x

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

Theorem: backref->loc$inline-backref-equiv-congruence-on-x

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