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Increment-elim

Vl-final-increwrite

Signature
(vl-final-increwrite x) → new-x
Arguments: x — Guard (vl-final-p x).
Returns: new-x — Type (vl-final-p new-x).

Definitions and Theorems

Function: vl-final-increwrite

(defun vl-final-increwrite (x)
  (declare (xargs :guard (vl-final-p x)))
  (let ((__function__ 'vl-final-increwrite))
    (declare (ignorable __function__))
    (b* (((vl-final x) (vl-final-fix x)))
      (b* ((stmt (vl-stmt-increwrite-flat x.stmt)))
        (change-vl-final x :stmt stmt)))))

Theorem: vl-final-p-of-vl-final-increwrite

(defthm vl-final-p-of-vl-final-increwrite
  (b* ((new-x (vl-final-increwrite x)))
    (vl-final-p new-x))
  :rule-classes :rewrite)

Theorem: vl-final-increwrite-of-vl-final-fix-x

(defthm vl-final-increwrite-of-vl-final-fix-x
  (equal (vl-final-increwrite (vl-final-fix x))
         (vl-final-increwrite x)))

Theorem: vl-final-increwrite-vl-final-equiv-congruence-on-x

(defthm vl-final-increwrite-vl-final-equiv-congruence-on-x
  (implies (vl-final-equiv x x-equiv)
           (equal (vl-final-increwrite x)
                  (vl-final-increwrite x-equiv)))
  :rule-classes :congruence)