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Increment-elim

Vl-initial-increwrite

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

Definitions and Theorems

Function: vl-initial-increwrite

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

Theorem: vl-initial-p-of-vl-initial-increwrite

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

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

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

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

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