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Increment-elim

Vl-finallist-increwrite

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

Definitions and Theorems

Function: vl-finallist-increwrite

(defun vl-finallist-increwrite (x)
  (declare (xargs :guard (vl-finallist-p x)))
  (let ((__function__ 'vl-finallist-increwrite))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (b* nil x))
         (car (vl-final-increwrite (car x)))
         (cdr (vl-finallist-increwrite (cdr x))))
      (cons-with-hint car cdr x))))

Theorem: vl-finallist-p-of-vl-finallist-increwrite

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

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

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

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

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