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Increment-elim

Vl-classlist-increwrite

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

Definitions and Theorems

Function: vl-classlist-increwrite

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

Theorem: vl-classlist-p-of-vl-classlist-increwrite

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

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

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

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

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