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Svstmt-while

Svstmt-while->next

Get the next field from a svstmt-while.

Signature
(svstmt-while->next x) → next
Arguments: x — Guard (svstmt-p x).
Returns: next — Type (svstmtlist-p next).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: svstmt-while->next$inline

(defun svstmt-while->next$inline (x)
  (declare (xargs :guard (svstmt-p x)))
  (declare (xargs :guard (equal (svstmt-kind x) :while)))
  (let ((__function__ 'svstmt-while->next))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (svstmt-kind x) :while) x)))
           (svstmtlist-fix (std::da-nth 2 (cdr x))))
         :exec (std::da-nth 2 (cdr x)))))

Theorem: svstmtlist-p-of-svstmt-while->next

(defthm svstmtlist-p-of-svstmt-while->next
  (b* ((next (svstmt-while->next$inline x)))
    (svstmtlist-p next))
  :rule-classes :rewrite)

Theorem: svstmt-while->next$inline-of-svstmt-fix-x

(defthm svstmt-while->next$inline-of-svstmt-fix-x
  (equal (svstmt-while->next$inline (svstmt-fix x))
         (svstmt-while->next$inline x)))

Theorem: svstmt-while->next$inline-svstmt-equiv-congruence-on-x

(defthm svstmt-while->next$inline-svstmt-equiv-congruence-on-x
  (implies (svstmt-equiv x x-equiv)
           (equal (svstmt-while->next$inline x)
                  (svstmt-while->next$inline x-equiv)))
  :rule-classes :congruence)

Theorem: svstmt-while->next-when-wrong-kind

(defthm svstmt-while->next-when-wrong-kind
  (implies (not (equal (svstmt-kind x) :while))
           (equal (svstmt-while->next x)
                  (svstmtlist-fix nil))))