		Search-engine friendly clone of the ACL2 documentation.

Syntax-abstraction

Empty-optional-tree-p

Signature
(empty-optional-tree-p tree) → y/n
Arguments: tree — Guard (abnf::treep tree).
Returns: y/n — Type (booleanp y/n).

Definitions and Theorems

Function: empty-optional-tree-p

(defun empty-optional-tree-p (tree)
  (declare (xargs :guard (abnf::treep tree)))
  (let ((__function__ 'empty-optional-tree-p))
    (declare (ignorable __function__))
    (and (abnf::tree-case tree :nonleaf)
         (equal (abnf::tree-nonleaf->rulename? tree)
                nil)
         (equal (abnf::tree-nonleaf->branches tree)
                nil))))

Theorem: booleanp-of-empty-optional-tree-p

(defthm booleanp-of-empty-optional-tree-p
  (b* ((y/n (empty-optional-tree-p tree)))
    (booleanp y/n))
  :rule-classes :rewrite)

Theorem: empty-optional-tree-p-of-tree-fix-tree

(defthm empty-optional-tree-p-of-tree-fix-tree
  (equal (empty-optional-tree-p (abnf::tree-fix tree))
         (empty-optional-tree-p tree)))

Theorem: empty-optional-tree-p-tree-equiv-congruence-on-tree

(defthm empty-optional-tree-p-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (empty-optional-tree-p tree)
                  (empty-optional-tree-p tree-equiv)))
  :rule-classes :congruence)