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• Bitsets

Bitset-union

(bitset-union X Y ...) constructs the set X U Y U ....

Definitions and Theorems

Function: bitset-binary-union$inline

(defun bitset-binary-union$inline (x y)
       (declare (type unsigned-byte x)
                (type unsigned-byte y))
       (declare (xargs :guard (and (natp x) (natp y))))
       (declare (xargs :split-types t))
       (let ((__function__ 'bitset-binary-union))
            (declare (ignorable __function__))
            (the unsigned-byte
                 (logior (the unsigned-byte (lnfix x))
                         (the unsigned-byte (lnfix y))))))

Theorem: natp-of-bitset-binary-union

(defthm natp-of-bitset-binary-union
        (b* ((bitset (bitset-binary-union$inline x y)))
            (natp bitset))
        :rule-classes :type-prescription)

Theorem: bitset-union-when-not-natp-left

(defthm bitset-union-when-not-natp-left
        (implies (not (natp x))
                 (equal (bitset-union x y) (nfix y))))

Theorem: bitset-union-when-not-natp-right

(defthm bitset-union-when-not-natp-right
        (implies (not (natp y))
                 (equal (bitset-union x y) (nfix x))))

Theorem: bitset-union-of-nfix-left

(defthm bitset-union-of-nfix-left
        (equal (bitset-union (nfix x) y)
               (bitset-union x y)))

Theorem: bitset-union-of-nfix-right

(defthm bitset-union-of-nfix-right
        (equal (bitset-union x (nfix y))
               (bitset-union x y)))

Theorem: bitset-members-of-bitset-union

(defthm bitset-members-of-bitset-union
        (equal (bitset-members (bitset-union x y))
               (union (bitset-members x)
                      (bitset-members y))))

Subtopics

Bitset-binary-union