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• Bitsets

Bitset-subsetp

(bitset-subsetp x y) efficiently determines if X is a subset of Y.

Signature

(bitset-subsetp x y) → subsetp

Arguments

x — Guard (natp x).

y — Guard (natp y).

Returns

subsetp — Type (booleanp subsetp).

Definitions and Theorems

Function: bitset-subsetp$inline

(defun acl2::bitset-subsetp$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-subsetp))
            (declare (ignorable __function__))
            (eql 0
                 (the unsigned-byte
                      (bitset-difference x y)))))

Theorem: booleanp-of-bitset-subsetp

(defthm acl2::booleanp-of-bitset-subsetp
        (b* ((subsetp (acl2::bitset-subsetp$inline x y)))
            (booleanp subsetp))
        :rule-classes :type-prescription)

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

(defthm bitset-subsetp-when-not-natp-left
        (implies (not (natp x))
                 (equal (bitset-subsetp x y) t)))

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

(defthm bitset-subsetp-when-not-natp-right
        (implies (not (natp y))
                 (equal (bitset-subsetp x y) (zp x))))

Theorem: bitset-subsetp-of-nfix-left

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

Theorem: bitset-subsetp-of-nfix-right

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

Theorem: bitset-subsetp-removal

(defthm bitset-subsetp-removal
        (equal (bitset-subsetp x y)
               (subset (bitset-members x)
                       (bitset-members y))))