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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))))