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• Bitsets

Bitset-difference

(bitset-difference x y) constructs the set X - Y.

Signature

(bitset-difference x y) → bitset

Arguments

x — Guard (natp x).

y — Guard (natp y).

Returns

bitset — Type (natp bitset).

Definitions and Theorems

Function: bitset-difference$inline

(defun acl2::bitset-difference$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-difference))
            (declare (ignorable __function__))
            (the unsigned-byte
                 (logandc1 (the unsigned-byte (lnfix y))
                           (the unsigned-byte (lnfix x))))))

Theorem: natp-of-bitset-difference

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

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

(defthm bitset-difference-when-not-natp-left
        (implies (not (natp x))
                 (equal (bitset-difference x y) 0)))

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

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

Theorem: bitset-difference-of-nfix-left

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

Theorem: bitset-difference-of-nfix-right

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

Theorem: bitset-members-of-bitset-difference

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