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• 4vmask

4vmask-union

(4vmask-union x y) unions the 4vmasks x and y, creating a new mask that includes all bits that are relevant for in either x or y.

Signature

(4vmask-union x y) → union

Arguments

x — Guard (4vmask-p x).

y — Guard (4vmask-p y).

Returns

union — Type (4vmask-p union).

Definitions and Theorems

Function: 4vmask-union$inline

(defun 4vmask-union$inline (x y)
  (declare (xargs :guard (and (4vmask-p x) (4vmask-p y))))
  (let ((__function__ '4vmask-union))
    (declare (ignorable __function__))
    (sparseint-bitor (4vmask-fix x)
                     (4vmask-fix y))))

Theorem: 4vmask-p-of-4vmask-union

(defthm 4vmask-p-of-4vmask-union
  (b* ((union (4vmask-union$inline x y)))
    (4vmask-p union))
  :rule-classes :type-prescription)

Theorem: 4vmask-union$inline-of-4vmask-fix-x

(defthm 4vmask-union$inline-of-4vmask-fix-x
  (equal (4vmask-union$inline (4vmask-fix x) y)
         (4vmask-union$inline x y)))

Theorem: 4vmask-union$inline-4vmask-equiv-congruence-on-x

(defthm 4vmask-union$inline-4vmask-equiv-congruence-on-x
  (implies (4vmask-equiv x x-equiv)
           (equal (4vmask-union$inline x y)
                  (4vmask-union$inline x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vmask-union$inline-of-4vmask-fix-y

(defthm 4vmask-union$inline-of-4vmask-fix-y
  (equal (4vmask-union$inline x (4vmask-fix y))
         (4vmask-union$inline x y)))

Theorem: 4vmask-union$inline-4vmask-equiv-congruence-on-y

(defthm 4vmask-union$inline-4vmask-equiv-congruence-on-y
  (implies (4vmask-equiv y y-equiv)
           (equal (4vmask-union$inline x y)
                  (4vmask-union$inline x y-equiv)))
  :rule-classes :congruence)

Theorem: 4vmask-subsumes-of-4vmask-union-1

(defthm 4vmask-subsumes-of-4vmask-union-1
  (4vmask-subsumes (4vmask-union x y) x))

Theorem: 4vmask-subsumes-of-4vmask-union-2

(defthm 4vmask-subsumes-of-4vmask-union-2
  (4vmask-subsumes (4vmask-union x y) y))