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4vec-operations

4vec-bitand

Bitwise logical AND of 4vecs.

Signature
(4vec-bitand x y) → x&y
Arguments: x — Guard (4vec-p x).; y — Guard (4vec-p y).
Returns: x&y — Type (3vec-p! x&y).

Definitions and Theorems

Function: 4vec-bitand

(defun 4vec-bitand (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '4vec-bitand))
    (declare (ignorable __function__))
    (3vec-bitand (3vec-fix x)
                 (3vec-fix y))))

Theorem: 3vec-p!-of-4vec-bitand

(defthm 3vec-p!-of-4vec-bitand
  (b* ((x&y (4vec-bitand x y)))
    (3vec-p! x&y))
  :rule-classes :rewrite)

Main correctness theorem: each result bit is just the ACL2::4v-and of the corresponding input bits.

Theorem: 4vec-bitand-bits

(defthm 4vec-bitand-bits
  (equal (4vec-idx->4v n (4vec-bitand x y))
         (acl2::4v-and (4vec-idx->4v n x)
                       (4vec-idx->4v n y))))

Theorem: 4vec-bitand-of-3vec-fix-x

(defthm 4vec-bitand-of-3vec-fix-x
  (equal (4vec-bitand (3vec-fix x) y)
         (4vec-bitand x y)))

Theorem: 4vec-bitand-3vec-equiv-congruence-on-x

(defthm 4vec-bitand-3vec-equiv-congruence-on-x
  (implies (3vec-equiv x x-equiv)
           (equal (4vec-bitand x y)
                  (4vec-bitand x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vec-bitand-of-3vec-fix-y

(defthm 4vec-bitand-of-3vec-fix-y
  (equal (4vec-bitand x (3vec-fix y))
         (4vec-bitand x y)))

Theorem: 4vec-bitand-3vec-equiv-congruence-on-y

(defthm 4vec-bitand-3vec-equiv-congruence-on-y
  (implies (3vec-equiv y y-equiv)
           (equal (4vec-bitand x y)
                  (4vec-bitand x y-equiv)))
  :rule-classes :congruence)