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4vec-operations

4vec-onset

Identity, except Z bits become 0.

Signature
(4vec-onset x) → res
Arguments: x — Guard (4vec-p x).
Returns: res — Type (4vec-p res).

The closest monotonic approximation of the onset of each of the bits of the input. It differs from the actual onset in that the 4vec-onset of an X bit is X.

Definitions and Theorems

Function: 4vec-onset

(defun 4vec-onset (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-onset))
    (declare (ignorable __function__))
    (b* (((4vec x)))
      (4vec x.upper (logand x.upper x.lower)))))

Theorem: 4vec-p-of-4vec-onset

(defthm 4vec-p-of-4vec-onset
  (b* ((res (4vec-onset x))) (4vec-p res))
  :rule-classes :rewrite)

Theorem: 4vec-onset-bits

(defthm 4vec-onset-bits
  (equal (4vec-idx->4v n (4vec-onset x))
         (let ((in (4vec-idx->4v n x)))
           (if (eq 'z in) 'f in))))

Theorem: 4vec-onset-of-4vec-fix-x

(defthm 4vec-onset-of-4vec-fix-x
  (equal (4vec-onset (4vec-fix x))
         (4vec-onset x)))

Theorem: 4vec-onset-4vec-equiv-congruence-on-x

(defthm 4vec-onset-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec-onset x)
                  (4vec-onset x-equiv)))
  :rule-classes :congruence)