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4vec-operations

4vec-xdet

Identity function for 2vecs, or all Xes when there are any X or Z bits.

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

This (arguably) matches the Verilog specification for unary +.

BOZO this is identical to 2vecx-fix.

Definitions and Theorems

Function: 4vec-xdet

(defun 4vec-xdet (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-xdet))
    (declare (ignorable __function__))
    (if (2vec-p x) (4vec-fix x) (4vec-x))))

Theorem: 4vec-p-of-4vec-xdet

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

Theorem: 4vec-xdet-of-2vecx-fix-x

(defthm 4vec-xdet-of-2vecx-fix-x
  (equal (4vec-xdet (2vecx-fix x))
         (4vec-xdet x)))

Theorem: 4vec-xdet-2vecx-equiv-congruence-on-x

(defthm 4vec-xdet-2vecx-equiv-congruence-on-x
  (implies (2vecx-equiv x x-equiv)
           (equal (4vec-xdet x)
                  (4vec-xdet x-equiv)))
  :rule-classes :congruence)