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A4vec-operations

A2vec-p

Construct an AIG that captures: when does an a4vec evaluate to a 2vec-p?

Signature
(a2vec-p x) → aig
Arguments: x — Guard (a4vec-p x).

This is a supporting function that is widely used by many of our a4vec-operations. For instance, operations like 4vec-plus return all Xes when there are any X/Z bits.

Definitions and Theorems

Function: a2vec-p

(defun a2vec-p (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'a2vec-p))
    (declare (ignorable __function__))
    (b* (((a4vec x)))
      (aig-=-ss x.upper x.lower))))

Theorem: a2vec-p-correct

(defthm a2vec-p-correct
  (equal (aig-eval (a2vec-p x) env)
         (2vec-p (a4vec-eval x env))))

Theorem: a2vec-p-of-a4vec-fix-x

(defthm a2vec-p-of-a4vec-fix-x
  (equal (a2vec-p (a4vec-fix x))
         (a2vec-p x)))

Theorem: a2vec-p-a4vec-equiv-congruence-on-x

(defthm a2vec-p-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a2vec-p x) (a2vec-p x-equiv)))
  :rule-classes :congruence)