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A4vec-operations

A4vec-mask

Symbolic version of 4vec-mask.

Signature
(a4vec-mask mask x) → masked-a4vec
Arguments: mask — Guard (4vmask-p mask).; x — Guard (a4vec-p x).
Returns: masked-a4vec — Type (a4vec-p masked-a4vec).

Definitions and Theorems

Function: a4vec-mask

(defun a4vec-mask (mask x)
  (declare (xargs :guard (and (4vmask-p mask) (a4vec-p x))))
  (let ((__function__ 'a4vec-mask))
    (declare (ignorable __function__))
    (b* (((a4vec x))
         (mask (4vmask-fix mask))
         ((when (and (a4vec-mask-check mask 0 x.upper t)
                     (a4vec-mask-check mask 0 x.lower nil)))
          (a4vec-fix x))
         (dontcare (sparseint-val (sparseint-bitnot mask)))
         (dc-aigs (aig-i2v dontcare))
         (ans (a4vec (aig-logior-ss dc-aigs x.upper)
                     (aig-logandc1-ss dc-aigs x.lower))))
      ans)))

Theorem: a4vec-p-of-a4vec-mask

(defthm a4vec-p-of-a4vec-mask
  (b* ((masked-a4vec (a4vec-mask mask x)))
    (a4vec-p masked-a4vec))
  :rule-classes :rewrite)

Theorem: a4vec-mask-correct

(defthm a4vec-mask-correct
  (equal (a4vec-eval (a4vec-mask mask x) env)
         (4vec-mask mask (a4vec-eval x env))))

Theorem: a4vec-mask-of-4vmask-fix-mask

(defthm a4vec-mask-of-4vmask-fix-mask
  (equal (a4vec-mask (4vmask-fix mask) x)
         (a4vec-mask mask x)))

Theorem: a4vec-mask-4vmask-equiv-congruence-on-mask

(defthm a4vec-mask-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (a4vec-mask mask x)
                  (a4vec-mask mask-equiv x)))
  :rule-classes :congruence)

Theorem: a4vec-mask-of-a4vec-fix-x

(defthm a4vec-mask-of-a4vec-fix-x
  (equal (a4vec-mask mask (a4vec-fix x))
         (a4vec-mask mask x)))

Theorem: a4vec-mask-a4vec-equiv-congruence-on-x

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