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A4vec-operations

A4vec-bit-extract

Signature
(a4vec-bit-extract n x) → res
Arguments: n — Guard (a4vec-p n).; x — Guard (a4vec-p x).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a4vec-bit-extract

(defun a4vec-bit-extract (n x)
  (declare (xargs :guard (and (a4vec-p n) (a4vec-p x))))
  (let ((__function__ 'a4vec-bit-extract))
    (declare (ignorable __function__))
    (b* (((a4vec x)) ((a4vec n)))
      (a4vec-ite (aig-andc2 (a2vec-p n)
                            (aig-sign-s n.upper))
                 (b* ((ubit (aig-logbitp-n2v 1 n.upper x.upper))
                      (lbit (aig-logbitp-n2v 1 n.upper x.lower)))
                   (a4vec (aig-scons ubit (aig-sterm nil))
                          (aig-scons lbit (aig-sterm nil))))
                 (a4vec-1x)))))

Theorem: a4vec-p-of-a4vec-bit-extract

(defthm a4vec-p-of-a4vec-bit-extract
  (b* ((res (a4vec-bit-extract n x)))
    (a4vec-p res))
  :rule-classes :rewrite)

Theorem: a4vec-bit-extract-correct

(defthm a4vec-bit-extract-correct
  (equal (a4vec-eval (a4vec-bit-extract n x) env)
         (4vec-bit-extract (a4vec-eval n env)
                           (a4vec-eval x env))))

Theorem: a4vec-bit-extract-of-a4vec-fix-n

(defthm a4vec-bit-extract-of-a4vec-fix-n
  (equal (a4vec-bit-extract (a4vec-fix n) x)
         (a4vec-bit-extract n x)))

Theorem: a4vec-bit-extract-a4vec-equiv-congruence-on-n

(defthm a4vec-bit-extract-a4vec-equiv-congruence-on-n
  (implies (a4vec-equiv n n-equiv)
           (equal (a4vec-bit-extract n x)
                  (a4vec-bit-extract n-equiv x)))
  :rule-classes :congruence)

Theorem: a4vec-bit-extract-of-a4vec-fix-x

(defthm a4vec-bit-extract-of-a4vec-fix-x
  (equal (a4vec-bit-extract n (a4vec-fix x))
         (a4vec-bit-extract n x)))

Theorem: a4vec-bit-extract-a4vec-equiv-congruence-on-x

(defthm a4vec-bit-extract-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a4vec-bit-extract n x)
                  (a4vec-bit-extract n x-equiv)))
  :rule-classes :congruence)