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S4vecs

S4vec-bit-extract

Signature
(s4vec-bit-extract n x) → bit
Arguments: n — Guard (s4vec-p n).; x — Guard (s4vec-p x).
Returns: bit — Type (s4vec-p bit).

Definitions and Theorems

Function: s4vec-bit-extract

(defun s4vec-bit-extract (n x)
  (declare (xargs :guard (and (s4vec-p n) (s4vec-p x))))
  (let ((__function__ 's4vec-bit-extract))
    (declare (ignorable __function__))
    (if (s4vec-index-p n)
        (s4vec-bit-index (sparseint-val (s4vec->upper n))
                         x)
      (s4vec-1x))))

Theorem: s4vec-p-of-s4vec-bit-extract

(defthm s4vec-p-of-s4vec-bit-extract
  (b* ((bit (s4vec-bit-extract n x)))
    (s4vec-p bit))
  :rule-classes :rewrite)

Theorem: s4vec-bit-extract-correct

(defthm s4vec-bit-extract-correct
  (b* ((common-lisp::?bit (s4vec-bit-extract n x)))
    (equal (s4vec->4vec bit)
           (4vec-bit-extract (s4vec->4vec n)
                             (s4vec->4vec x)))))

Theorem: s4vec-bit-extract-of-s4vec-fix-n

(defthm s4vec-bit-extract-of-s4vec-fix-n
  (equal (s4vec-bit-extract (s4vec-fix n) x)
         (s4vec-bit-extract n x)))

Theorem: s4vec-bit-extract-s4vec-equiv-congruence-on-n

(defthm s4vec-bit-extract-s4vec-equiv-congruence-on-n
  (implies (s4vec-equiv n n-equiv)
           (equal (s4vec-bit-extract n x)
                  (s4vec-bit-extract n-equiv x)))
  :rule-classes :congruence)

Theorem: s4vec-bit-extract-of-s4vec-fix-x

(defthm s4vec-bit-extract-of-s4vec-fix-x
  (equal (s4vec-bit-extract n (s4vec-fix x))
         (s4vec-bit-extract n x)))

Theorem: s4vec-bit-extract-s4vec-equiv-congruence-on-x

(defthm s4vec-bit-extract-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-bit-extract n x)
                  (s4vec-bit-extract n x-equiv)))
  :rule-classes :congruence)