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S4vecs

S4vec-bit-index

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

Definitions and Theorems

Function: s4vec-bit-index

(defun s4vec-bit-index (n x)
 (declare (xargs :guard (and (natp n) (s4vec-p x))))
 (let ((__function__ 's4vec-bit-index))
  (declare (ignorable __function__))
  (if-s2vec-p
   (x)
   (s2vec (int-to-sparseint (sparseint-bit n (s2vec->val x))))
   (make-s4vec
    :upper (int-to-sparseint (sparseint-bit n (s4vec->upper x)))
    :lower (int-to-sparseint (sparseint-bit n (s4vec->lower x)))))))

Theorem: s4vec-p-of-s4vec-bit-index

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

Theorem: s4vec-bit-index-correct

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

Theorem: s4vec-bit-index-of-nfix-n

(defthm s4vec-bit-index-of-nfix-n
  (equal (s4vec-bit-index (nfix n) x)
         (s4vec-bit-index n x)))

Theorem: s4vec-bit-index-nat-equiv-congruence-on-n

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

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

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

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

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