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S4vecs

S4vec-equal

Signature
(s4vec-equal x y) → *
Arguments: x — Guard (s4vec-p x).; y — Guard (s4vec-p y).

Definitions and Theorems

Function: s4vec-equal

(defun s4vec-equal (x y)
 (declare (xargs :guard (and (s4vec-p x) (s4vec-p y))))
 (let ((__function__ 's4vec-equal))
  (declare (ignorable __function__))
  (mbe
      :logic (equal (s4vec->4vec x) (s4vec->4vec y))
      :exec (if-s2vec-p (x y)
                        (sparseint-equal (s2vec->val x)
                                         (s2vec->val y))
                        (and (sparseint-equal (s4vec->upper x)
                                              (s4vec->upper y))
                             (sparseint-equal (s4vec->lower x)
                                              (s4vec->lower y)))))))

Theorem: s4vec-equal-of-s4vec-fix-x

(defthm s4vec-equal-of-s4vec-fix-x
  (equal (s4vec-equal (s4vec-fix x) y)
         (s4vec-equal x y)))

Theorem: s4vec-equal-s4vec-equiv-congruence-on-x

(defthm s4vec-equal-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-equal x y)
                  (s4vec-equal x-equiv y)))
  :rule-classes :congruence)

Theorem: s4vec-equal-of-s4vec-fix-y

(defthm s4vec-equal-of-s4vec-fix-y
  (equal (s4vec-equal x (s4vec-fix y))
         (s4vec-equal x y)))

Theorem: s4vec-equal-s4vec-equiv-congruence-on-y

(defthm s4vec-equal-s4vec-equiv-congruence-on-y
  (implies (s4vec-equiv y y-equiv)
           (equal (s4vec-equal x y)
                  (s4vec-equal x y-equiv)))
  :rule-classes :congruence)