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4vec

4vec-index-p

Signature
(4vec-index-p x) → *
Arguments: x — Guard (4vec-p x).

Definitions and Theorems

Function: 4vec-index-p

(defun 4vec-index-p (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-index-p))
    (declare (ignorable __function__))
    (and (2vec-p x) (<= 0 (2vec->val x)))))

Theorem: 4vec-index-p-implies

(defthm 4vec-index-p-implies
  (implies (4vec-index-p x)
           (and (equal (4vec->lower x) (4vec->upper x))
                (<= 0 (4vec->lower x))))
  :rule-classes :forward-chaining)

Theorem: 4vec-index-p-of-4vec-fix-x

(defthm 4vec-index-p-of-4vec-fix-x
  (equal (4vec-index-p (4vec-fix x))
         (4vec-index-p x)))

Theorem: 4vec-index-p-4vec-equiv-congruence-on-x

(defthm 4vec-index-p-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec-index-p x)
                  (4vec-index-p x-equiv)))
  :rule-classes :congruence)