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S4vecs

S4vec-xdet

Signature
(s4vec-xdet x) → res
Arguments: x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-xdet

(defun s4vec-xdet (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec-xdet))
    (declare (ignorable __function__))
    (if (s4vec-2vec-p x)
        (s4vec-fix x)
      (s4vec-x))))

Theorem: s4vec-p-of-s4vec-xdet

(defthm s4vec-p-of-s4vec-xdet
  (b* ((res (s4vec-xdet x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-xdet-correct

(defthm s4vec-xdet-correct
  (b* ((?res (s4vec-xdet x)))
    (equal (s4vec->4vec res)
           (4vec-xdet (s4vec->4vec x)))))

Theorem: s4vec-xdet-of-s4vec-fix-x

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

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

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