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A4vec-operations

A4vec-xdet

Symbolic version of 4vec-xdet.

Signature
(a4vec-xdet x) → res
Arguments: x — Guard (a4vec-p x).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a4vec-xdet

(defun a4vec-xdet (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'a4vec-xdet))
    (declare (ignorable __function__))
    (a4vec-ite (a2vec-p x)
               (a4vec-fix x)
               (a4vec-x))))

Theorem: a4vec-p-of-a4vec-xdet

(defthm a4vec-p-of-a4vec-xdet
  (b* ((res (a4vec-xdet x)))
    (a4vec-p res))
  :rule-classes :rewrite)

Theorem: a4vec-xdet-correct

(defthm a4vec-xdet-correct
  (equal (a4vec-eval (a4vec-xdet x) env)
         (4vec-xdet (a4vec-eval x env))))

Theorem: a4vec-xdet-of-a4vec-fix-x

(defthm a4vec-xdet-of-a4vec-fix-x
  (equal (a4vec-xdet (a4vec-fix x))
         (a4vec-xdet x)))

Theorem: a4vec-xdet-a4vec-equiv-congruence-on-x

(defthm a4vec-xdet-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a4vec-xdet x)
                  (a4vec-xdet x-equiv)))
  :rule-classes :congruence)