		Search-engine friendly clone of the ACL2 documentation.

A4vec-operations

A4vec-uminus

Symbolic version of 4vec-uminus.

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

Definitions and Theorems

Function: a4vec-uminus

(defun a4vec-uminus (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'a4vec-uminus))
    (declare (ignorable __function__))
    (a4vec-ite (a2vec-p x)
               (b* (((a4vec x))
                    (res (aig-+-ss t nil (aig-lognot-s x.upper))))
                 (a4vec res res))
               (a4vec-x))))

Theorem: a4vec-p-of-a4vec-uminus

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

Theorem: a4vec-uminus-correct

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

Theorem: a4vec-uminus-of-a4vec-fix-x

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

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

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