		Search-engine friendly clone of the ACL2 documentation.

Bit-blasting

Nat-bool-a4vec-p

Signature
(nat-bool-a4vec-p x) → *
Arguments: x — Guard (a4vec-p x).

Definitions and Theorems

Function: nat-bool-a4vec-p

(defun nat-bool-a4vec-p (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'nat-bool-a4vec-p))
    (declare (ignorable __function__))
    (b* (((a4vec x) x))
      (and (nat-bool-listp x.upper)
           (nat-bool-listp x.lower)))))

Theorem: __deffixtype-a4vec-equiv-means-equal-of-a4vec-fix

(defthm acl2::__deffixtype-a4vec-equiv-means-equal-of-a4vec-fix
  (implies (a4vec-equiv x y)
           (equal (a4vec-fix x) (a4vec-fix y)))
  :rule-classes nil)

Theorem: nat-bool-a4vec-p-of-a4vec-fix-x

(defthm nat-bool-a4vec-p-of-a4vec-fix-x
  (equal (nat-bool-a4vec-p (a4vec-fix x))
         (nat-bool-a4vec-p x)))

Theorem: nat-bool-a4vec-p-a4vec-equiv-congruence-on-x

(defthm nat-bool-a4vec-p-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (nat-bool-a4vec-p x)
                  (nat-bool-a4vec-p x-equiv)))
  :rule-classes :congruence)