		Search-engine friendly clone of the ACL2 documentation.

Bit-blasting

Nat-bool-a4env-p

Signature
(nat-bool-a4env-p x) → *
Arguments: x — Guard (svex-a4vec-env-p x).

Definitions and Theorems

Function: nat-bool-a4env-p

(defun nat-bool-a4env-p (x)
  (declare (xargs :guard (svex-a4vec-env-p x)))
  (let ((__function__ 'nat-bool-a4env-p))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (if (mbt (consp (car x)))
               (nat-bool-a4vec-p (cdar x))
             t)
           (nat-bool-a4env-p (cdr x))))))

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

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

Theorem: nat-bool-a4env-p-of-svex-a4vec-env-fix-x

(defthm nat-bool-a4env-p-of-svex-a4vec-env-fix-x
  (equal (nat-bool-a4env-p (svex-a4vec-env-fix x))
         (nat-bool-a4env-p x)))

Theorem: nat-bool-a4env-p-svex-a4vec-env-equiv-congruence-on-x

(defthm nat-bool-a4env-p-svex-a4vec-env-equiv-congruence-on-x
  (implies (svex-a4vec-env-equiv x x-equiv)
           (equal (nat-bool-a4env-p x)
                  (nat-bool-a4env-p x-equiv)))
  :rule-classes :congruence)