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Bit-blasting

Nat-bool-a4env-vars

Signature
(nat-bool-a4env-vars x) → *
Arguments: x — Guard (nat-bool-a4env-p! x).

Definitions and Theorems

Function: nat-bool-a4env-vars

(defun nat-bool-a4env-vars (x)
  (declare (xargs :guard (nat-bool-a4env-p! x)))
  (let ((__function__ 'nat-bool-a4env-vars))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (append (and (mbt (consp (car x)))
                   (nat-bool-a4vec-vars (cdar x)))
              (nat-bool-a4env-vars (cdr x))))))

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

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

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

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