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Nat-bool-list-nats

Signature

(nat-bool-list-nats x) → *

Arguments

x — Guard (nat-bool-listp x).

Definitions and Theorems

Function: nat-bool-list-nats

(defun nat-bool-list-nats (x)
  (declare (xargs :guard (nat-bool-listp x)))
  (let ((__function__ 'nat-bool-list-nats))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (if (booleanp (car x))
          (nat-bool-list-nats (cdr x))
        (cons (lnfix (car x))
              (nat-bool-list-nats (cdr x)))))))

Theorem: nat-bool-list-nats-of-list-fix

(defthm nat-bool-list-nats-of-list-fix
  (equal (nat-bool-list-nats (list-fix x))
         (nat-bool-list-nats x)))

Theorem: nat-bool-list-nats-of-aig-sterm

(defthm nat-bool-list-nats-of-aig-sterm
  (equal (nat-bool-list-nats (aig-sterm x))
         (if (booleanp x) nil (list (nfix x)))))

Theorem: nat-bool-list-nats-of-aig-scons-bool

(defthm nat-bool-list-nats-of-aig-scons-bool
  (implies (booleanp x)
           (equal (nat-bool-list-nats (aig-scons x y))
                  (nat-bool-list-nats y))))

Theorem: nat-bool-list-nats-of-aig-scons-nat

(defthm nat-bool-list-nats-of-aig-scons-nat
  (implies (and (natp x)
                (not (member x (nat-bool-list-nats y))))
           (equal (nat-bool-list-nats (aig-scons x y))
                  (cons x (nat-bool-list-nats y)))))