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• Faig-constructors

F-aig-not

(f-aig-not a) negates the FAIG a.

Signature

(f-aig-not a) → *

Definitions and Theorems

Function: f-aig-not

(defun f-aig-not (a)
  (declare (xargs :guard t))
  (let ((__function__ 'f-aig-not))
    (declare (ignorable __function__))
    (b* (((faig a1 a0) a))
      (cons (aig-not (aig-and a1 (aig-not a0)))
            (aig-not (aig-and a0 (aig-not a1)))))))

Theorem: faig-eval-of-f-aig-not

(defthm faig-eval-of-f-aig-not
  (equal (faig-eval (f-aig-not a) env)
         (f-aig-not (faig-eval a env))))

Theorem: faig-fix-equiv-implies-equal-f-aig-not-1

(defthm faig-fix-equiv-implies-equal-f-aig-not-1
  (implies (faig-fix-equiv a a-equiv)
           (equal (f-aig-not a)
                  (f-aig-not a-equiv)))
  :rule-classes (:congruence))

Theorem: faig-equiv-implies-faig-equiv-f-aig-not-1

(defthm faig-equiv-implies-faig-equiv-f-aig-not-1
  (implies (faig-equiv a a-equiv)
           (faig-equiv (f-aig-not a)
                       (f-aig-not a-equiv)))
  :rule-classes (:congruence))