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Faig-constructors

T-aig-not

(t-aig-not a) negates the FAIG a, assuming that it cannot evaluate to Z.

Signature
(t-aig-not a) → *

Definitions and Theorems

Function: t-aig-not$inline

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

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

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

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

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

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

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