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Faig-constructors

T-aig-xor

(t-aig-xor a b) xors together the FAIGs a and b, assuming they cannot evaluate to Z.

Signature
(t-aig-xor a b) → *

Definitions and Theorems

Function: t-aig-xor

(defun t-aig-xor (a b)
  (declare (xargs :guard t))
  (let ((__function__ 't-aig-xor))
    (declare (ignorable __function__))
    (t-aig-or (t-aig-and a (t-aig-not b))
              (t-aig-and (t-aig-not a) b))))

Theorem: faig-eval-of-t-aig-xor

(defthm faig-eval-of-t-aig-xor
  (equal (faig-eval (t-aig-xor a b) env)
         (t-aig-xor (faig-eval a env)
                    (faig-eval b env))))

Theorem: faig-fix-equiv-implies-equal-t-aig-xor-1

(defthm faig-fix-equiv-implies-equal-t-aig-xor-1
  (implies (faig-fix-equiv a a-equiv)
           (equal (t-aig-xor a b)
                  (t-aig-xor a-equiv b)))
  :rule-classes (:congruence))

Theorem: faig-fix-equiv-implies-equal-t-aig-xor-2

(defthm faig-fix-equiv-implies-equal-t-aig-xor-2
  (implies (faig-fix-equiv b b-equiv)
           (equal (t-aig-xor a b)
                  (t-aig-xor a b-equiv)))
  :rule-classes (:congruence))

Theorem: faig-equiv-implies-faig-equiv-t-aig-xor-2

(defthm faig-equiv-implies-faig-equiv-t-aig-xor-2
  (implies (faig-equiv b b-equiv)
           (faig-equiv (t-aig-xor a b)
                       (t-aig-xor a b-equiv)))
  :rule-classes (:congruence))

Theorem: faig-equiv-implies-faig-equiv-t-aig-xor-1

(defthm faig-equiv-implies-faig-equiv-t-aig-xor-1
  (implies (faig-equiv a a-equiv)
           (faig-equiv (t-aig-xor a b)
                       (t-aig-xor a-equiv b)))
  :rule-classes (:congruence))