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• Faig-constructors

T-aig-ite

(t-aig-ite c a b) constructs a (less conservative) FAIG representing (if c a b), assuming these input FAIGs cannot evaluate to Z.

Signature

(t-aig-ite c a b) → *

This is a less-conservative version of t-aig-ite* that emits a in the case that c is unknown but a = b. See 4v-ite for discussion related to this issue.

Definitions and Theorems

Function: t-aig-ite

(defun t-aig-ite (c a b)
  (declare (xargs :guard t))
  (let ((__function__ 't-aig-ite))
    (declare (ignorable __function__))
    (b* (((faig a1 a0) a)
         ((faig b1 b0) b)
         ((faig c1 c0) c))
      (cons (aig-or (aig-and c1 a1) (aig-and c0 b1))
            (aig-or (aig-and c1 a0)
                    (aig-and c0 b0))))))

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

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

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

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

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

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

Theorem: faig-fix-equiv-implies-equal-t-aig-ite-3

(defthm faig-fix-equiv-implies-equal-t-aig-ite-3
  (implies (faig-fix-equiv b b-equiv)
           (equal (t-aig-ite c a b)
                  (t-aig-ite c a b-equiv)))
  :rule-classes (:congruence))

Theorem: faig-equiv-implies-faig-equiv-t-aig-ite-3

(defthm faig-equiv-implies-faig-equiv-t-aig-ite-3
  (implies (faig-equiv b b-equiv)
           (faig-equiv (t-aig-ite c a b)
                       (t-aig-ite c a b-equiv)))
  :rule-classes (:congruence))

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

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

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

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