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Aig-and

Aig-and-pass3

Level 2 Contradiction Rule 2 and all Level 4 Rules.

Signature
(aig-and-pass3 x y) → (mv status arg1 arg2)

Definitions and Theorems

Function: aig-and-pass3$inline

(defun aig-and-pass3$inline (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'aig-and-pass3))
    (declare (ignorable __function__))
    (b* (((unless (and (not (aig-atom-p x))
                       (not (eq (cdr x) nil))))
          (mv :fail x y))
         ((unless (and (not (aig-atom-p y))
                       (not (eq (cdr y) nil))))
          (mv :fail x y))
         (a (car x))
         (b (cdr x))
         (c (car y))
         (d (cdr y))
         ((when (or (aig-negation-p a c)
                    (aig-negation-p a d)
                    (aig-negation-p b c)
                    (aig-negation-p b d)))
          (mv :subterm nil nil))
         ((when (hons-equal a c))
          (mv :reduced x d))
         ((when (hons-equal b c))
          (mv :reduced x d))
         ((when (hons-equal b d))
          (mv :reduced x c))
         ((when (hons-equal a d))
          (mv :reduced x c)))
      (mv :fail x y))))

Theorem: aig-and-pass3-correct

(defthm aig-and-pass3-correct
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass3$inline x y)))
    (equal (and (aig-eval arg1 env)
                (aig-eval arg2 env))
           (and (aig-eval x env)
                (aig-eval y env))))
  :rule-classes nil)

Theorem: aig-and-pass3-reduces-count

(defthm aig-and-pass3-reduces-count
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass3$inline x y)))
    (implies (eq status :reduced)
             (< (+ (aig-and-count arg1)
                   (aig-and-count arg2))
                (+ (aig-and-count x)
                   (aig-and-count y)))))
  :rule-classes nil)

Theorem: aig-and-pass3-subterm-convention

(defthm aig-and-pass3-subterm-convention
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass3$inline x y)))
    (implies (equal status :subterm)
             (equal arg2 arg1))))

Theorem: aig-and-pass3-normalize-status

(defthm aig-and-pass3-normalize-status
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass3$inline x y)))
    (implies (and (not (equal status :subterm))
                  (not (equal status :reduced)))
             (and (equal status :fail)
                  (equal arg1 x)
                  (equal arg2 y)))))