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Aig-and

Aig-and-pass5

Level 2, Resolution Rule.

Signature
(aig-and-pass5 x y) → (mv status arg1 arg2)

Definitions and Theorems

Function: aig-and-pass5$inline

(defun aig-and-pass5$inline (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'aig-and-pass5))
    (declare (ignorable __function__))
    (b* (((unless (and (not (aig-atom-p x))
                       (eq (cdr x) nil)
                       (not (aig-atom-p (car x)))
                       (not (eq (cdar x) nil))))
          (mv :fail x y))
         ((unless (and (not (aig-atom-p y))
                       (eq (cdr y) nil)
                       (not (aig-atom-p (car y)))
                       (not (eq (cdar y) nil))))
          (mv :fail x y))
         (a (caar x))
         (b (cdar x))
         (c (caar y))
         (d (cdar y))
         ((when (or (and (hons-equal a d)
                         (aig-negation-p b c))
                    (and (hons-equal a c)
                         (aig-negation-p b d))))
          (let ((ans (aig-not a)))
            (mv :subterm ans ans)))
         ((when (or (and (hons-equal b d)
                         (aig-negation-p a c))
                    (and (hons-equal b c)
                         (aig-negation-p a d))))
          (let ((ans (aig-not b)))
            (mv :subterm ans ans))))
      (mv :fail x y))))

Theorem: aig-and-pass5-correct

(defthm aig-and-pass5-correct
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass5$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-pass5-never-reduced

(defthm aig-and-pass5-never-reduced
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass5$inline x y)))
    (not (equal status :reduced))))

Theorem: aig-and-pass5-subterm-convention

(defthm aig-and-pass5-subterm-convention
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass5$inline x y)))
    (implies (equal status :subterm)
             (equal arg2 arg1))))

Theorem: aig-and-pass5-normalize-status

(defthm aig-and-pass5-normalize-status
  (b* (((mv ?status ?arg1 ?arg2)
        (aig-and-pass5$inline x y)))
    (implies (and (not (equal status :subterm))
                  (not (equal status :reduced)))
             (and (equal status :fail)
                  (equal arg1 x)
                  (equal arg2 y)))))