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Bed-from-aig

Match-aig-andc2

Signature
(match-aig-andc2 x) → (mv okp arg1 arg2)
Arguments: x — AIG to pattern match.
Returns: okp — Whether x matches (andc2 arg1 arg2).; arg1 — On success, arg1 from the match.; arg2 — On success, arg2 from the match.

Definitions and Theorems

Function: match-aig-andc2

(defun match-aig-andc2 (x)
  (declare (xargs :guard t))
  (let ((__function__ 'match-aig-andc2))
    (declare (ignorable __function__))
    (b* (((mv okp a nb) (match-aig-and x))
         ((unless okp) (mv nil nil nil))
         ((mv okp b) (match-aig-not nb))
         ((unless okp) (mv nil nil nil)))
      (mv t a b))))

Theorem: match-aig-andc2-correct

(defthm match-aig-andc2-correct
  (b* (((mv okp arg1 arg2)
        (match-aig-andc2 x)))
    (implies okp
             (equal (aig-eval x env)
                    (and (aig-eval arg1 env)
                         (not (aig-eval arg2 env)))))))

Theorem: acl2-count-of-match-aig-andc2-weak-1

(defthm acl2-count-of-match-aig-andc2-weak-1
  (b* (((mv & arg1 &) (match-aig-andc2 x)))
    (<= (acl2-count arg1) (acl2-count x)))
  :rule-classes ((:rewrite) (:linear)))

Theorem: acl2-count-of-match-aig-andc2-weak-2

(defthm acl2-count-of-match-aig-andc2-weak-2
  (b* (((mv & & arg2) (match-aig-andc2 x)))
    (<= (acl2-count arg2) (acl2-count x)))
  :rule-classes ((:rewrite) (:linear)))

Theorem: acl2-count-of-match-aig-andc2-strong-1

(defthm acl2-count-of-match-aig-andc2-strong-1
  (b* (((mv okp arg1 &) (match-aig-andc2 x)))
    (implies okp
             (< (acl2-count arg1) (acl2-count x))))
  :rule-classes ((:rewrite) (:linear)))

Theorem: acl2-count-of-match-aig-andc2-strong-2

(defthm acl2-count-of-match-aig-andc2-strong-2
  (b* (((mv okp & arg2) (match-aig-andc2 x)))
    (implies okp
             (< (acl2-count arg2) (acl2-count x))))
  :rule-classes ((:rewrite) (:linear)))