		Search-engine friendly clone of the ACL2 documentation.

Bed-from-aig

Match-aig-xor

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

Definitions and Theorems

Function: match-aig-xor

(defun match-aig-xor (x)
  (declare (xargs :guard t))
  (let ((__function__ 'match-aig-xor))
    (declare (ignorable __function__))
    (b* (((mv okp a b) (match-aig-xor-1 x))
         ((when okp) (mv okp a b)))
      (match-aig-xor-2 x))))

Theorem: match-aig-xor-correct

(defthm match-aig-xor-correct
  (b* (((mv okp arg1 arg2) (match-aig-xor x)))
    (implies okp
             (equal (aig-eval x env)
                    (xor (aig-eval arg1 env)
                         (aig-eval arg2 env))))))

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

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

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

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

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

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

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

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