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Aig-var-fix

Signature

(aig-var-fix x) → new-x

Arguments

x — Guard (acl2::aig-var-p x).

Returns

new-x — Type (acl2::aig-var-p new-x).

Definitions and Theorems

Function: aig-var-fix

(defun aig-var-fix (x)
  (declare (xargs :guard (acl2::aig-var-p x)))
  (let ((__function__ 'aig-var-fix))
    (declare (ignorable __function__))
    (mbe :logic (if (acl2::aig-var-p x) x 0)
         :exec x)))

Theorem: aig-var-p-of-aig-var-fix

(defthm aig-var-p-of-aig-var-fix
  (b* ((new-x (aig-var-fix x)))
    (acl2::aig-var-p new-x))
  :rule-classes :rewrite)

Theorem: aig-var-fix-when-aig-var-p

(defthm aig-var-fix-when-aig-var-p
  (implies (acl2::aig-var-p x)
           (equal (aig-var-fix x) x)))

Function: aig-var-equiv$inline

(defun aig-var-equiv$inline (x y)
  (declare (xargs :guard (and (acl2::aig-var-p x)
                              (acl2::aig-var-p y))))
  (equal (aig-var-fix x) (aig-var-fix y)))

Theorem: aig-var-equiv-is-an-equivalence

(defthm aig-var-equiv-is-an-equivalence
  (and (booleanp (aig-var-equiv x y))
       (aig-var-equiv x x)
       (implies (aig-var-equiv x y)
                (aig-var-equiv y x))
       (implies (and (aig-var-equiv x y)
                     (aig-var-equiv y z))
                (aig-var-equiv x z)))
  :rule-classes (:equivalence))

Theorem: aig-var-equiv-implies-equal-aig-var-fix-1

(defthm aig-var-equiv-implies-equal-aig-var-fix-1
  (implies (aig-var-equiv x x-equiv)
           (equal (aig-var-fix x)
                  (aig-var-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: aig-var-fix-under-aig-var-equiv

(defthm aig-var-fix-under-aig-var-equiv
  (aig-var-equiv (aig-var-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))