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• Ubdd/level

Ubdd/level-equiv

Basic equivalence relation for ubdd/level structures.

Definitions and Theorems

Function: ubdd/level-equiv$inline

(defun ubdd/level-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (ubdd/level-p x)
                              (ubdd/level-p acl2::y))))
  (equal (ubdd/level-fix x)
         (ubdd/level-fix acl2::y)))

Theorem: ubdd/level-equiv-is-an-equivalence

(defthm ubdd/level-equiv-is-an-equivalence
  (and (booleanp (ubdd/level-equiv x y))
       (ubdd/level-equiv x x)
       (implies (ubdd/level-equiv x y)
                (ubdd/level-equiv y x))
       (implies (and (ubdd/level-equiv x y)
                     (ubdd/level-equiv y z))
                (ubdd/level-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubdd/level-equiv-implies-equal-ubdd/level-fix-1

(defthm ubdd/level-equiv-implies-equal-ubdd/level-fix-1
  (implies (ubdd/level-equiv x x-equiv)
           (equal (ubdd/level-fix x)
                  (ubdd/level-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubdd/level-fix-under-ubdd/level-equiv

(defthm ubdd/level-fix-under-ubdd/level-equiv
  (ubdd/level-equiv (ubdd/level-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubdd/level-fix-1-forward-to-ubdd/level-equiv

(defthm equal-of-ubdd/level-fix-1-forward-to-ubdd/level-equiv
  (implies (equal (ubdd/level-fix x) acl2::y)
           (ubdd/level-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubdd/level-fix-2-forward-to-ubdd/level-equiv

(defthm equal-of-ubdd/level-fix-2-forward-to-ubdd/level-equiv
  (implies (equal x (ubdd/level-fix acl2::y))
           (ubdd/level-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: ubdd/level-equiv-of-ubdd/level-fix-1-forward

(defthm ubdd/level-equiv-of-ubdd/level-fix-1-forward
  (implies (ubdd/level-equiv (ubdd/level-fix x)
                             acl2::y)
           (ubdd/level-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: ubdd/level-equiv-of-ubdd/level-fix-2-forward

(defthm ubdd/level-equiv-of-ubdd/level-fix-2-forward
  (implies (ubdd/level-equiv x (ubdd/level-fix acl2::y))
           (ubdd/level-equiv x acl2::y))
  :rule-classes :forward-chaining)