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Ubdd-to-aignet-memo

Ubdd-to-aignet-memo-equiv

Basic equivalence relation for ubdd-to-aignet-memo structures.

Definitions and Theorems

Function: ubdd-to-aignet-memo-equiv$inline

(defun ubdd-to-aignet-memo-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (ubdd-to-aignet-memo-p x)
                              (ubdd-to-aignet-memo-p acl2::y))))
  (equal (ubdd-to-aignet-memo-fix x)
         (ubdd-to-aignet-memo-fix acl2::y)))

Theorem: ubdd-to-aignet-memo-equiv-is-an-equivalence

(defthm ubdd-to-aignet-memo-equiv-is-an-equivalence
  (and (booleanp (ubdd-to-aignet-memo-equiv x y))
       (ubdd-to-aignet-memo-equiv x x)
       (implies (ubdd-to-aignet-memo-equiv x y)
                (ubdd-to-aignet-memo-equiv y x))
       (implies (and (ubdd-to-aignet-memo-equiv x y)
                     (ubdd-to-aignet-memo-equiv y z))
                (ubdd-to-aignet-memo-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubdd-to-aignet-memo-equiv-implies-equal-ubdd-to-aignet-memo-fix-1

(defthm
  ubdd-to-aignet-memo-equiv-implies-equal-ubdd-to-aignet-memo-fix-1
  (implies (ubdd-to-aignet-memo-equiv x x-equiv)
           (equal (ubdd-to-aignet-memo-fix x)
                  (ubdd-to-aignet-memo-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubdd-to-aignet-memo-fix-under-ubdd-to-aignet-memo-equiv

(defthm ubdd-to-aignet-memo-fix-under-ubdd-to-aignet-memo-equiv
  (ubdd-to-aignet-memo-equiv (ubdd-to-aignet-memo-fix x)
                             x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubdd-to-aignet-memo-fix-1-forward-to-ubdd-to-aignet-memo-equiv

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

Theorem: equal-of-ubdd-to-aignet-memo-fix-2-forward-to-ubdd-to-aignet-memo-equiv

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

Theorem: ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-1-forward

(defthm
     ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-1-forward
  (implies (ubdd-to-aignet-memo-equiv (ubdd-to-aignet-memo-fix x)
                                      acl2::y)
           (ubdd-to-aignet-memo-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-2-forward

(defthm
     ubdd-to-aignet-memo-equiv-of-ubdd-to-aignet-memo-fix-2-forward
 (implies
     (ubdd-to-aignet-memo-equiv x (ubdd-to-aignet-memo-fix acl2::y))
     (ubdd-to-aignet-memo-equiv x acl2::y))
 :rule-classes :forward-chaining)