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Undocumented

Bdd-equiv

This is a universal equivalence, introduced using def-universal-equiv.

Function: bdd-equiv

(defun bdd-equiv (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (prog2$ (throw-nonexec-error 'bdd-equiv
                               (list x y))
          (let ((env (bdd-equiv-witness x y)))
            (and (equal (eval-bdd x env)
                        (eval-bdd y env))))))

Definitions and Theorems

Theorem: bdd-equiv-necc

(defthm bdd-equiv-necc
  (implies (not (and (equal (eval-bdd x env)
                            (eval-bdd y env))))
           (not (bdd-equiv x y))))

Theorem: bdd-equiv-is-an-equivalence

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