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Bfr-env-equiv

This is a universal equivalence, introduced using ACL2::def-universal-equiv.

Function: bfr-env-equiv

(defun bfr-env-equiv (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (prog2$ (acl2::throw-nonexec-error 'bfr-env-equiv
                                     (list x y))
          (let ((v (bfr-env-equiv-witness x y)))
            (and (iff (bfr-lookup v x)
                      (bfr-lookup v y))))))

Definitions and Theorems

Theorem: bfr-env-equiv-necc

(defthm bfr-env-equiv-necc
  (implies (not (and (iff (bfr-lookup v x)
                          (bfr-lookup v y))))
           (not (bfr-env-equiv x y))))

Theorem: bfr-env-equiv-is-an-equivalence

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