		Search-engine friendly clone of the ACL2 documentation.

Bfr-equiv

Semantics equivalence of BFRs, i.e., equal evaluation under every possible environment.

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

Function: bfr-equiv

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

Definitions and Theorems

Theorem: bfr-equiv-necc

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

Theorem: bfr-equiv-is-an-equivalence

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