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Undocumented

Eval-formula-equiv

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

Function: eval-formula-equiv

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

Definitions and Theorems

Theorem: eval-formula-equiv-necc

(defthm eval-formula-equiv-necc
  (implies (not (and (equal (eval-formula x env)
                            (eval-formula acl2::y env))))
           (not (eval-formula-equiv x acl2::y))))

Theorem: eval-formula-equiv-is-an-equivalence

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