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An Archimedean ordered integral domain is Dedekind complete if
For all terms and , the open interval is inhabited.
For all terms , the lower bounded open interval is inhabited.
For all terms , the upper bounded open interval is inhabited.
For all terms and , if and only if is a subinterval of
For all terms and , if and only if is a subinterval of
For all terms and , if , then is a subinterval of the union of and
For all terms and , the intersection of and is a subinterval of