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, ? , by definition of an RDF summary, there ex-2 = f (n 1 ) p f (n 2 ). Moreover, since n 1 p n 2 is in G ? , f 1 (n 1 ) p f 1 (n 2 ) is in (G ? ) /? . Therefore, since for every f, vol.2, p.1
? such that n 1 type c = f 1 (n 1 ) type c. Further, if n 1 type c is in G ? , then f (n 1 ) type c is in (G /? ) ? (Theorem 1), hence f 2 (f (n 1 )) type c is in ((G /? ) ? ) /? . Therefore, ? since for every f 1 (n 1 ) type c edge in (G ? ) /? , there is an edge f 2 (f (n 1 )) type c in ((G /? ) ? ) /? , and ? since ?(f 1 (n)) = f 2 (f (n)), for n any G ? node, is a bijective function from all (G ? ) /? nodes to all, G ? ) /? , by definition of an RDF summary ,
, ? , by definition of an RDF summary, there exists an in (G ? ) /? . Therefore, since for every f 2 (f (n 1 )) type c edge in ((G /? ) ? ) /? , there is an edge f 1 (n 1 ) type c in (G ? ) /? , and since ?(f 1 (n)) = f 2 (f (n)), for n any G ? node, is a bijective function from all (G ? ) /? nodes to all, ? n 1 type c triples through ? ?1 (**'). From (*) and (**), and, (*') and (**')