By Michel Léonard (auth.)
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But if "create PLAYER" does not lie within the range, there is the risk of the database being incoherent: in fact, when entities of PLAYER relating to this team are created, it would be possible to create a team without its captain. It would not be very precise for this sole case to introduce "create PLAYER" into this range. It would be better to define a new primitive "create TEAM" which would allow one to create PLAYER entities of a new team, and insert this ne"' primitive into the range. Note how the study of integrity rules has brought about an enrichment of the model by causing the designer to create this new primitive "create TEAM".
4 Equivalence relation and order relation Take two integrity rules ir1 and ir2 having the same context: R1... ~ (if n the irs are intra-relational; otherwise they are inter-relational). = 1, ir1 and ir2 are equivalent if every set of instances (iR 1.. i~) that verifies one, verifies the other, and inversely. ir1 is more restrictive than ir2 if every set of instances (iR 1.. i~) that verifies ir1 , verifies ir2 - described as ir1 ::;; ir2 . ir 1 is trivial (or equal to 1) if every set of instances (iR 1..
Thus not focus (R/X) c focus (not R/X). (from e5). Reciprocally (R+ c X): focus (not R(X) = (not Re)[X]. X = x. We know that there exists at least such an entity re of notRe by definition of projection. R+ and sore does not belong to not Re . X = x, ree not Re . Thus xenot (Re[x]) and focus (not R/X) c not focus (R/X). A Relational Data Model (f6a) If Y c X c R+ then focus (focus (R/X)/Y) =focus (R/Y) = R[Y]. The proof is simple, (f6b) If R+ c X then focus (focus (R/X)/Y) =focus (R/Y). focus (focus (R/X)/Y) =(focus (R/X))e[Y] = (Re[x])e[Y].