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. Cl,

R. ?-for-setu-p(g, (. B)).-;-a-=-b, and B. , Deletion of a sub-class relation.) If B = Resource or A = B we do nothing

Y. S. ?x, (. Dom, A. Dom, (. , and B. , ¬P Sub

Y. S. ?x, (. Rng, A. Rng, (. , B. et al.,

, Proof ok for this case

R. ?-for-setu-p(g and . Sub, Rng(B, RB)} ? G then do nothing else (do the update P r(B, Resource, Resource)): ¬Cl(B) ?X¬Dom(X, B) ? ¬P r(X)(*) ? ?Y

?. Csub,

¬. Csub, (. Xsc, and Y. Csub, ), both) or exception 18, Choice

?. Xp1, XP2 such that PSub(XP1, XP2) and Dom(XP1,Xsc) and Dom (XP2,XC) then Choice (¬ PSub(XP1, XP2), ¬ Dom(XP1,Xsc), ¬ Dom (XP2,XC), all them) or exception, p.22

?. Xp1, XP2 such that PSub(XP1, XP2) and Rng(XP1,Xsc) and Rng (XP2,XC) then Choice (¬ PSub(XP1, XP2), ¬ Rng(XP1,Xsc) ¬ Rng (XP2,XC), p.23

¬. Psub, (. Xsp, . Xp)-non-deterministe, and . Situation,

?. Psub, Xsp, Y) and PSub(Y,XP) then Choice (¬ PSub, p.20

¬. Dom, Xp, XD) ¬ Pr(Xp), p.15

¬. Rng, Xp, XR) ¬ Pr(Xp), p.15

¬. Ci(xi, XC) if XC = ressource then ¬ Indiv, p.14

S. Non-deterministe,

, ? YC such that CI(Xi, YC) and CSub(YC,XC) then Choice (¬ CI(Xi,YC), ¬ CSub(YC, XC), both) or exception, p.26

?. Yi, Zp such that PI, p.24

?. Yi, Zp such that PI(Xi, Yi, Zp) and Rng(Zp,XC) then Choice (¬ PI(Xi, Yi, Zp), ¬ Rng(Zp,XC), both) or exception, p.25

¬. Pi(xi, Y. Xp, ). Non-deterministe, and . Situations,

?. Yp and Y. Xi, Yp) and PSub(Yp,Xp) then Choice ( ¬ PI(Xi,Yi, Yp), ¬ PSub(Yp,Xp), both) or exception, p.27

, UpdCond table for deletions, Table 3