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--- sav08:definition_of_set_constraints [2008/05/22 11:51]
vkuncak
+++ sav08:definition_of_set_constraints [2008/05/22 11:51]
vkuncak
@@ Line 130: / Line 130: @@
 \]
 ++
-An important property we would like to have in this semantic is a very intuitive one : \[ [[f^{-1}(f(S_1, S_2))]] = [[S_1]] \]
-This property is in fact not conserved as we can easily see using a very simple counter-example :
-\[ [[f^{-1}(f(S_1, \emptyset))]] = [[f^{-1}(\lbrace f(t_1, t_2) | t_1 \in [[S_1]] \wedge t_2 \in \emptyset \rbrace)]] = [[f^{-1}(\emptyset)]] = \emptyset \]
-The correct interpretation of this property is :
-\begin{displaymath} [[f^{-1}(f(S_1, S_2))]] = \left\{ \begin{array}{ll}
- \emptyset & if [[S_2]] = \emptyset &
-[[S_1]] & otherwise \\
-\end{array} \right \end{displaymath}