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sav08:backward_vcg [2009/03/12 12:41] vkuncak |
sav08:backward_vcg [2009/03/12 12:45] vkuncak |
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\[ | \[ | ||
\begin{array}{rl} | \begin{array}{rl} | ||
- | wp(\Delta_F,Q) & = \{x \mid \forall x'. (x,x') \in \Delta_F \rightarrow x' \in Q \} \\ | + | wp(\Delta_F,Q) & = \{s \mid \forall s'. (s,s') \in \Delta_F \rightarrow s' \in Q \} \\ |
- | & = \{ x \mid \forall x'. (x \in F \land x=x') \rightarrow x' \in Q \} \\ | + | & = \{ s \mid \forall s'. (s \in F \land s=s') \rightarrow s' \in Q \} \\ |
- | & = \{ x \mid x \in F \rightarrow x \in Q \} | + | & = \{ s \mid s \in F \rightarrow s \in Q \} |
\end{array} | \end{array} | ||
\] | \] | ||
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\[ | \[ | ||
\begin{array}{rl} | \begin{array}{rl} | ||
- | wp(x=e,\{(x,y) \mid Q(x,y)\}) & = \{(x,y) \mid \forall x',y'. x'=e \land y'=y \rightarrow Q(x',y') \} \\ | + | wp(x=e,\{(x,y) \mid Q(x,y)\}) & = \{(x,y) \mid \forall x'.\forall y'.\ x'=e \land y'=y \rightarrow Q(x',y') \} \\ |
& = \{(x,y) \mid Q(e,y) \} = \{(x,y) \mid Q[x:=e]\} | & = \{(x,y) \mid Q(e,y) \} = \{(x,y) \mid Q[x:=e]\} | ||
\end{array} | \end{array} |