Jack O'Brien comments on Introduction to Cartesian Frames

[Jack O'Brien]

Definition: $\text{Prevent}\left(C\right)=\{S\subseteq W|\exists a\in A,\forall e\in E,a\cdot e\notin S\}$.

A useful alternate definition of this is:
$$\text{Prevent}\left(C\right)=\{S^C|S\in \text{Ensure}(C\left)\right\}$$
Where $S^C$ refers to $W\setminus S$. Proof:

$$\begin{array}{cc}\text{Prevent}\left(C\right)& =\{S\subseteq W|\exists a\in A\text{s.t.}\forall e\in E,a\cdot e\notin S\}\\ & =\{S\subseteq W|\exists a\in A\text{s.t.}\forall e\in E,a\cdot e\in S^C\}\\ & =\{S^C|S\in \text{Ensure}(C\left)\right\}\end{array}$$