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# Lab for Automated Reasoning and Analysis LARA

# Differences

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equivalence_relation [2007/03/30 20:45] vkuncak |
equivalence_relation [2007/03/30 20:45] (current) vkuncak |
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* $x \sim y\ \land\ y \sim z\ \rightarrow\ x \sim z$ | * $x \sim y\ \land\ y \sim z\ \rightarrow\ x \sim z$ | ||

- | Given an equivalence relation $\sim$, we define the set of equivalence classes $A_{\sim}$ by | + | Given an equivalence relation $\sim$, we define the set of equivalence classes $A_{/\sim}$ by |

\begin{equation*} | \begin{equation*} | ||

- | A_{\sim} = \{ \{y \mid x \sim y\} \mid x \in A \} | + | A_{/\sim} = \{ \{y \mid x \sim y\} \mid x \in A \} |

\end{equation*} | \end{equation*} | ||

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x \sim y\ \iff\ \exists S \in P. \{x,y\} \subseteq S | x \sim y\ \iff\ \exists S \in P. \{x,y\} \subseteq S | ||

\end{equation*} | \end{equation*} | ||

- | is an equivalence relation such that $A_{\sim} = P$. | + | is an equivalence relation such that $A_{/\sim} = P$. |