## Equivalence relation

### Set

 context $X$
 definiendum $\sim \in \text{EquivRel}(X)$
 context $\sim \in \mathrm{Rel}(X)$ $x,y,z\in X$
 postulate $x\sim x$ postulate $x\sim y \Leftrightarrow y\sim x$ postulate $x\sim y \land y\sim z \Leftrightarrow x\sim z$

### Discussion

The relation $\sim$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence