refl | reflexive |

sym | symmetric |

trans | transitive |

The equal to relation is reflexive.

$$\forall x \in S : x = x$$```
refl: ?t = ?t
```

Proof unavailable

The equal to relation is symmetric.

$$\forall x,y \in S : x = y \Rightarrow y = x$$```
sym: ?s = ?t \(\Longrightarrow\) ?t = ?s
```

Proof unavailable

The equal to relation is transitive.

$$\forall x,y,z \in S : x = y \wedge y = z \Rightarrow x = z$$```
trans: ?r = ?s \(\Longrightarrow\) ?s = ?t \(\Longrightarrow\) ?r = ?t
```

Proof unavailable

The equal to relation is an equivalence relation.