Equivalence Relation is Congruence for Constant Operation

Theorem
Every equivalence relation is a congruence relation for the constant operation.

Proof
Let $c \in S$.

By the definition of the constant operation:
 * $\forall x, y \in S: x \sqbrk c y = c$

Let $\RR$ be an equivalence relation on $S$.

Every equivalence relation is reflexive, so:
 * $c \mathrel \RR c$

So:

Hence the result.