$R$ is a reflexive and transitive binary relation with field $A$.
Prove that equivalence relation $S$ in $A$ exists and partial ordering $T$ in $A/S$, such that for arbitrary $x$ and $y$ from $A$ the following is true:
$\langle x,y\rangle\in R \iff \langle [x]_S, [y]_S\rangle \in T$