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Proposition: Let R be an equivalence relation on S. [x]R contains x, for every x in S:
forall S, R: R is equivalence relation on S => forall x in S: x in [x]R.
Let x and y be elements of S. The equivalence classes of x and y with respect to R are either identical or disjoint:
forall S, R: R is equivalence relation on S => forall x in S, y in S: [x]R = [y]R \/ [x]R intersection [y]R = 0.