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Proposition: Let R be an equivalence relation on S. Then R is the relation induced by the quotient set of S with respect to R:
forall S, R: R is equivalence relation on S => R = ~ S/R.
Let D be a partition of S. Then D is the quotient set of the relation induced by D:
forall S, D: D is partition of S => D = S/ ~ D.
Each construction is the inverse of the other.