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Definition: composition of two binary relations R and S.
R o S := {<a, c>: a in domain(R) /\ c in range(S) /\ (exists b: <a, b> in R /\ <b, c> in S)}.
Proposition: The composition of a relation from A to B and of a relation from B to C is a relation from A to C.
forall R, S, A, B, C: (R subset A x B /\ S subset B x C) => R o S subset A x C.