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Composition of Relations

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.

Author: Wolfgang Schreiner
Last Modification: October 14, 1999

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