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Transitive Closure

Definition: The transitive closure of R on S is the smallest relation that contains R and is transitive on S:

transitiveS(R) :=
   such R' subset S x S:
      R subset R' /\  R' is transitive on S /\ 
      forall R": (R subset R" /\  R" is transitive on S) => R' subset R".

Add transitivity to relation (how?).

Author: Wolfgang Schreiner
Last Modification: January 26, 2000

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