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

transitive _{S}(R) :=suchR' subsetSxS:RsubsetR' /\R' is transitive onS/\forallR": (RsubsetR" /\R" is transitive onS) =>R' subsetR".

*Add transitivity to relation (how?).*

Author: Wolfgang Schreiner

Last Modification: January 26, 2000