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*Definition:*
Let `R` be a binary relation on `S`.
The *reflexive closure* of `R` on `S`
is the smallest relation that contains `R` and is reflexive on `S`:

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

*Proposition:*

forallS,R:RsubsetSxS=> reflexive_{S}(R) =Runion {<x,x>:xinS}.

*Add reflexivity to relation.*

Author: Wolfgang Schreiner

Last Modification: January 26, 2000