let T be TopAugmentation of R; :: thesis: T is transitive
RelStr(# the carrier of T, the InternalRel of T #) = RelStr(# the carrier of R, the InternalRel of R #) by Def4;
then the InternalRel of T is_transitive_in the carrier of T by ORDERS_2:def 3;
hence T is transitive ; :: thesis: verum