T | p is ParametrizedSubset of D

proof

( rng (T | p) c= rng T & rng T c= D ) by Def9, Th34;
hence rng (T | p) c= D by XBOOLE_1:1; :: according to TREES_2:def 9 :: thesis: verum

end;

hence T | p is DecoratedTree of D ; :: thesis: verum