consider W being Tree;
consider d being Element of D;
set f = W --> d;
dom (W --> d) = W by FUNCOP_1:19;
then reconsider f = W --> d as DecoratedTree by Def8;
A1: rng f = {d} by FUNCOP_1:14;
f is ParametrizedSubset of D

proof

let x be set ; :: according to TARSKI:def 3,TREES_2:def 9 :: thesis: ( not x in rng f or x in D )
assume x in rng f ; :: thesis: x in D
then x = d by A1, TARSKI:def 1;
hence x in D ; :: thesis: verum

end;

hence ex b₁ being ParametrizedSubset of D st
( b₁ is DecoratedTree-like & b₁ is Function-like ) ; :: thesis: verum