theorem Th36:
  i <> 0 implies (i |-> x is DTree-yielding iff x is DecoratedTree)
proof
  assume
A1: i <> 0;
  i |-> x = (Seg i) --> x by FINSEQ_2:def 2;
  then rng (i |-> x) = {x} by A1,FUNCOP_1:8;
  then x is DecoratedTree iff rng (i |-> x) is constituted-DTrees by Th14;
  hence thesis;
end;
