reserve x, y, z for object,
  i, j, n for Nat,
  p, q, r for FinSequence,
  v for FinSequence of NAT;
reserve T,T9 for DecoratedTree,
  x,y for set;
reserve D1, D2 for non empty set,
  T for DecoratedTree of D1,D2,
  d1 for Element of D1,
  d2 for Element of D2,
  F for non empty DTree-set of D1,D2,
  F1 for non empty (DTree-set of D1),
  F2 for non empty DTree-set of D2;

theorem
  <:root-tree x, root-tree y:> = root-tree [x,y]
proof reconsider x9 = x as Element of {x} by TARSKI:def 1;
  reconsider y9 = y as Element of {y} by TARSKI:def 1;
   (root-tree [x9,y9])`1 = root-tree x & (root-tree [x9,y9])`2 = root-tree y
  by Th25;
  hence thesis by TREES_3:40;
end;
