reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;

theorem Th17:
  {x,y} is constituted-DTrees iff x is DecoratedTree & y is DecoratedTree
proof
  thus {x,y} is constituted-DTrees implies
  x is DecoratedTree & y is DecoratedTree
  proof
    assume
A1: for z st z in {x,y} holds z is DecoratedTree;
A2: x in {x,y} by TARSKI:def 2;
    y in {x,y} by TARSKI:def 2;
    hence thesis by A1,A2;
  end;
  assume that
A3: x is DecoratedTree and
A4: y is DecoratedTree;
  let z;
  thus thesis by A3,A4,TARSKI:def 2;
end;
