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
  X is constituted-Trees iff X c= Trees
proof
  thus X is constituted-Trees implies X c= Trees
  proof
    assume
A1: for x st x in X holds x is Tree;
    let x be object;
    assume x in X;
    then x is Tree by A1;
    hence thesis by Def1;
  end;
  assume
A2: X c= Trees;
  let x;
  assume x in X;
  hence thesis by A2,Def1;
end;
