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 Th12:
  {x} is constituted-Trees iff x is Tree
proof
  thus {x} is constituted-Trees implies x is Tree
  proof
    assume
A1: for y st y in {x} holds y is Tree;
    x in {x} by TARSKI:def 1;
    hence thesis by A1;
  end;
  assume
A2: x is Tree;
  let y;
  thus thesis by A2,TARSKI:def 1;
end;
